Papers by Stefan Hartmann
Experimental Mechanics, Sep 7, 2022
Background Thermographic images provide two-dimensional information of the surface temperatures o... more Background Thermographic images provide two-dimensional information of the surface temperatures on specific selected component regions. If these components have curved surfaces, there is the question of calculating the surface temperature assigned to the material points concerned on the one hand and determining the associated temperature gradient on the other. Apart from general objects, special problems might occur with additively manufactured components as the surfaces are often rough and rippled. Objectives In this paper, the image information from 2D-thermography as well as 3D-digital image correlation data are combined to determine both the temperature at the material points as well as the temperature gradients concerned. Thus, on the one hand, the basic theoretical equations of the transformations are provided and, on the other hand, the required steps in the experiment are discussed. Methods Since both discrete data sets of thermography and digital image correlation have to be interpolated, radial basis functions are drawn on. In this context, both a consistent presentation of the underlying equations as well as the error propagation of the occurring uncertainties are addressed as well. First, this is demonstrated at a pure verification example to estimate the expected accuracies. Second, the concept is investigated at real samples made of 3D-printed polymer as well as a wire-arc additively manufactured steel specimen. Results It turns out that (a) edge effects can lead to more uncertain data at the boundaries of the evaluated region, and (b) a required oblique tripod attached to the specimen are essential uncertainty factors. However, the uncertainty of the temperature determination due to the projection scheme is in the order of general temperature dispersions. Conclusions Thus, an additional cheap and reliable experimental device in form of a oblique tripod is required which both camera systems have to detect. Then, the evaluation tool can map the 2D-data onto the curvilinear surface. Moreover, the temperature gradient calculation is possible.
Mathematical and Computational Applications
Multiscale FE2 computations enable the consideration of the micro-mechanical material structure i... more Multiscale FE2 computations enable the consideration of the micro-mechanical material structure in macroscopical simulations. However, these computations are very time-consuming because of numerous evaluations of a representative volume element, which represents the microstructure. In contrast, neural networks as machine learning methods are very fast to evaluate once they are trained. Even the DNN-FE2 approach is currently a known procedure, where deep neural networks (DNNs) are applied as a surrogate model of the representative volume element. In this contribution, however, a clear description of the algorithmic FE2 structure and the particular integration of deep neural networks are explained in detail. This comprises a suitable training strategy, where particular knowledge of the material behavior is considered to reduce the required amount of training data, a study of the amount of training data required for reliable FE2 simulations with special focus on the errors compared to ...
Journal of Mechanics of Materials and Structures, 2017
Dynamical systems in finite elements yield systems of second-order differential equations. Incorp... more Dynamical systems in finite elements yield systems of second-order differential equations. Incorporating inelastic material properties, thermomechanical coupling and particular Dirichlet boundary conditions essentially changes the underlying mathematical problem. In this respect, we investigate the behavior of a number of subproblems such as reaction force computation, high-order time-integration, time-adaptivity, etc., which yield (depending on the underlying problem) systems of differential-algebraic equations or a mixture of systems of second-order and first-order ordinary differential equations (especially if the constitutive equations are of evolutionary-type, as in the case of viscoelasticity and viscoplasticity). The main goals are to provide higher-order time integration schemes using diagonally implicit Runge-Kutta methods and the generalized-α method so that they may be applied to the constitutive equations, and to apply time-adaptivity via embedded schemes so that step-sizes are chosen automatically. The constitutive equations are given by a thermoviscoplasticity model of Perzyna/Chaboche-type with nonlinear kinematic hardening. JoMMS peer-review and production is managed by EditFLOW ® from Mathematical Sciences Publishers.
Archive of Applied Mechanics, Feb 1, 2021
In this article, several aspects of material parameter identification are addressed. We compare s... more In this article, several aspects of material parameter identification are addressed. We compare several methods to identify material parameters of a constitutive model for small strain, linear elastic transverse isotropy based on experimental data of specimens made from composite plates. These approaches range from identifying the five material parameters from purely analytical considerations to the fully numerical identification on the basis of finite elements and various data provided by digital image correlation (DIC). The underlying experimental tests range from purely uniaxial tensile tests with varying fiber orientation to shear and compression tests. A specific measuring instrument has been developed for the latter tests to obtain unique material parameters-motivated by the concept of local identifiability. Besides, we compare the numerical differentiation, which is the common procedure in parameter identification, with the fully analytical derivation of sensitivities within the DIC/FEM approach.
