Stefan Hartmann | Clausthal University of Technology (original) (raw)

Uploads

Papers by Stefan Hartmann

Research paper thumbnail of FE2 Computations with Deep Neural Networks: Algorithmic Structure, Data Generation, and Implementation

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 ...

Research paper thumbnail of Time-adaptive finite element simulations of dynamical problems for temperature-dependent materials

Journal of Mechanics of Materials and Structures, 2017

Research paper thumbnail of Material parameter identification of unidirectional fiber-reinforced composites

Archive of Applied Mechanics, Feb 1, 2021

Research paper thumbnail of Parameter identification of the passive response in arteries

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.

Research paper thumbnail of From Experiment to Material Parameter Identification

Proceedings in applied mathematics & mechanics, Dec 1, 2018

Research paper thumbnail of Numerical modeling of active response of arteries

Proceedings in applied mathematics & mechanics, Dec 1, 2017

Research paper thumbnail of p-FEM is locking-free for finite strain hyperelasticity

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.

Research paper thumbnail of Calculation verifcation in finite deformation applications using higher-order methods

Research paper thumbnail of Geometrical and material nonlinear high order finite elements (p-FEMs) for the simulation of powder compaction

Research paper thumbnail of p-FEM for a Class of Finite Deformation Pressure Dependent Plasticity Models Validated by Experimental Observations

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].

Research paper thumbnail of Time-adaptive non-linear finite-element computations for thermo-mechanically coupled analysis in inelastic dynamical systems

Proceedings in applied mathematics & mechanics, Oct 1, 2016

Research paper thumbnail of Second-order time-integration in inelastic dynamical systems

Proceedings in applied mathematics & mechanics, Dec 1, 2014

Research paper thumbnail of Experiment, modeling and simulation of bypassing holes in composites

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.

Research paper thumbnail of Problems in parameter identification of the passive response in human arteries

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)

Research paper thumbnail of Simulating the temporal change of the active response of arteries by finite elements with high-order time-integrators

Computational Mechanics, Jun 27, 2019

Research paper thumbnail of Material parameter identification using finite elements with time-adaptive higher-order time integration and experimental full-field strain information

Computational Mechanics, Apr 24, 2021

Research paper thumbnail of Uncertainty estimation using Gaussian error propagation in metal forming process simulation

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 ...

Research paper thumbnail of Thickness determination of laminate core layers from microscopy images

Research paper thumbnail of Constitutive Modeling and Finite Element Simulation of Metal-Polymer-Metal Sandwich Structures

VIII Conference on Mechanical Response of Composites, 2021

Research paper thumbnail of Experimental characterization, analytical and numerical investigations of metal/polymer/metal sandwich composites – Part 1: Deep drawing

Composite Structures, 2018

Research paper thumbnail of FE2 Computations with Deep Neural Networks: Algorithmic Structure, Data Generation, and Implementation

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 ...

Research paper thumbnail of Time-adaptive finite element simulations of dynamical problems for temperature-dependent materials

Journal of Mechanics of Materials and Structures, 2017

Research paper thumbnail of Material parameter identification of unidirectional fiber-reinforced composites

Archive of Applied Mechanics, Feb 1, 2021

Research paper thumbnail of Parameter identification of the passive response in arteries

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.

Research paper thumbnail of From Experiment to Material Parameter Identification

Proceedings in applied mathematics & mechanics, Dec 1, 2018

Research paper thumbnail of Numerical modeling of active response of arteries

Proceedings in applied mathematics & mechanics, Dec 1, 2017

Research paper thumbnail of p-FEM is locking-free for finite strain hyperelasticity

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.

Research paper thumbnail of Calculation verifcation in finite deformation applications using higher-order methods

Research paper thumbnail of Geometrical and material nonlinear high order finite elements (p-FEMs) for the simulation of powder compaction

Research paper thumbnail of p-FEM for a Class of Finite Deformation Pressure Dependent Plasticity Models Validated by Experimental Observations

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].

Research paper thumbnail of Time-adaptive non-linear finite-element computations for thermo-mechanically coupled analysis in inelastic dynamical systems

Proceedings in applied mathematics & mechanics, Oct 1, 2016

Research paper thumbnail of Second-order time-integration in inelastic dynamical systems

Proceedings in applied mathematics & mechanics, Dec 1, 2014

Research paper thumbnail of Experiment, modeling and simulation of bypassing holes in composites

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.

Research paper thumbnail of Problems in parameter identification of the passive response in human arteries

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)

Research paper thumbnail of Simulating the temporal change of the active response of arteries by finite elements with high-order time-integrators

Computational Mechanics, Jun 27, 2019

Research paper thumbnail of Material parameter identification using finite elements with time-adaptive higher-order time integration and experimental full-field strain information

Computational Mechanics, Apr 24, 2021

Research paper thumbnail of Uncertainty estimation using Gaussian error propagation in metal forming process simulation

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 ...

Research paper thumbnail of Thickness determination of laminate core layers from microscopy images

Research paper thumbnail of Constitutive Modeling and Finite Element Simulation of Metal-Polymer-Metal Sandwich Structures

VIII Conference on Mechanical Response of Composites, 2021

Research paper thumbnail of Experimental characterization, analytical and numerical investigations of metal/polymer/metal sandwich composites – Part 1: Deep drawing

Composite Structures, 2018