Constitutive Modeling

The combination of Inconel material properties and the geometric freedom of additive manufacturing provides special opportunity for the production of engineered structures with exceptional strength
and stability at elevated temperatures. The present work deals with the high temperature flow behavior of an additively manufactured Inconel 625 superalloy in a wide temperature range of 800 °C–1100 °C
under the various strain rates of 0.001, 0.01, and 0.1 s−1. The strain hardening rate analysis was utilized to reveal the critical condition for the occurrence of the restoration processes. The additively manufactured material was capable to be dynamically recrystallized at various thermomechanical conditions. In this regard, the effect of the Zener–Hollomon parameter (Z) on the characteristic points of the flow curves (critical, peak and steady state stresses and strains) was studied using the power law relations. A phenomenological hyperbolic sine constitutive model was proposed to predict the high temperature flow behavior of the manufactured material; and the model was modified considering the
effect of imposed strain. Interestingly, the flow stress levels and the average hot deformation activation energy for the additively manufactured Inconel 625 alloy were found to be lower than that for the same alloy which have been fabricated through hot forging. This was attributed to the complex alloy composition and the specified solidified microstructure of the additively manufactured materials.

Transgenic tomato (Solanum lycopersicum) plants that overexpress the Prosystemin gene (35S::PS) and plants with a mutation in the JA biosynthetic pathway (def1) are known to exhibit a constitutive or reduced wound response, respectively. Here it is demonstrated that several independent 35S::PS lines emit high levels of specific volatiles in addition to increased accumulation of proteinase inhibitors (PIs). Furthermore, the temporal dynamics of systemically induced volatile compounds including green-leaf volatiles, terpenes, and shikimic acid-derivatives from 35S::PS and def1 plants in response to herbivore wounding and treatment with jasmonic acid (JA) are described. Application of JA induced defense protein accumulation and volatile emissions in wild type plants, but did not further increase systemic volatile emissions from 35S::PS plants. Wounding by Manduca sexta larvae induced synthesis of defense proteins and emission of volatiles in wild type plants, but not in def1 plants. Application of jasmonic acid restored the local and systemic accumulation of defense proteins in def1, as well as enhanced herbivore-induced volatile emissions. These results provide strong support for the role of prosysteminand JA-signaling in the regulation of volatile emissions in tomato plants.

A rearrangement of the hypoplastic constitutive equation is proposed that enables the incorporation of an asymptotic state boundary surface of an arbitrary predefined shape into the model, with any corresponding asymptotic strain-rate direction. This opens the way for further development of hypoplastic models. To demonstrate the flexibility of the proposed approach, a hypoplastic equivalent of the modified Cam-clay model is developed. A comparison of the predictions of the elasto-plastic and hypoplastic models reveals the merits of the hypoplastic formulation. Although both models predict the same asymptotic states, hypoplasticity predicts a smooth transition between overconsolidated and normally consolidated states, and thus accounts for the non-linearity of the soil behaviour inside the state boundary surface in a natural manner.

ABSTRACT:  Magnetorheological fluids (MRF) are increasingly used for the design of dampers in many cases when a given response is critical for desired performance. Some recent examples are self-powered magnetorheological dampers, cable vibration control and wheeled vehicle dampers. Loads of this type can be very big, especially in the case of seismic-dampers as well as in heavy vehicles and aircraft landing gear. This problem can be more efficiently dealt with by using an inverse-problem strategy, where the required performance is specified a priori, and the fluid parameters are changed accordingly by means of a variable magnetic field. The effect on the flow of the time-variation of the parameters of the Herschel-Bulkley constitutive model is analyzed in this paper. In this way, the influence of a varying magnetic field on the unsteady flow of a magnetic fluid is explored. Yield stress, viscosity and power index are assumed time-dependent. In particular, linear variations in time of these parameters are considered, and the case where the yield stress and viscosity oscillate in time is explored in detail. The characteristics of the velocity field are analyzed for different values of the constants that determine the time structure of the constitutive parameters.

This paper presents a new constitutive model for clays. The model is developed on the basis of generalized hypoplasticity principles, which are combined with traditional critical state soil mechanics. The positions of the isotropic normal compression line and the critical state line correspond to the Modified Cam clay model, the Matsuoka–Nakai failure surface is taken as the limit stress criterion and the non-linear behaviour of soils with different overconsolidation ratios is governed by the generalized hypoplastic formulation.

The model requires five constitutive parameters, which correspond to the parameters of the Modified Cam clay model and are simple to calibrate on the basis of standard laboratory experiments. This makes the model particularly suitable for practical applications. The basic model may be simply enhanced by the intergranular strain concept, which allows reproducing the behaviour at very small strains. The model is evaluated on the basis of high quality laboratory experiments on reconstituted London clay. Contrary to a reference hypoplastic relation, the proposed model may be applied to highly overconsolidated clays. Improvement of predictions in the small strain range at different stress levels is also demonstrated.