This article discusses the passive response of arteries, with a particular focus on the material ... more This article discusses the passive response of arteries, with a particular focus on the material parameter identification process of constitutive model of anisotropic hyperelasticity. The arterial wall is composed of three layers: tunica intima, tunica media and tunica adventitia. However, only the media and the adventitia are assumed to be mechanically relevant tissue layers. Thus, it is necessary to determine a set of material parameters for each contributing layer, based on inhomogeneous stress-strain state in an experimental setup. In these tests, tensile and internal pressure loading paths are applied on a human mammary artery, which is embedded in a tank filled with Krebs solution. The artery was proved, in previous works, to be slightly compressible and anisotropic. We draw on the model of Nolan et al. (2014) to identify the material parameters, based on the experimental data provided by contour lines and using digital imaging analysis. The experimental protocol is explained in detail. From the experiments, the axial reaction force and displacement in the radial direction are used to determine the material parameters by using finite element simulations. A particular focus lies on the highly correlated solution between material parameters in the layer, emphasizing the extreme difficulties of a “unique” identification.
Proceedings in applied mathematics & mechanics, Dec 1, 2018
Constitutive modeling requires the calibration of the constitutive model to experimental data. Th... more Constitutive modeling requires the calibration of the constitutive model to experimental data. This calibration is called material parameter identification. Simple experiments lead to specified deformation and stress states, which is not guaranteed in all situation. Thus, finite elements must be drawn on to calculate the deformation state solving the entire boundary-value problem. There are several basic questions, which must be addressed apart from experiments doable for the material under consideration: first, what optimization technique is suitable? Second, are the material parameters identifiable by the given experiments, and what is the quality of the result? Third, there have been open questions of the connection between engineering and mathematical literature showing that in Engineering Science the procedures have already been developed in Numerical Mathematics. These question will be discussed in this overview.
Proceedings in applied mathematics & mechanics, Dec 1, 2017
Even though many studies have been conducted to understand and model the passive response of arte... more Even though many studies have been conducted to understand and model the passive response of arteries, very few studies have been performed to develop constitutive equation for the active response of arteries and to perform numerical simulations. In this paper, the diffusion of the neurotransmitter, for example noradrenaline, is combined with the anisotropic constitutive model to describe the temporal contraction of the smooth muscle cells in the artery wall.
The p-version of the finite element method based on the displacement formulation is known to be f... more The p-version of the finite element method based on the displacement formulation is known to be free from volumetric locking beyond a moderate polynomial order for nearly-incompressible problems in linear elasticity, as was shown by Babuska Suri [4,5] and Suri [6] . Informally, locking means that the numerical solution deteriorates as a characteristic parameter approaches a critical limit e.g. for volumetric locking in linear elasticity as the Poisson ratio ? approaches 0.5. We demonstrate that the volumetric locking-free property of the p-version carries over to finite-deformation analysis of nearly incompressible Neo-Hookean materials.
The p-version of the finite element method (p-FEM) performs very well for linear elastic problems... more The p-version of the finite element method (p-FEM) performs very well for linear elastic problems. Recently highly non-linear problems, as cold isostatic pressing (CIP) of metal powders (finite deformations and complex constitutive models) have became of interest. These problems require enhancement of p-FEMs to geometrically and physically non-linear capabilities, where good performance is expected, and results should be validated by experimental observations. This task is being performed by designing a set of experimental techniques for a) adoption of a constitutive model that describes qualitatively the experimental observation and b) identification of the material parameters. This talk presents the results of a 3-years project by five different groups in developing a p-FEM simulation tool for CIP processes validated by experimental observation. The p-FEM academic code AdhoC has been extended to incorporate geometrical and physical non-linear constitutive models of evolutionary type. This includes stress computation and consistent linearization of the inelastic model. On the basis of experimental observations (for particular powder metals) a finite strain viscoplasticity model was developed [1]. This constitutive model was incorporated both in AdhoC (implicit) and in the commercial h-FE code HKS/Abaqus/Explicit. The material parameters for the specific constitutive model were identified on the basis of the designed experimental observations. Experiments on relatively complex geometries were then performed in parallel to p- and h-FEM simulations, and results are compared for validat ion purposes. The excellent results obtained by p-FEM simulations in comparison to experiments and h-FEMs will be presented [2-4].
Proceedings in applied mathematics & mechanics, Oct 1, 2016
In structural dynamics the initial boundary-value problem has to be solved in the space and time ... more In structural dynamics the initial boundary-value problem has to be solved in the space and time domain. The spatial discretization is done using finite elements yielding systems of differential equations of second-order. Incorporating inelastic material properties, thermo-mechanical coupling and particular Dirichlet boundary conditions essentially changes the underlying mathematical problem. The main goal is to provide higher-order time integration schemes using diagonally-implicit Runge-Kutta methods (DIRK) and the Generalized α-method consistently applied to the semi-discretized ODE-system comprising the semi-discretized equations of motion, the unsteady semi-discrete heat equation and constitutive equations of evolutionarytype. Furthermore, we want to show the applicability of time-adaptivity by embedded schemes so that step-sizes are chosen automatically. The inelastic constitutive equations are given by a thermo-viscoplasticity model of Perzyna/Chaboche-type with non-linear kinematic hardening.
