ABSTRACT. The present paper introduces a new nonlocal coupled damage-plasticity model aiming at p... more ABSTRACT. The present paper introduces a new nonlocal coupled damage-plasticity model aiming at predicting crack paths within plates made of ductile material and subjected to pure tensile loading. This model is inspired by Nguyen's model [1] for quasi-brittle material. It uses the Houlsby and Puzrin [2] framework that makes the model formulation internally consistent by linking the damage and the yield functions via a dissipation potential. However, as in Lemaitre [3], the damage law is explicitly defined in order to ease the implementation.
Journal of the Mechanics and Physics of Solids, 2014
We study the mechanical failure of cemented granular materials (e.g., sandstones) using a constit... more We study the mechanical failure of cemented granular materials (e.g., sandstones) using a constitutive model based on breakage mechanics for grain crushing and damage mechanics for cement fracture. The theoretical aspects of this model are presented in Part I: Tengattini et al. (2014), A thermomechanical constitutive model for cemented granular materials with quantifiable internal variables, Part I -Theory (Journal of the Mechanics and Physics of Solids, http://dx.doi.org/ 10.1016/j.jmps.2014.05.021). In this Part II we investigate the constitutive and structural responses of cemented granular materials through analyses of Boundary Value Problems (BVPs).
Novel metrics designed to evaluate the skill of geophysical models in simulating discontinuities ... more Novel metrics designed to evaluate the skill of geophysical models in simulating discontinuities and linear features are introduced and tested using a sea-ice model and remotely sensed observations of leads. The metrics are formulated as frequency-based indices of agreement, thus maintaining the simplicity desired in model development and operational applications, while remedying known shortcomings of common existing skill metrics. User-selectable
This paper presents a nonlocal coupled damage-plasticity model for the analysis of ductile fractu... more This paper presents a nonlocal coupled damage-plasticity model for the analysis of ductile fracture. The proposed model makes use of both damage mechanics and plasticity theories and hence is able to capture the pre-peak hardening and post-peak softening responses as well as the stiffness reduction of the material during the deformation and fracture processes. Nonlocal regularisation technique is used as an enhancement to the proposed damage-plasticity model to deal with softening related problems in the constitutive modelling and the failure analysis. Emphasis is put on the determination of model parameters with a novel calibration procedure, based on the experimental technique (Korsunsky and Kim, 2005) on the measurement of essential and non-essential works of fracture, proposed and effectively used for the model calibration. It is shown that all model parameters can be properly calibrated based on the proposed method, and experimental results, making the model attractive for practical applications. The proposed nonlocal model enables the stress update to be carried out pointwise, and hence facilitates the implementation of the model in existing finite element codes. Numerical examples are used to demonstrate the capability of the proposed model.
We study the mechanical failure of cemented granular materials (e.g., sandstones) using a constit... more We study the mechanical failure of cemented granular materials (e.g., sandstones) using a constitutive model based on breakage mechanics for grain crushing and damage mechanics for cement fracture. The theoretical aspects of this model are presented in Part I: Tengattini et al. (2014), A thermomechanical constitutive model for cemented granular materials with quantifiable internal variables, Part I – Theory (Journal of the Mechanics and Physics of Solids, 10.1016/j.jmps.2014.05.021). In this Part II we investigate the constitutive and structural responses of cemented granular materials through analyses of Boundary Value Problems (BVPs).
The multiple failure mechanisms captured by the proposed model enable the behavior of cemented granular rocks to be well reproduced for a wide range of confining pressures. Furthermore, through comparison of the model predictions and experimental data, the micromechanical basis of the model provides improved understanding of failure mechanisms of cemented granular materials. In particular, we show that grain crushing is the predominant inelastic deformation mechanism under high pressures while cement failure is the relevant mechanism at low pressures. Over an intermediate pressure regime a mixed mode of failure mechanisms is observed. Furthermore, the micromechanical roots of the model allow the effects on localized deformation modes of various initial microstructures to be studied. The results obtained from both the constitutive responses and BVP solutions indicate that the proposed approach and model provide a promising basis for future theoretical studies on cemented granular materials.
This is the first of two papers introducing a novel thermomechanical continuum constitutive model... more This is the first of two papers introducing a novel thermomechanical continuum constitutive model for cemented granular materials. Here, we establish the theoretical foundations of the model, and highlight its novelties. At the limit of no cement, the model is fully consistent with the original Breakage Mechanics model. An essential ingredient of the model is the use of measurable and micro-mechanics based internal variables, describing the evolution of the dominant inelastic processes. This imposes a link between the macroscopic mechanical behavior and the statistically averaged evolution of the microstructure. As a consequence this model requires only a few physically identifiable parameters, including those of the original breakage model and new ones describing the cement: its volume fraction, its critical damage energy and bulk stiffness, and the cohesion.