The undrained response of cohesive soils is of paramount importance in geomechanics and it has been modelled extensively for the last 50 years. In comparison, drained behaviour of clays has received only modest attention. Drained and undrained behaviour is significantly affected by past consolidation stress history. This paper evaluates the capabilities of the MIT-S1 effective stress model, described in a companion paper, for predicting the anisotropic stress-strain-strength behaviour of clays. The paper illustrates the selection of model parameters for Lower Cromer Till, using data from standard types of laboratory tests. Comparison of model simulations with measured response for Lower Cromer Till and Boston Blue Clay illustrate model capabilities. The work focuses initially on comparisons of model predictions with measurements from undrained triaxial and plane strain tests on initially K 0 -consolidated specimens. Comparisons with measured data from undrained shear tests performed in different modes of shearing for LCT and BBC show that the model: (a) gives excellent predictions of maximum shear stress conditions and accurately describes the non-linear shear stress-strain behaviour; (b) accurately describes the anisotropic shear stress-strain-strength conditions for different consolidation stress histories; and (c) gives realistic description of mobilized friction angles, especially at large OCR's. The paper then focuses on the effects of consolidation stress history for isotropically consolidated specimens of resedimented Lower Cromer Till and Boston Blue Clay. Finally, the paper compares model predictions for drained shear tests on K 0 and isotropically consolidated specimens with overconsolidation ratios, OCR410; used to evaluate particular aspects of the critical state framework of soil behaviour. Overall, the model gives excellent predictions of the effect of initial anisotropy and overconsolidation stress history on the shear stress-strain and volumetric behaviour of clays.

Functionally graded materials have been defined by Hirai [1] to be "a new generation of engineered materials wherein the microstructural details are spatially varied through a non-uniform distribution of the reinforcement phase(s)...". Extending this paradigm to the field of cellular solids, a functionally graded foam material (FGFM) may be thought of as a foam for which microstructural features such as cell size, and strut and wall (for closed cell foams) thickness vary in a continuous manner across the volume of the foam. These features may be varied globally by variation of the foam's density, ρ f . Cui et al., [2] and Kiernan et al., [3] have shown some potential benefits of FGFMs under dynamic conditions using discretely layered Finite Element foam models. In their work the ABAQUS crushable foam model defines the constitutive response of each element layer of a regularly shaped specimen. The density, and corresponding Young's modulus, E f , and hardening law of each layer is unique, thus defining a quasi-graded response. Motivated by their results, this paper attempts to describe the large strain compressive response of a generic foam, ultimately using ρ f as the only independent input parameter. Experimental data is gathered from a number of expanded polystyrene foam specimens of different densities, and important foam characteristics are defined as functions of ρ f . Results compare excellently to those of the ABAQUS foam model, and limitations of the modeling approach are discussed.

A new constitutive model is introduced which is formulated in the framework of classical theory of plasticity. In the model the total strains are calculated using a stress-dependent stiffness, different for both virgin loading and un-/reloading. The plastic strains are calculated by introducing a multi-surface yield criterion. Hardening is assumed to be isotropic depending on both the plastic shear and volumetric strain. For the frictional hardening a non-associated and for the cap hardening an associated flow rule is assumed.

Comparing to the other critical state model, the thermodynamics-based critical state (TCS) model can meet principle of the thermodynamics without introduction of plastic potential function. This model can be used to model the influence of K 0 consolidation by modification of it. The return-mapping algorithm is utilized to conduct the redevelopment of TCS model in ABAQUS. The certification of this model can be given by the comparison with modified Cam-Clay (MCC) model offered by ABAQUS. Otherwise, the variation of the yield surface shape controlled by two parameters is discussed. The influence of these two parameters on the stress-strain relationship and dilatancy is also analyzed. The modification of parameter in TCS model can be used to describe non-ellipse yield surface extending available range of TCS model. Different parameters have different influences on the shape and size of yield surface. Meanwhile, it is shown that the stress-strain relationship and dilatancy are different between described by TCS model where the K 0 consolidation and stress rotational hardening are considered and described by MCC model without consideration of them are shown. For the real soils, K 0 consolidation and rotational hardening are basic mechanical properties of soils. This paper demonstrates that TCS model can be used to describe these features of soils compared with MCC model where the rotational hardening and K 0 consolidation are not considered. So, it is more available.

This paper studies the accuracy of the three-dimensional finite-element predictions of a displacement field induced by tunneling using new Austrian tunneling method (NATM) in stiff clays with high K0 conditions. The studies are applied to the Heathrow express trial tunnel. Two different constitutive models are used to represent London Clay, namely a hypoplastic model for clays and the modified Cam-clay (MCC) model. Good quality laboratory data are used for parameter calibration and accurate field measurements are used to initialize K0 and void ratio. The hypoplastic model gives better predictions than the MCC model with satisfactory estimate for the displacement magnitude and slightly overestimated width of the surface settlement trough. Parametric studies demonstrate the influence of variation of the predicted soil behavior in the very-small-strain to large-strain range and the influence of the time dependency of the shotcrete lining behavior.