Proceedings in applied mathematics & mechanics, Dec 1, 2014
In structural dynamics the initial boundary value problem has to be solved in the space and time ... more In structural dynamics the initial boundary value problem has to be solved in the space and time domain. The spatial discretization is done using finite elements. For the temporal discretization two classes of Runge-Kutta methods and the generalized-α method are compared. The representatives for the Runge-Kutta methods are diagonally implicit Runge-Kutta schemes (DIRK) and diagonally implicit Runge-Kutta-Nyström schemes (DIRKN).
Composite Structures, Feb 1, 2020
Abstract This article discusses modeling aspects of fiber circumplacement around a hole using con... more Abstract This article discusses modeling aspects of fiber circumplacement around a hole using continuous functions. Here, spatially inhomogeneous transversal isotropy is formulated on the basis of patches using B-spline approaches generating the fiber orientation. For this purpose, experiments with different fiber orientations and “hole”-concepts are provided for both the identification of material parameters as well as for model validation. The validation examples are a plate with uniform fiber distribution, where the hole is drilled after the production process, and a plate with circumplacement around the hole, where the fibers are bypassed before the matrix material is injected. The entire numerical problems are treated using finite elements. Furthermore, the material parameters are identified using – within a least-square approach – the combination of finite element simulations and optical results of a digital image correlation system.
Proceedings in applied mathematics & mechanics, Oct 1, 2016
Identification of unique material parameters for the media and adventitia in the case of arteries... more Identification of unique material parameters for the media and adventitia in the case of arteries involves many challenges. Tension‐inflation experiments were performed on the internal mammary artery and the axial force and the radial displacements were used to identify the material parameters. It will be shown that these experimental data are not sufficient to uniquely identify the material parameters of the passive response in human arteries. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Computational Mechanics, Jun 27, 2019
A new numerical method to model the active response of arteries is proposed. Vasoconstrictors and... more A new numerical method to model the active response of arteries is proposed. Vasoconstrictors and vasodilators in the bloodstream diffuse from the lumen into the arterial wall through the intima and cause the smooth muscle cells, mostly in the media, to contract. We combine the diffusion process with the mechanical model in Yosibash and Priel (Comput Methods Appl Mech Eng 237-240:51-66, 2012). Finite element computations of the fully coupled field problem using time-adaptive, high-order time-integration methods based on diagonally-implicit Runge-Kutta methods are investigated with respect to their convergence behavior for linear and non-linear loading paths. Since the blood pressure is periodic, highly non-linear external loading path, the step-size estimation has to be adapted to minimize step-size rejections. An example of an artery analysis that illustrates the advantage of the proposed time-adaptive scheme is provided.
Computational Mechanics, Apr 24, 2021
In this article, we follow a thorough matrix presentation of material parameter identification us... more In this article, we follow a thorough matrix presentation of material parameter identification using a least-square approach, where the model is given by non-linear finite elements, and the experimental data is provided by both force data as well as fullfield strain measurement data based on digital image correlation. First, the rigorous concept of semi-discretization for the direct problem is chosen, where-in the first step-the spatial discretization yields a large system of differential-algebraic equation (DAE-system). This is solved using a time-adaptive, high-order, singly diagonally-implicit Runge-Kutta method. Second, to study the fully analytical versus fully numerical determination of the sensitivities, required in a gradient-based optimization scheme, the force determination using the Lagrange-multiplier method and the strain computation must be provided explicitly. The consideration of the strains is necessary to circumvent the influence of rigid body motions occurring in the experimental data. This is done by applying an external strain determination tool which is based on the nodal displacements of the finite element program. Third, we apply the concept of local identifiability on the entire parameter identification procedure and show its influence on the choice of the parameters of the rate-type constitutive model. As a test example, a finite strain viscoelasticity model and biaxial tensile tests applied to a rubber-like material are chosen.
PAMM
The ease of estimating the uncertainties of numerical simulations in metal forming is of particul... more The ease of estimating the uncertainties of numerical simulations in metal forming is of particular interest. This uncertainty arises from, for example, material parameter identification, geometric dimensions, external loads, and contact conditions. In this paper, we aim to address this issue with the extension to geometric influences, and boundary as well as friction conditions. The uncertainty quantification from material parameter identification – here, in terms of sensitivities of the resulting simulations based on the confidence interval of the parameters – is transferred from the literature and the individual proportions are quantified and compared, respectively. For material parameter identification, experiments on steel and glass fiber reinforced plastic are used and the confidence intervals are determined. Particularly in the case of sequential determination of the parameters, the uncertainties are estimated with the aid of Gaussian error propagation. This concept can also ...
VIII Conference on Mechanical Response of Composites, 2021
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Papers by Stefan Hartmann