It is well known that classical constitutive models fail to capture the post-peak material behavi... more It is well known that classical constitutive models fail to capture the post-peak material behaviour, due to localisation of deformation. In such cases the concept of Representative Volume Element (RVE) on which classical continuum models rest ceases to exist and hence the smearing out of local inhomogeneities over the whole RVE is no longer correct. This paper presents a new approach to capturing localised failure in quasi-brittle materials, focusing on the kinematic enrichment of the constitutive model to describe correctly the behaviour of a volume element with an embedded localisation band. The resulting models possess an intrinsic length scale which in this case is the width of the embedded localisation band. The behaviour therefore scales with both the width of the localisation band and the size of the volume on which the model is defined. As a consequence, size effects are automatically captured in addition to the model capability in capturing behaviour at the scale of the localisation zone.
Inspired by the hierarchical structure of nacre, an aluminium alloy (AA) 7075 based composite fea... more Inspired by the hierarchical structure of nacre, an aluminium alloy (AA) 7075 based composite featuring layer waviness and cohesive interface is studied as a low weight impact resistant material. To investigate the mechanical response and the ballistic performance of this laminated structure, a numerical study of the proposed nacre-like composite plates made of 1.1-mm thick AA 7075 tablets bonded with toughened epoxy resin was performed using Abaqus/Explicit. Target thicknesses of 5.4-mm, 7.5-mm and 9.6-mm impacted by a rigid hemi-spherical projectile were simulated. The epoxy material was modelled using a user-defined interface cohesive element with compressive strength enhancement. A significant performance improvement was recorded for the 5.4-mm nacre-like plate (compared to the same thickness bulk plate), which was explained by the hierarchical structure facilitating both localised energy absorption (by deformation of the tablet) and more globalized energy absorption (by inter-layered delamination and friction). For a given projectile, however, the performance improvement of using the proposed composite decreased with increasing laminate thickness, which was attributed to the increased likelihood of ductile failure occurring prior to perforation in thicker bulk plates. For 5.4-mm thick plates impacted at high velocity, the nacre-like plate had a better ballistic performance than that of the plates made of continuous (flat and wavy) layers, which was attributed to the larger area of plastic deformation (observed in the nacre-like plate after impact) due to the tablets arrangement.
A constitutive model for interface debonding is proposed which is able to account for mixed-mode ... more A constitutive model for interface debonding is proposed which is able to account for mixed-mode coupled debonding and plasticity, as well as further coupling between debonding and friction including post-delamination friction. The work is an extension of a previous model which focuses on the coupling between mixed-mode delamination and plasticity. By distinguishing the interface into two parts, a cracked one where friction can occur and an integral one where further damage takes place, the coupling between frictional dissipation and energy loss through damage is seamlessly achieved. A simple framework for coupled dissipative processes is utilised to derive a single yield function which accurately captures the evolution of interface strength with increasing damage, for both tensile and compressive regimes. The new material model is implemented as a user-defined interface element in the commercial package ABAQUS and is used to predict delamination under compressive loads in several test cases.
We propose a constitutive modelling framework with enhanced kinematics to capture localised mode ... more We propose a constitutive modelling framework with enhanced kinematics to capture localised mode of deformation. The total strain is decomposed into two components to reflect an inelastic localisation band embedded in an elastic bulk. This is the usual case in numerical analysis of localised failure in geomaterials, when the size of the localisation band is very small compared to an element of the discretised domain under consideration. The proposed framework takes into account the sizes and corresponding behaviours of the two inelastic and elastic zones and hence gives derived constitutive models a length scale. This is an essential feature in dealing with size effect issues as a consequence of localised failure in geomaterials. The proposed framework is applied to a constitutive model for the failure analysis of quasi-brittle materials. The implementation algorithms are developed and novel features are illustrated through numerical examples.
This paper presents the application of a continuum model based on breakage mechanics in studying ... more This paper presents the application of a continuum model based on breakage mechanics in studying pile penetration into crushable granular media. Our model is able to track the evolution of the grain size distribution due to grain crushing near and surrounding the pile. The numerical study is based on an Eulerian Finite Element model, describing idealized steady ground conditions at relatively deep depths during the penetration. The effects of grain crushing on the permeability reduction in the vicinity of the pile are then quantified. In doing that, the paper highlights the advantages of using a micromechanics-based constitutive model that captures grain crushing phenomena for geotechnical applications.