An Overview of what has been referred to as "Seven Higher Heaven" in Metaphysics, and what The Book of Urantia refers to as "Superuniverses" has been explicated. It is elucidated that the first (outer) 84 dimensions of Cosmos provide the means for some form of physical embodiment (be it in the form of light) to take place. This realm may be divided into a conglomeration of 7 distinct domains each constituting a universal system comprised of 12 dimensions each of which has been dubbed as a "Superuniverse" or a "Higher Heaven." And, these realms of physicality constitute domains with increasing spectral density of constitution and diminishing extent of frequency of light of consciousness with loss of propinquity with respect to the central God-SOURCE. It is, once again, emphasized that a dimension epitomizes a space-time domain in which the concept of 'space' represents congealment of 'time,' which represents the conversion of Void into a realm that is characterized by a fabric of space-time and its distinguishing curvature, always occupying the same location, yet varying in dimension according to the extent of speed of progression of time (free spinning of the fundamental quantum particles) or 'frequency-light quotient' within its domain. It is further elucidated that the remaining inner portion of the 356 dimensions of Cosmos is comprised of energetic contours at which photonic beings can still anchor their consciousness, sequentially vibrating in time within contrasting conjugate-mirrored space-times.

This thesis is dedicated to developing the computational procedures required in implementing the finite element method for finite deformation, rate-independent plasticity and finite deformation viscoplasticity theory based on overstress. The classical rate-independent, von Mises plasticity is formulated using both hypoelastic-plastic model and hyperelastic-plastic model. In the hypoelastic-plastic model, a relationship between an objective rate of Kirchhoff stress, based on a new recently proposed logarithmic spin [13], and the elastic part of rate of deformation tensor is postulated. In the hyperelastic-plastic model, the deformation gradient is decomposed into elastic and plastic deformations, a relationship between Kirchhoff stress and the logarithm of the elastic left stretch tensor is used. Numerical procedures for the integration of both models are developed. The isotropic, viscoplasticity theory based on overstress consisting of a flow law and two tensor valued and one scalar valued stress-like state variables is extended to finite deformation. To this end the Cauchy stress rate and the rates of the two tensor-valued state variables are interpreted as Eulerian tensors. The rate of deformation is equal to the sum of the elastic (the rate form of Hooke's law) and the inelastic rate of deformation, which depends on the overstress. The model does not contain a strain like quantity. Two integration schemes are considered: (i) a one step time integration scheme based on the forward gradient approximation and (ii) unconditionally stable implicit integration scheme based on backward Euler. The finite deformation, anisotropic, viscoplasticity theory based on overstress is formulated. A hypoelastic relation between the Lagrangian, rotated, logarithmic Cauchy stress rate and the rotated rate of deformation is used. The deformation induced anisotropy is modeled using a compliance tensor that allowed to grow according to Armstrong-Frederick law for fourth order tensors that needs no further constants, except for a function that influences how quickly the compliance tensors grow. An implicit numerical integration scheme based on backward Euler is used.

The near wellbore region is subjected to cyclic loads due to repeated changes of the mean effective stress. These repeated loads result in plastic deformation and sanding problems which can occur in injection or production wells. The difficulty is more pronounced in weakly consolidated reservoirs since they are more prone to sanding. Therefore it is required to investigate the material response to cyclic loading.
In this research, the mechanical behaviour of uncemented and cemented sands under monotonic and cyclic loading are studied. Emphasis is placed on the constitutive modeling. A critical state constitutive model which was developed at the University of Alberta for monotonic behavior of cohesionless sands was chosen as the base model.
First with modification of the hardening law, plastic volumetric strain increment and unloading plastic modulus, the original model was modified to describe sand behavior under cyclic loading. The modified model was calibrated and validated against triaxial cyclic loading tests for Fuji River sand, Toyoura sand and Niigata sand. Comparison between the measured and predicted results suggests that the model can capture the main features of sands under cyclic loading. Second the original model was modified for cemented sands. Formulation of the yield function, elastic moduli, plastic modulus, flow rule and other components of the original model were modified. Having incorporated these changes, the radial mapping formulation of bounding surface plasticity was incorporated in the model. The modified model was assessed against monotonic triaxial tests. Third to simulate the mechanical behaviour of cemented sand/soft sandstone under cyclic loading, some further modifications were incorporated into the model. Destruction of the cementation bonds by plastic deformation was considered as the reason for the mechanical degradation of cemented sands. To model cyclic response, the unloading plastic and elastic moduli were formulated based on those of loading. The proposed model was evaluated against laboratory triaxial tests, and the model agreed with experimental observations. Fourth the application of the proposed constitutive model was ultimately extended to cases that are not under conventional triaxial conditions. This was performed by incorporating the inherent anisotropy and -parameter into formulation of the proposed model.

Stress-dilatancy relationship or plastic potential function are crucial components of every elastoplastic constitutive model developed for sand or cemented sand. This is because the associated flow rule usually does not produce acceptable outcomes for sand or cemented sand. Many formulas have been introduced based on the experimental observations in conventional and advanced plasticity models in order to capture ratio of plastic volumetric strain increment to plastic deviatoric strain increment (i.e. dilatancy rate). Lack of an article that gathers these formulas is clear in the literature. Thus, this paper is an attempt to summarize plastic potentials and specially stress-dilatancy relations so far proposed for constitutive modelling of cohesionless and cemented sands. Stress-dilatancy relation is usually not the same under compression and extension conditions. Furthermore, it may also be different under loading and unloading conditions. Therefore, the focus in this paper mainly places on the proposed stress-dilatancy relations for compressive monotonic loading. Moreover because plastic potential function can be calculated by integration of stress-dilatancy relationship, more weight is allocated to stress-dilatancy relationship in this research.

Conventional seismic rehabilitation methods may not be suitable for some buildings owing to their high cost and time-consuming foundation work. In recent years, viscoelastic damp-ers (VEDs) have been widely used in many mid-and high-rise buildings. This study introduces a viscoelastic passive control system called rotary rubber braced damper (RRBD). The RRBD is an economical, lightweight, and easy-to-assemble device. A finite element model considering nonlinearity, large deformation, and material damage is developed to conduct a parametric study on different damper sizes under pushover cyclic loading. The fundamental characteristics of this VED system are clarified by analyzing building structures under cyclic loading. The result show excellent energy absorption and stable hysteresis loops in all specimens. Additionally, by using a sinusoidal shaking table test, the effectiveness of the RRBD to manage the response displacement and acceleration of steel frames is considered. The RRBD functioned at early stages of lateral displacement, indicating that the system is effective for all levels of vibration. Moreover, the proposed damper shows significantly better performance in terms of the column compression force resulting from the brace action compared to chevron bracing (CB).

The 2D load-reduction method for simulating NATM tunnels using plane strain finite elements is evaluated in the paper by comparison with fully 3D simulations. Three real shallow tunnels in urban environment in different stiff clays were simulated. The soil behaviour was described by an advanced non-linear soil constitutive model based on the hypoplasticity theory. Time-dependent behaviour of shotcrete lining was considered in 3D simulations, whereas constant final stiffness was used in the plane strain analyses. The 2D analyses were thus controlled by a single parameter that accounts for 3D effects. It is shown that for an optimum value of this parameter, the displacement field predicted by the 2D method agrees well with the 3D simulations. In some cases only, a discrepancy was observed in the close vicinity of the tunnel. The controlling parameter was, however, found to be dependent on the problem simulated (for the same material) and also on the material properties (for the same tunnelling problem). Considering the material properties, the shear modulus at very small strain was found to be more influential than the shear modulus at large strain. The initial K0 stress state did not influence the controlling parameter substantially.

The paper demonstrates the application of a hypoplastic model in class A predictions of a NATM tunnel in an urban environment. The tunnel, excavated in a stiff clay, is 14 m wide with 6 m to 21 m of overburden thickness. The constitutive model was calibrated using laboratory data (oedometric and triaxial tests) and the parameters were optimised using monitoring data from an exploratory drift. Based on the optimised data set, the future tunnel was simulated. After the tunnel excavation, it could be concluded that the model predicted correctly surface settlements, surface horizontal displacements, and the distribution of vertical displacements with depth. It overpredicted horizontal displacements in the vicinity of the tunnel.

This paper evaluates the performance of a generalized effective stress soil model for predicting the rate independent behaviour of freshly deposited sands, while a companion paper describes model capabilities for clays and silts. Most material parameters can be obtained from standard laboratory data, including hydrostatic or one-dimensional compression, drained and undrained triaxial shear testing. A compilation of data on compression behaviour allows for estimation of compression parameters when this type of data is not available. Extensive comparisons of model predictions with measured data from undrained triaxial shear tests shows that the model gives excellent predictions of the transition from dilative to contractive shear response as the confining pressure and/or the initial formation void ratio increases. A parametric study of drained response shows that the model describes realistically the variation of peak friction angle and dilation rate as a function of confining pressure and density when compared with an empirical correlation valid for many sands. The proposed formulation predicts a unique critical state locus for both drained and undrained triaxial testing which is non-linear over the entire range of stresses and is in excellent agreement with recent experimental data. Overall, the model provides excellent predictions of the stress-strain-strength relationships over a wide range of confining pressures and formation densities.