Localised failure in geomaterials is preceded and
accompanied by intensive deformation and irreve... more Localised failure in geomaterials is preceded and accompanied by intensive deformation and irreversible micro-structural changes of the material in a small but finite size region. Shear, compaction, and dilation bands observed in soils and porous rocks are typical examples of phenomena that lead to localised failure. The width h of the localisation band has been experimentally shown to be a physical quantity related to the microstructure of the material. On the other hand, numerical methods for the solution of boundary value problems usually introduce another length scale H, as a result of the spatial discretisation of the considered domain into smaller ones over which the constitutive response of the material is defined in terms of incremental stressstrain relationships. While h, as a physical quantity, is fixed, H varies with the resolution of the numerical discretisation. Since h scales with the material microstructure and therefore is usually much smaller than the resolution of the numerical discretisation, the case H > h is considered in this study, e.g. failure behaviour governed by a localisation band of width h embedded in an elastic bulk of nominal side H. We present a general constitutive modelling framework to connect these two scales, and corresponding responses of the materials inside and outside the localisation zone. We demonstrate how this approach can help obtain physically meaningful solutions that are independent of the spatial discretisation in numerical analysis. Numerical analyses of localised failure in quasi-brittle materials are used to further highlight the features and applicability of the proposed approach.
We develop a novel constitutive modeling approach for the analysis of fracture propagation in qua... more We develop a novel constitutive modeling approach for the analysis of fracture propagation in quasi-brittle materials using the Material Point Method. The kinematics of constitutive models is enriched with an additional mode of localized deformation to take into account the strain discontinuity once cracking has occurred. The crack details therefore can be stored at material point level and there is no need to enrich the kinematics of finite elements to capture the localization caused by fracturing processes. This enhancement also removes the drawback of classical smeared crack approach in producing unphysical snapping back constitutive responses when the spatial resolution is not fine enough. All these facilitate the implementation of the new approach in the Material Point Method for analysis of large scale problems. Numerical examples of fracture propagation are used to demonstrate the effectiveness and potentials of the new approach.
We develop a framework for constitutive modeling of unsaturated soils that has the embedded eleme... more We develop a framework for constitutive modeling of unsaturated soils that has the embedded elements of lower scale grain to grain contacts. Continuum models developed from this framework will possess two different phases idealizing the solid grains and their interactions. As a consequence, two different constitutive relationships, corresponding to the grain to grain contact and bulk behavior, co-exist in a constitutive model and govern the response of the model. To be specific, grain to grain sliding under dry or wet condition is idealized and appears as a simple contact law embedded in a continuum framework. There is no need to define plastic strain, as this quantity naturally emerges at the continuum scale as the consequence of frictional sliding at the lower scale. In addition, the effective stress can be naturally worked out from the grain to grain contact law embedded in the model without being subjected to any interpretation. This, in our opinion, is a closer representation of unsaturated soil behavior, compared to existing continuum approaches that map everything onto a single stress-strain relationship. In this paper, the framework is presented in its simplest form that takes into account sliding on a single orientation. Grain to grain contact law with capillary effects is used for the demonstration of the concept, and the technical details behind it. Generalization of the framework for better representation of unsaturated soil behavior will also be sketched out.
We analyze the propagation of compaction bands in high porosity sandstones using a constitutive m... more We analyze the propagation of compaction bands in high porosity sandstones using a constitutive model based on breakage mechanics theory. This analysis follows the work by Das et al. [2011] on the initiation of compaction bands employing the same theory. In both studies, the theory exploits the links between the stresses and strains, and the micromechanics of grain crushing and pore collapse, giving the derived constitutive models advantages over previous models. In the current post localization analysis, the bifurcation instability of the continuum model is suppressed by the use of a rate-dependent regularization. This allows us to perform a series of finite element analyses of drained triaxial tests on porous sandstone specimens. The obtained numerical results compare well with experimental counterparts, in terms of both the initiation and propagation of compaction bands, besides the macroscopic stress-strain responses. On this basis, a parametric study is carried out to explore the effects of loading rate, degree of structural imperfections, and confining pressure on the propagation of compaction bands.