This work is a comprehensive overall view of a complex field still far from being settled on firm grounds, that of the constitutive structure of non-colloidal suspensions. Suspensions in industrial manufacturing processes are prevalent across a spectrum of diverse industries. It is critically important that the behavior of non-colloidal suspensions under forcing is predicted on a sound basis from an industrial operational point of view not to mention the fundamental scientific significance, thus the raison d'être of the present work, a comprehensive up-to-date review of constitutive equations formulated to describe the flow of suspensions either dilute or dense under driving forces. This review only takes up the formulation of constitutive structures for non-colloidal suspensions and does not get into the rheology of suspensions per se. Thus, it is substantially more comprehensive in that sense than other reviews, which may have been published over the last two decades. It is also written not only for researchers in the field, but for those in related fields as well who may find it interesting, useful and related to their own research. Efforts have not been spared to be thorough in the presentation with commentaries about the successes and failures of each theory in their historical context and the reasons behind them. The link between different theories and the naturally unfolding succession of theories over time borne out of the necessity for better predictions as well as the challenges in the field at this time are given much emphasis at the expanse of a detailed in-depth account of various theories. For a detailed in-depth exposition, the reader is referred to the extensive reference list.

Dual phase (DP) steel is of great interest for automotive part manufacturers due to its excellent combinations of strength and formability. Complex components involving three- dimensional stampings are usually fabricated through multistage sheet forming operations. The ability of a sheet metal to be deformed into a specific desired shape by distributing strain over arbitrary tool surface depends on complex interaction of material, process and design variables. The strain-based forming limit diagram (ε-FLD) is often used as a measure of formability in the press shop due to convenience of measuring the limiting strain. However, it was reported by previous researchers that the ε-FLD of sheet metal shifts after pre-strain due to the initial forming operations. Hence, this work proposes a mathematical framework for constructing σ-FLD of different pre-strained sheets incorporating Barlat-89 yield criterion with different hardening laws. The formability of biaxially pre-strained DP600 was evaluated experimentally in two stages. The forming behaviour of pre-strained material was predicted by finite element model using the σ-FLD, and the predicted results matched very closely with the experimental data. It was also observed that the σ-FLD was robust and
underwent insignificant changes due to the change in the pre-strain path.

In this paper, a finite strain material model for complex plastic anisotropy with nonlinear isotropic and kinematic hardening is consistently derived. The model is based on the classical multiplicative decomposition of the deformation gradient and derived in a thermodynamically consistent way. An important new aspect of the work is the straightforward implementation of general and anisotropic yield criteria into a constitutive model, which is entirely formulated in the reference configuration. Nevertheless, and for the sake of illustrating the potential of the model, in this work a Barlat-type (Yld2004-18p) yield criterion is employed. The kinematic hardening formulation follows the continuum mechanical extension of the classical rheological model of Armstrong–Frederick hardening. The numerical integration of the evolution equations is carried out using the exponential map approach, which is able to preserve plastic incompressibility. For numerical efficiency purposes, the exponential tensor functions are evaluated in a closed form using the spectral decomposition, and special attention is given to the preservation of the internal variables' symmetry. The model is assessed by means of several numerical simulations for anisotropic materials at finite strains, including sheet metal forming processes with comparison to experimental data.

The mechanical behaviour of natural clays is significantly affected by their in situ or initial structure in the form of cementation or interparticle bonding. This behaviour can differ substantially from the behaviour of reconstituted clays. Suction as well as plastic volumetric strains drive isotropic hardening/softening as this is a simple way to account for the phenomenon of volumetric collapse upon wetting and the stiffening effect that suction has on the soil skeletal response. A model that combines unsaturated and structured behavior is presented and then used to simulate stress strain behaviour observed for an unsaturated natural clay subjected to isotropic load paths. A parametric analysis is performed to observe the influence suction hardening has on mobilized strengths. It is also shown that the model can predict the maximum of collapse of unsaturated soils.

Numerical analysis of any boundary
value problems requires a constitutive model to be
used. Depending on the type of the problem to be
solved and the material characteristics involved in the
analysis, the constitutive model to be used in the
analysis should be selected properly, so that the results
close to the real behavior of the analyzed problems.
Again, numerical prediction of any constitutive model
depends highly on the correct selection of the model
parameters. These model parameters for a given
material are generally determined from different
experimental data. Therefore, selection of a
constitutive model and determination of its parameters
for a given material are must in any numerical
analysis.

It can be seen from literature that modified cam clay
model is mostly used in numerical analysis of
geomechanics problems requiring realistic soil models.
To use this model for analyzing any problems in a
given soil, the different model parameters for that soil
are to be determined carefully. In the present study,
selection and determination of the modified cam clay
model parameters for some soils is done. The soils used
in the study are collected from inside the NERIST
campus, which is situated in Papumpare district of
Arunachal Pradesh.

A strategy for adaptive control and energetic optimization of aerobic fermentors was implemented, with both air flow and agitation speed as manipulated variables. This strategy is separable in its components: control, optimization, estimation. We optimized parameter’s estimation (from the usual KLa correlation) using sinusoidal excitation of air flow and agitation speed. We have implemented parameter’s estimation trough recursive least squares algorithm with forgetting factor. We carried separate essays on control, optimization and estimation algorithms. We carried our essays using an original computational simulation environment, with noise and delay generating facilities for data sampling and filtering.

Our results show the convergence and robustness of the estimation algorithm used, improved with use of both forgetting factor and KLa dead-band facilities. Control algorithm used in our work compares favorably with PID using the integrated area criteria for deviation between oxygen molarity and critical molarity (set point). Optimization algorithm clearly reduces energetic consumption, respecting critical molarity. Integration of control, optimization and adaptive algorithms was implemented, but future work is needed for stability. Methods were defined and implemented for stability improvement. We have implemented data acquisition and computer manipulation of air flow and agitation speed for actual fermentors.

A new elasto-plastic model for unsaturated soils incorporating the effect of evolving fabric anisotropy is presented. The model is formulated in terms of mean net stress, deviator stress and suction and reduces to the Barcelona Basic Model for an isotropic material. Model simulations are performed and compared against experimentally observed behaviour from constant suction triaxial tests on isotropically and anisotropically compacted kaolin samples along a variety of stress paths. Simulations indicate an improvement in the prediction of the size and shape of the yield surface compared to the Barcelona Basic Model. In addition, the deformation generated during shearing are better predicted than in the Barcelona Basic Model, even though experimentally observed strains are still grossly over-estimated. Further refinement to model assumptions are required to improve predictions of experimental data and the reformulation of the model in terms of average skeleton stresses, instead of net stresses, might help in this respect as outlined in Al-Sharrad (2013).

The paper presents a mechanical model for non-isothermal behaviour of unsaturated soils. The model is based on an incrementally non-linear hypoplastic model for saturated clays and can therefore tackle the non-linear behaviour of overconsolidated soils. A hypoplastic model for non-isothermal behaviour of saturated soils was developed and combined with the existing hypoplastic model for unsaturated soils based on the effective stress principle. Features of the soil behaviour that are included into the model, and those that are not, are clearly distinguished. The number of model parameters is kept to a minimum, and they all have a clear physical interpretation, to facilitate the model usefulness for practical applications. The step-by-step procedure used for the parameter calibration is described. The model is finally evaluated using a comprehensive set of experimental data for the thermo-mechanical behaviour of an unsaturated compacted silt.

Constitutive model for saturated cohesive soils based on the bounding surface plasticity notion with anisotropic hardening law is presented in the paper. The model predicts inelastic behaviour of overconsolidated cohesive soils. The projection centre is the only point in the stress space which represents elastic soil behaviour. Approximation of the plastic modulus within the preconsolidation domain is made using the radial mapping rule between a projection centre and a reflecting point on the bounding surface. The projection centre changes its position each time when stress path turns rapidly of more than 90º. The configuration of the elliptic bounding surface is governed by preconsolidation effective pressure p’c which depends on change of plastic both volumetric and deviatoric strain. Associated flow rule has been assumed in the formulation.
Integration of constitutive relations is done according to forward Euler scheme with error control proposed by Sloan. The effectiveness of the proposed model is illustrated in both monotonic and cyclic loading in the homogeneous triaxial drained and undrained conditions.

This paper presents a review of the main constitutive models for peat and other highly organic soils having extremely high water content. At present, predictions of the geomechanical behaviour of such soils for design practice are mostly based on constitutive theories developed for fine-grained mineral soils. Concepts of primary consolidation and secondary compression as applied to peat are explained using the two-level structure assumption of micropores and macropores. As background, the historical development of consolidation hypotheses A&B regarding the concepts of primary consolidation and secondary compression is reviewed for both mineral and organic soils. Based on microscopic examinations and in-situ testing, it is generally accepted that hypothesis B is more suitable for peat. The micro-mechanical rheological model proposed by Berry and Poskitt and the isotache-compression model developed by den Haan were reported to have good agreement with experimental laboratory results for fibrous and amorphous peats. Attention is given to the structural anisotropy of peat material, inherent by its fibrous nature, in these constitutive frameworks.