Modern numerical techniques utilised to model crack propagation tend to be optimized for tracking... more Modern numerical techniques utilised to model crack propagation tend to be optimized for tracking the evolution of a single crack. Real fracture processes are however complex, involving the initiation and propagation of opening (activated) cracks, while other may close (deactivate) and undergo frictional dissipations. Accounting for the correct loss of energy (through debonding and friction) is essential to achieving a realistic description of the fracture process. One common strategy has been to make small adaptations to traditional techniques to tackle multiple cracking, in effect relying on extensive complicated computational algorithms. A typical example is the use of cohesive models in combination with the eXtended finite Element method where cracks, sometimes intersecting, need to be defined explicitly. In this study the Material Point Method is used for the analysis of fracture propagation. Crack states, as internal variables, are stored within the material points and mapped as strong discontinuities to the elements during the Lagrangian phase of the solution. Consequently, material points carrying cracks of different sizes and orientations are allowed to cohabit within the same element, yielding a natural description of the fracture/fragmentation process. The three-point bending test is used to demonstrate the features of the new approach.
A new formula is proposed for the end-bearing capacity of piles penetrating into crushable soils.... more A new formula is proposed for the end-bearing capacity of piles penetrating into crushable soils. The formula is based on a breakage mechanics model that accounts for the evolution of the grain size distribution (GSD) due to grain crushing with only physically meaningful parameters. The model is integrated using the finite-element method to study the penetration problem. Predictions of GSDs surrounding piles and pile end-bearing capacities are validated against experiments. Next, a parametric study is carried out to quantify the effects of grain crushing on the bearing capacity, and then to establish the formula. The predictive capability of the new formula is highlighted against predictions by previous formulae, which highlights its superior origins.
Localised failure of geomaterials involves deformation at two scales: a narrow localisation zone ... more Localised failure of geomaterials involves deformation at two scales: a narrow localisation zone and the surrounding bulk. The behaviour associated with both scales should be properly taken into account in the development of constitutive models. This article presents a general constitutive modelling framework to connect these two scales, each of which is associated with a different stage of the material behaviour. It is demonstrated how this approach can be applied to any geomaterial model and how it could help obtain solutions independent of the spatial discretisation in numerical analysis.
A generic approach to constitutive modelling of composite delamination under mixed mode loading c... more A generic approach to constitutive modelling of composite delamination under mixed mode loading conditions is developed. The proposed approach is thermodynamically consistent and takes into account two major dissipative mechanisms in composite delamination: debonding (creation of new surfaces) and plastic/frictional deformation (plastic deformation of resin and/or friction between crack surfaces). The coupling between these two mechanisms, experimentally observed at the macro scales through the stiffness reduction and permanent crack openings, is usually not considered in depth in many cohesive models in the literature. All model parameters are shown to be identifiable and measurable from experiments. The model prediction of mixed-mode delamination is in good agreement with benchmarked mixed-mode bending experiments. It is further shown that accounting for all major dissipative mechanisms in the modelling of delamination is the key to the accurate prediction of both resistance and damage of the interface.
ABSTRACT. The present paper introduces a new nonlocal coupled damage-plasticity model aiming at p... more ABSTRACT. The present paper introduces a new nonlocal coupled damage-plasticity model aiming at predicting crack paths within plates made of ductile material and subjected to pure tensile loading. This model is inspired by Nguyen's model [1] for quasi-brittle material. It uses the Houlsby and Puzrin [2] framework that makes the model formulation internally consistent by linking the damage and the yield functions via a dissipation potential. However, as in Lemaitre [3], the damage law is explicitly defined in order to ease the implementation.
Journal of the Mechanics and Physics of Solids, 2014
We study the mechanical failure of cemented granular materials (e.g., sandstones) using a constit... more We study the mechanical failure of cemented granular materials (e.g., sandstones) using a constitutive model based on breakage mechanics for grain crushing and damage mechanics for cement fracture. The theoretical aspects of this model are presented in Part I: Tengattini et al. (2014), A thermomechanical constitutive model for cemented granular materials with quantifiable internal variables, Part I -Theory (Journal of the Mechanics and Physics of Solids, http://dx.doi.org/ 10.1016/j.jmps.2014.05.021). In this Part II we investigate the constitutive and structural responses of cemented granular materials through analyses of Boundary Value Problems (BVPs).