The paper presents a bounding surface model that describes the gradual yielding of unsaturated soils subjected to isotropic loads. The model originates from consideration of the capillary bonding between soil grains, which leads to the definition of a “unified normal compression line” that is valid in both saturated and unsaturated conditions. This line has the same slope and intercept of the saturated normal compression line but is formulated in terms of a “scaled stress” variable, which takes into account the mechanical effect of capillarity by factoring the average skeleton stress (also known as Bishop’s stress) with a power function of degree of saturation. The normal compression behaviour of unsaturated soils is therefore described by only one additional parameter, which is the exponent of the degree of saturation in the scaled stress expression. For over-consolidated soils, the occurrence of gradual yielding is introduced by assuming that, as the soil state moves towards the unified normal compression line, the slope of the loading curve tends towards the slope of the unified normal compression line according to an expression requiring only one extra parameter. Interestingly, this expression can be integrated in a closed form to provide a general equation for all loading paths in saturated and unsaturated conditions. Different loading curves are simply distinguished by the different values of the integration constants. Unloading paths are also simulated in a similar way. The proposed model requires a total of five parameters, which include the three standard parameters for saturated soils (i.e. the slope and intercept of the saturated normal compression line and the slope of the swelling line) plus one parameter to describe unsaturated behaviour and one parameter to describe the gradual yielding of over-consolidated soils subjected to loading.

A new rate-independent hypoplastic model for clays is developed. The model is based on the recently proposed approach enabling explicit incorporation of the predefined asymptotic state boundary surface and corresponding asymptotic strain rate direction into hypoplasticity. Several shortcomings of the existing hypoplastic model for clays are identified and corrected using the proposed approach. Thanks to the independent formulation of the individual model components, the new model is more suitable to form a basis for further developments and enhancements than the original one.

We present a multiscale dislocation density-based constitutive model for the strain-hardening behavior in twinning-induced plasticity (TWIP) steels. The approach is a physics-based strain rate- and temperature-sensitive model which reflects microstructural investigations of twins and dislocation structures in TWIP steels. One distinct advantage of the approach is that the model parameters, some of which are derived by ab initio predictions, are physics-based and known within an order of magnitude. This allows more complex microstructural information to be included in the model without losing the ability to identify reasonable initial values and bounds for all parameters.
Dislocation cells, grain size and twin volume fraction evolution are included. Particular attention is placed on the mechanism by
which new deformation twins are nucleated, and a new formulation for the critical twinning stress is presented. Various temperatures were included in the parameter optimization process. Dissipative heating is also considered. The use of physically justified parameters enables the identification of a universal parameter set for the example of an Fe–22Mn–0.6C TWIP steel.

For an incompressible solid, which many rubber-like materials closely approximate, the commonly accepted value for Poisson's ratio is 1/2. The value 1/2 arises when the incompressibility condition is approximated by only the linear terms. Retention of the normally neglected nonlinear terms leads to the conclusion that the value 1/2 is precisely correct only in the limiting case of zero strain. This limiting behavior is demonstrated for triaxial and biaxial loading of an isotropic material governed by a Hooke's law like stress-strain law, and for a uniaxially stressed rod. In the latter case Poisson's ratio takes on values less than 1/2 for tension, and greater than 1/2 for compression. The uniaxial behavior is used to formulate a revised (bimodular) constitutive equation for the biaxial loading of rubber-like materials.

In the paper, we present newly developed hydro-mechanical hypoplastic model for partially saturated soils predicting small strain stiffness. Hysteretic void ratio dependent water retention model has been incorporated into the existing hypoplastic model. This required thorough revision of the model structure to allow for the hydro-mechanical coupling dependencies. The model is formulated in terms of degree of saturation, rather than of suction. Subsequently, the small strain stiffness effects were incorporated using the intergranular strain concept modified for unsaturated conditions. New features included degree of saturation-dependent size of the elastic range and an updated evolution equation for the intergranular strain. The model has been evaluated using two comprehensive data sets on completely decomposed tuff from Hong-Kong and Zenos Kaolin from Iran. It has been shown that the modified intergranular strain formulation coupled with the hysteretic water retention model correctly reproduces the effects of both the stress and suction histories on small strain stiffness evolution. The model can correctly predict also different other aspects of partially saturated soil behaviour, starting from the very small strain range up to the asymptotic large-strain response.

This paper presents a constitutive model for describing the stress-strain response of sands under cyclic loading. The model, formulated using the critical state theory within the bounding surface plasticity framework, is an upgraded version of an existing model developed for monotonic behaviour of cohesionless sands. With modification of the hardening law, plastic volumetric strain increment and unloading plastic modulus, the original model was modified to simulate cyclic loading. The proposed model was validated against triaxial cyclic loading tests for Fuji River sand, Toyoura sand and Nigata sand. Comparison between the measured and predicted results suggests that the proposed modified model can capture the main features of cohesionless sands under drained and undrained cyclic loading.

A new hypoplastic model for clays with meta-stable structure is presented in the paper. A new method for incorporation of structure effects into hypoplastic models based on the modification of barotropy and pyknotropy factors is proposed and applied to an existing hypoplastic model for reconstituted clays. The new model is characterised by a simple calibration procedure and a small number of parameters. This makes the model particularly suitable for practical applications. The model is evaluated using experimental data on two natural soft clays. Thanks to the incrementally non-linear character of the hypoplastic equation, the proposed model predicts behaviour of
overconsolidated clays comparably to advanced kinematic hardening elasto-plastic models.

A 3D hysteretic, fully reversible constitutive model with rate-independent damping and with variable secant stiffness is proposed. A reversible dilatancy–contractancy effect is an optional feature as described in the companion paper (Niemunis et al. in Acta Geotech, 2011). The present paper describes the basic aspects of the model only. A strain path reversal is defined, and a treatment of the past reversals using a stack structure is proposed.

Knee osteoarthritis is one of the most common musculoskeletal pathologies, and results in severe joint pain, loss of mobility, compromised quality of life, and high medical costs. With no cure other than total joint replacement, and the incidence of osteoarthritis rising worldwide, the need to understand how the disease develops has reached a critical level. The mechanism(s) underlying the initiation and progression of knee osteoarthritis remain unknown despite years of extensive research. Alterations in the spatial loading pattern on the joint’s articular cartilage, for example, due to knee injury, have been hypothesized to trigger the onset of the disease. The theory presupposes that the mechanical properties of knee cartilage are non-uniform such that the underlying cartilage is unable to sustain the new loading pattern and deteriorates. However, this tenet is challenging to test directly because it requires detailed knowledge of spatial mechanical properties of the cartilage, which is currently unknown.
Therefore, this dissertation sought to address current knowledge gaps by mapping the elastic modulus of healthy human knee articular cartilage across the joint surface. This work represented the first such mapping with fine spatial resolution and employing a physiologically relevant compressive strain rate.  Significant variations in modulus were found across the femur and tibial cartilage. Moreover, these variations conformed to a consistent regional pattern across knees, which has not previously been demonstrated.
These findings subsequently motivated the development of a constitutive relation that could successfully simulate spatially dependent, high strain rate mechanics. A transversely isotropic hyperelastic model was developed and compared with isotropic hyperelastic models to determine which constitutive relation best represented the natural cartilage mechanics. The transversely isotropic model replicated the spatial mechanical dependence of the tissue through variations in a single model parameter. The model is mechanistic, has a structure and parameters that are analogous to human cartilage physiology, is computationally efficient, and is straightforward to implement in commercial finite element packages. The transversely isotropic model represents a novel method for implementing the non-uniform mechanics of knee cartilage that are critical to understanding the initiation and progression of knee osteoarthritis. The characterization of regional mechanical properties of human knee cartilage performed herein has contributed essential baseline knowledge that will fundamentally advance experimental and computational studies of knee osteoarthritis development toward widespread prevention of this devastating disease.

Sand response changes with intensity of cementation bonds between sand grains, magnitude of intermediate principal stress and with fabric anisotropy. First a critical state bounding surface plasticity model is presented in this paper. In this constitutive model, the loading surface always passes through the current stress state regardless of location or position of the stress path. Second to simulate hollow cylinder tests which represent different modes of shearing including triaxial compression and triaxial extension, the fabric anisotropy and b-parameter are incorporated in the model. Simultaneous integration of cohesion, non-associated flow rule, fabric anisotropy, kinematic hardening, critical state and state parameter makes the proposed model unique compared to previous proposed bounding surface models. Comparison of model outcomes and hollow cylinder experimental tests shows great predictive capability of the proposed model. Sensitivity analysis also suggests that triaxial compression and triaxial extension are respectively strongest and weakest modes of shearing.

In this paper, the rheological characteristics of aqueous PEO (Polyethylene oxide) solution with very high molecular weight 4×106 g/mol is investigated. Shear flow measurements were carried out in steady and transient modes. The unique behavior of PEO is found to be heavily dependent on the input shear rate and the mechanism of data generation. Generally, PEO is found to be shear-thinning throughout the experiments, but at the start of the experiments at low shear rates, minimum input shear value also affects the shear-thinning behavior. In this study, we investigate the critical method of applying input shear to the samples in the lower shear rate regime. Surprisingly, different input methods yield different results. Viscosity curves obtained through shear flow experiments are found to be significantly dependent on the input method of shear rate. Experimental measurements were validated by Cross and Carreau-Yasuda models.

This presentation was held in the occasion of the doctoral school in Bayonne, France on the 26 May 2015. This school was the prelude to the 33rd edition of the "Rencontres Universitaires de Génie Civil" organized by the French University Association of Civil Engineering in collaboration with the Université de Pau et des Pays de l'Adour.

The lecture in this video provides an introduction to the phenomena of capillarity in unsaturated soils and to the relevant constitutive laws of material behaviour. The lecture also provides a brief description of the techniques employed for the measurement of suction in unsaturated soils.