Novel metrics designed to evaluate the skill of geophysical models in simulating discontinuities ... more Novel metrics designed to evaluate the skill of geophysical models in simulating discontinuities and linear features are introduced and tested using a sea-ice model and remotely sensed observations of leads. The metrics are formulated as frequency-based indices of agreement, thus maintaining the simplicity desired in model development and operational applications, while remedying known shortcomings of common existing skill metrics. User-selectable
This paper presents a nonlocal coupled damage-plasticity model for the analysis of ductile fractu... more This paper presents a nonlocal coupled damage-plasticity model for the analysis of ductile fracture. The proposed model makes use of both damage mechanics and plasticity theories and hence is able to capture the pre-peak hardening and post-peak softening responses as well as the stiffness reduction of the material during the deformation and fracture processes. Nonlocal regularisation technique is used as an enhancement to the proposed damage-plasticity model to deal with softening related problems in the constitutive modelling and the failure analysis. Emphasis is put on the determination of model parameters with a novel calibration procedure, based on the experimental technique (Korsunsky and Kim, 2005) on the measurement of essential and non-essential works of fracture, proposed and effectively used for the model calibration. It is shown that all model parameters can be properly calibrated based on the proposed method, and experimental results, making the model attractive for practical applications. The proposed nonlocal model enables the stress update to be carried out pointwise, and hence facilitates the implementation of the model in existing finite element codes. Numerical examples are used to demonstrate the capability of the proposed model.
We study the mechanical failure of cemented granular materials (e.g., sandstones) using a constit... more We study the mechanical failure of cemented granular materials (e.g., sandstones) using a constitutive model based on breakage mechanics for grain crushing and damage mechanics for cement fracture. The theoretical aspects of this model are presented in Part I: Tengattini et al. (2014), A thermomechanical constitutive model for cemented granular materials with quantifiable internal variables, Part I – Theory (Journal of the Mechanics and Physics of Solids, 10.1016/j.jmps.2014.05.021). In this Part II we investigate the constitutive and structural responses of cemented granular materials through analyses of Boundary Value Problems (BVPs).
The multiple failure mechanisms captured by the proposed model enable the behavior of cemented granular rocks to be well reproduced for a wide range of confining pressures. Furthermore, through comparison of the model predictions and experimental data, the micromechanical basis of the model provides improved understanding of failure mechanisms of cemented granular materials. In particular, we show that grain crushing is the predominant inelastic deformation mechanism under high pressures while cement failure is the relevant mechanism at low pressures. Over an intermediate pressure regime a mixed mode of failure mechanisms is observed. Furthermore, the micromechanical roots of the model allow the effects on localized deformation modes of various initial microstructures to be studied. The results obtained from both the constitutive responses and BVP solutions indicate that the proposed approach and model provide a promising basis for future theoretical studies on cemented granular materials.
This is the first of two papers introducing a novel thermomechanical continuum constitutive model... more This is the first of two papers introducing a novel thermomechanical continuum constitutive model for cemented granular materials. Here, we establish the theoretical foundations of the model, and highlight its novelties. At the limit of no cement, the model is fully consistent with the original Breakage Mechanics model. An essential ingredient of the model is the use of measurable and micro-mechanics based internal variables, describing the evolution of the dominant inelastic processes. This imposes a link between the macroscopic mechanical behavior and the statistically averaged evolution of the microstructure. As a consequence this model requires only a few physically identifiable parameters, including those of the original breakage model and new ones describing the cement: its volume fraction, its critical damage energy and bulk stiffness, and the cohesion.
It is well known that classical constitutive models fail to capture the post-peak material behavi... more It is well known that classical constitutive models fail to capture the post-peak material behaviour, due to localisation of deformation. In such cases the concept of Representative Volume Element (RVE) on which classical continuum models rest ceases to exist and hence the smearing out of local inhomogeneities over the whole RVE is no longer correct. This paper presents a new approach to capturing localised failure in quasi-brittle materials, focusing on the kinematic enrichment of the constitutive model to describe correctly the behaviour of a volume element with an embedded localisation band. The resulting models possess an intrinsic length scale which in this case is the width of the embedded localisation band. The behaviour therefore scales with both the width of the localisation band and the size of the volume on which the model is defined. As a consequence, size effects are automatically captured in addition to the model capability in capturing behaviour at the scale of the localisation zone.
Inspired by the hierarchical structure of nacre, an aluminium alloy (AA) 7075 based composite fea... more Inspired by the hierarchical structure of nacre, an aluminium alloy (AA) 7075 based composite featuring layer waviness and cohesive interface is studied as a low weight impact resistant material. To investigate the mechanical response and the ballistic performance of this laminated structure, a numerical study of the proposed nacre-like composite plates made of 1.1-mm thick AA 7075 tablets bonded with toughened epoxy resin was performed using Abaqus/Explicit. Target thicknesses of 5.4-mm, 7.5-mm and 9.6-mm impacted by a rigid hemi-spherical projectile were simulated. The epoxy material was modelled using a user-defined interface cohesive element with compressive strength enhancement. A significant performance improvement was recorded for the 5.4-mm nacre-like plate (compared to the same thickness bulk plate), which was explained by the hierarchical structure facilitating both localised energy absorption (by deformation of the tablet) and more globalized energy absorption (by inter-layered delamination and friction). For a given projectile, however, the performance improvement of using the proposed composite decreased with increasing laminate thickness, which was attributed to the increased likelihood of ductile failure occurring prior to perforation in thicker bulk plates. For 5.4-mm thick plates impacted at high velocity, the nacre-like plate had a better ballistic performance than that of the plates made of continuous (flat and wavy) layers, which was attributed to the larger area of plastic deformation (observed in the nacre-like plate after impact) due to the tablets arrangement.
A constitutive model for interface debonding is proposed which is able to account for mixed-mode ... more A constitutive model for interface debonding is proposed which is able to account for mixed-mode coupled debonding and plasticity, as well as further coupling between debonding and friction including post-delamination friction. The work is an extension of a previous model which focuses on the coupling between mixed-mode delamination and plasticity. By distinguishing the interface into two parts, a cracked one where friction can occur and an integral one where further damage takes place, the coupling between frictional dissipation and energy loss through damage is seamlessly achieved. A simple framework for coupled dissipative processes is utilised to derive a single yield function which accurately captures the evolution of interface strength with increasing damage, for both tensile and compressive regimes. The new material model is implemented as a user-defined interface element in the commercial package ABAQUS and is used to predict delamination under compressive loads in several test cases.
We propose a constitutive modelling framework with enhanced kinematics to capture localised mode ... more We propose a constitutive modelling framework with enhanced kinematics to capture localised mode of deformation. The total strain is decomposed into two components to reflect an inelastic localisation band embedded in an elastic bulk. This is the usual case in numerical analysis of localised failure in geomaterials, when the size of the localisation band is very small compared to an element of the discretised domain under consideration. The proposed framework takes into account the sizes and corresponding behaviours of the two inelastic and elastic zones and hence gives derived constitutive models a length scale. This is an essential feature in dealing with size effect issues as a consequence of localised failure in geomaterials. The proposed framework is applied to a constitutive model for the failure analysis of quasi-brittle materials. The implementation algorithms are developed and novel features are illustrated through numerical examples.
This paper presents the application of a continuum model based on breakage mechanics in studying ... more This paper presents the application of a continuum model based on breakage mechanics in studying pile penetration into crushable granular media. Our model is able to track the evolution of the grain size distribution due to grain crushing near and surrounding the pile. The numerical study is based on an Eulerian Finite Element model, describing idealized steady ground conditions at relatively deep depths during the penetration. The effects of grain crushing on the permeability reduction in the vicinity of the pile are then quantified. In doing that, the paper highlights the advantages of using a micromechanics-based constitutive model that captures grain crushing phenomena for geotechnical applications.
Localised failure in geomaterials is preceded and
accompanied by intensive deformation and irreve... more Localised failure in geomaterials is preceded and accompanied by intensive deformation and irreversible micro-structural changes of the material in a small but finite size region. Shear, compaction, and dilation bands observed in soils and porous rocks are typical examples of phenomena that lead to localised failure. The width h of the localisation band has been experimentally shown to be a physical quantity related to the microstructure of the material. On the other hand, numerical methods for the solution of boundary value problems usually introduce another length scale H, as a result of the spatial discretisation of the considered domain into smaller ones over which the constitutive response of the material is defined in terms of incremental stressstrain relationships. While h, as a physical quantity, is fixed, H varies with the resolution of the numerical discretisation. Since h scales with the material microstructure and therefore is usually much smaller than the resolution of the numerical discretisation, the case H > h is considered in this study, e.g. failure behaviour governed by a localisation band of width h embedded in an elastic bulk of nominal side H. We present a general constitutive modelling framework to connect these two scales, and corresponding responses of the materials inside and outside the localisation zone. We demonstrate how this approach can help obtain physically meaningful solutions that are independent of the spatial discretisation in numerical analysis. Numerical analyses of localised failure in quasi-brittle materials are used to further highlight the features and applicability of the proposed approach.
We develop a novel constitutive modeling approach for the analysis of fracture propagation in qua... more We develop a novel constitutive modeling approach for the analysis of fracture propagation in quasi-brittle materials using the Material Point Method. The kinematics of constitutive models is enriched with an additional mode of localized deformation to take into account the strain discontinuity once cracking has occurred. The crack details therefore can be stored at material point level and there is no need to enrich the kinematics of finite elements to capture the localization caused by fracturing processes. This enhancement also removes the drawback of classical smeared crack approach in producing unphysical snapping back constitutive responses when the spatial resolution is not fine enough. All these facilitate the implementation of the new approach in the Material Point Method for analysis of large scale problems. Numerical examples of fracture propagation are used to demonstrate the effectiveness and potentials of the new approach.
We develop a framework for constitutive modeling of unsaturated soils that has the embedded eleme... more We develop a framework for constitutive modeling of unsaturated soils that has the embedded elements of lower scale grain to grain contacts. Continuum models developed from this framework will possess two different phases idealizing the solid grains and their interactions. As a consequence, two different constitutive relationships, corresponding to the grain to grain contact and bulk behavior, co-exist in a constitutive model and govern the response of the model. To be specific, grain to grain sliding under dry or wet condition is idealized and appears as a simple contact law embedded in a continuum framework. There is no need to define plastic strain, as this quantity naturally emerges at the continuum scale as the consequence of frictional sliding at the lower scale. In addition, the effective stress can be naturally worked out from the grain to grain contact law embedded in the model without being subjected to any interpretation. This, in our opinion, is a closer representation of unsaturated soil behavior, compared to existing continuum approaches that map everything onto a single stress-strain relationship. In this paper, the framework is presented in its simplest form that takes into account sliding on a single orientation. Grain to grain contact law with capillary effects is used for the demonstration of the concept, and the technical details behind it. Generalization of the framework for better representation of unsaturated soil behavior will also be sketched out.
We analyze the propagation of compaction bands in high porosity sandstones using a constitutive m... more We analyze the propagation of compaction bands in high porosity sandstones using a constitutive model based on breakage mechanics theory. This analysis follows the work by Das et al. [2011] on the initiation of compaction bands employing the same theory. In both studies, the theory exploits the links between the stresses and strains, and the micromechanics of grain crushing and pore collapse, giving the derived constitutive models advantages over previous models. In the current post localization analysis, the bifurcation instability of the continuum model is suppressed by the use of a rate-dependent regularization. This allows us to perform a series of finite element analyses of drained triaxial tests on porous sandstone specimens. The obtained numerical results compare well with experimental counterparts, in terms of both the initiation and propagation of compaction bands, besides the macroscopic stress-strain responses. On this basis, a parametric study is carried out to explore the effects of loading rate, degree of structural imperfections, and confining pressure on the propagation of compaction bands.
Modern numerical techniques utilised to model crack propagation tend to be optimized for tracking... more Modern numerical techniques utilised to model crack propagation tend to be optimized for tracking the evolution of a single crack. Real fracture processes are however complex, involving the initiation and propagation of opening (activated) cracks, while other may close (deactivate) and undergo frictional dissipations. Accounting for the correct loss of energy (through debonding and friction) is essential to achieving a realistic description of the fracture process. One common strategy has been to make small adaptations to traditional techniques to tackle multiple cracking, in effect relying on extensive complicated computational algorithms. A typical example is the use of cohesive models in combination with the eXtended finite Element method where cracks, sometimes intersecting, need to be defined explicitly. In this study the Material Point Method is used for the analysis of fracture propagation. Crack states, as internal variables, are stored within the material points and mapped as strong discontinuities to the elements during the Lagrangian phase of the solution. Consequently, material points carrying cracks of different sizes and orientations are allowed to cohabit within the same element, yielding a natural description of the fracture/fragmentation process. The three-point bending test is used to demonstrate the features of the new approach.
A new formula is proposed for the end-bearing capacity of piles penetrating into crushable soils.... more A new formula is proposed for the end-bearing capacity of piles penetrating into crushable soils. The formula is based on a breakage mechanics model that accounts for the evolution of the grain size distribution (GSD) due to grain crushing with only physically meaningful parameters. The model is integrated using the finite-element method to study the penetration problem. Predictions of GSDs surrounding piles and pile end-bearing capacities are validated against experiments. Next, a parametric study is carried out to quantify the effects of grain crushing on the bearing capacity, and then to establish the formula. The predictive capability of the new formula is highlighted against predictions by previous formulae, which highlights its superior origins.
Localised failure of geomaterials involves deformation at two scales: a narrow localisation zone ... more Localised failure of geomaterials involves deformation at two scales: a narrow localisation zone and the surrounding bulk. The behaviour associated with both scales should be properly taken into account in the development of constitutive models. This article presents a general constitutive modelling framework to connect these two scales, each of which is associated with a different stage of the material behaviour. It is demonstrated how this approach can be applied to any geomaterial model and how it could help obtain solutions independent of the spatial discretisation in numerical analysis.
A generic approach to constitutive modelling of composite delamination under mixed mode loading c... more A generic approach to constitutive modelling of composite delamination under mixed mode loading conditions is developed. The proposed approach is thermodynamically consistent and takes into account two major dissipative mechanisms in composite delamination: debonding (creation of new surfaces) and plastic/frictional deformation (plastic deformation of resin and/or friction between crack surfaces). The coupling between these two mechanisms, experimentally observed at the macro scales through the stiffness reduction and permanent crack openings, is usually not considered in depth in many cohesive models in the literature. All model parameters are shown to be identifiable and measurable from experiments. The model prediction of mixed-mode delamination is in good agreement with benchmarked mixed-mode bending experiments. It is further shown that accounting for all major dissipative mechanisms in the modelling of delamination is the key to the accurate prediction of both resistance and damage of the interface.
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Papers by Giang Nguyen
The multiple failure mechanisms captured by the proposed model enable the behavior of cemented granular rocks to be well reproduced for a wide range of confining pressures. Furthermore, through comparison of the model predictions and experimental data, the micromechanical basis of the model provides improved understanding of failure mechanisms of cemented granular materials. In particular, we show that grain crushing is the predominant inelastic deformation mechanism under high pressures while cement failure is the relevant mechanism at low pressures. Over an intermediate pressure regime a mixed mode of failure mechanisms is observed. Furthermore, the micromechanical roots of the model allow the effects on localized deformation modes of various initial microstructures to be studied. The results obtained from both the constitutive responses and BVP solutions indicate that the proposed approach and model provide a promising basis for future theoretical studies on cemented granular materials.
accompanied by intensive deformation and irreversible
micro-structural changes of the material in a small but
finite size region. Shear, compaction, and dilation bands
observed in soils and porous rocks are typical examples
of phenomena that lead to localised failure. The width h
of the localisation band has been experimentally shown
to be a physical quantity related to the microstructure
of the material. On the other hand, numerical methods
for the solution of boundary value problems usually
introduce another length scale H, as a result of the
spatial discretisation of the considered domain into
smaller ones over which the constitutive response of
the material is defined in terms of incremental stressstrain
relationships. While h, as a physical quantity,
is fixed, H varies with the resolution of the numerical
discretisation. Since h scales with the material
microstructure and therefore is usually much smaller
than the resolution of the numerical discretisation,
the case H > h is considered in this study, e.g. failure
behaviour governed by a localisation band of width
h embedded in an elastic bulk of nominal side H. We
present a general constitutive modelling framework to
connect these two scales, and corresponding responses
of the materials inside and outside the localisation zone.
We demonstrate how this approach can help obtain
physically meaningful solutions that are independent
of the spatial discretisation in numerical analysis.
Numerical analyses of localised failure in quasi-brittle
materials are used to further highlight the features and
applicability of the proposed approach.
The multiple failure mechanisms captured by the proposed model enable the behavior of cemented granular rocks to be well reproduced for a wide range of confining pressures. Furthermore, through comparison of the model predictions and experimental data, the micromechanical basis of the model provides improved understanding of failure mechanisms of cemented granular materials. In particular, we show that grain crushing is the predominant inelastic deformation mechanism under high pressures while cement failure is the relevant mechanism at low pressures. Over an intermediate pressure regime a mixed mode of failure mechanisms is observed. Furthermore, the micromechanical roots of the model allow the effects on localized deformation modes of various initial microstructures to be studied. The results obtained from both the constitutive responses and BVP solutions indicate that the proposed approach and model provide a promising basis for future theoretical studies on cemented granular materials.
accompanied by intensive deformation and irreversible
micro-structural changes of the material in a small but
finite size region. Shear, compaction, and dilation bands
observed in soils and porous rocks are typical examples
of phenomena that lead to localised failure. The width h
of the localisation band has been experimentally shown
to be a physical quantity related to the microstructure
of the material. On the other hand, numerical methods
for the solution of boundary value problems usually
introduce another length scale H, as a result of the
spatial discretisation of the considered domain into
smaller ones over which the constitutive response of
the material is defined in terms of incremental stressstrain
relationships. While h, as a physical quantity,
is fixed, H varies with the resolution of the numerical
discretisation. Since h scales with the material
microstructure and therefore is usually much smaller
than the resolution of the numerical discretisation,
the case H > h is considered in this study, e.g. failure
behaviour governed by a localisation band of width
h embedded in an elastic bulk of nominal side H. We
present a general constitutive modelling framework to
connect these two scales, and corresponding responses
of the materials inside and outside the localisation zone.
We demonstrate how this approach can help obtain
physically meaningful solutions that are independent
of the spatial discretisation in numerical analysis.
Numerical analyses of localised failure in quasi-brittle
materials are used to further highlight the features and
applicability of the proposed approach.