Philipp Junker

Leibniz Universität Hannover · Institute of Continuum Mechanics

We investigate the influence of stress-induced damage on the effective viscoelastic response of two-phase composites having constituents that undergo solid-solid phase transitions. Such composites are prone to experience damage near the interfaces separating phase-transforming inclusions and the non-transforming matrix. By accounting for inelastici...

Previous works of Junker and Hackl (2016) have presented a variational growth approach to topology optimization in which the problem of checkerboarding was suppressed by means of a discontinuous regularization scheme. This approach did not require additional filter techniques and also optimization algorithms were not needed any more. However, growt...

In this paper, we contribute to the methodology of material modeling by presenting a potential-based approach for non-isothermal inelastic processes. It is based on the principle of the minimum of the dissipation potential which was used previously only in the isothermal context. In contrast to the principle of maximum dissipation, the presented pr...

Numerical simulations are a powerful tool to analyze the complex thermo-mechanically coupled material behavior of shape memory alloys during product engineering. The benefit of the simulations strongly depends on the quality of the underlying material model. In this contribution, we discuss a variational approach which is based solely on energetic...

Numerical simulation of bone remodelling enables the investigation of short-and long-term stability of bone implants and thus can be an essential tool for surgical planning. The first development of related mathematical models dates back to the early 90's, and these models have been continuously refined since then. However, one issue which has been...

This paper presents a novel experimental method to study the abrasion mechanism of car tires. It is based on the detection of microscopic movements associated with material damage (cracking) on the rubber tread. This is referred to as degrading layer relaxation. It correlates with the wear rate and, interestingly, the direction of the pattern’s mov...

We formulate variational material modeling in a space-time context. The starting point is the description of the space-time cylinder and the definition of a thermodynamically consistent Hamilton functional which accounts for all boundary conditions on the cylinder surface. From the mechanical perspective, the Hamilton principle then yields thermo-m...

This paper deals with the mathematical modeling of bacterial co-aggregation and its numerical implementation in a FEM framework. Since the concept of co-aggregation refers to the physical binding between cells of different microbial species, a system composed of two species is considered in the modeling framework. The extension of the model to an a...

Accounting for the real material behavior in topology optimization is essential since it determines the final optimal structure. For considering a plastic material behavior, we propose a surrogate plasticity model within the thermodynamic topology optimization to handle this complex material behavior in a resource‐efficient manner. We model physica...

Simulating stochastic structures with inelastic material behavior is often done with Monte Carlo simulations. The method is robust but needs a huge computational effort. We propose a new approach for the dynamic simulation of viscoelastic stochastic structures with a computational effort in the magnitude of one deterministic simulation. It is based...

To make implants, especially oral implants, safer and more durable in patients bodies, in silico models proof to be a useful tool to investigate the growth behavior of harmful biofilms causing implant loss. In literature, most growth models fall into one of two categories: either the growth is calculated volumetricly or by adjusting the density of...

Modeling and simulation of materials with stochastic properties is typically computationally expensive, especially for nonlinear materials or dynamic simulations. Time-separated stochastic mechanics (TSM) is a technique to efficiently compute the stochastic characteristics of stress and reaction force of materials. It has successfully been used for...

Topology optimization and additive manufacturing complement one another where the first one results in possibly complex structures, and the second one allows for manufacturing of those. For computing optimized components that also fit to the manufacturing limits, the building processes need to be accounted for already during the optimization proces...

In this application‐oriented work, we examine the performance of topology‐optimized structures as compared to the reference I‐beam. We make use of the thermodynamic topology optimization based on a linear elastic compliance minimization, i. e. minimization of the elastic strain energy of the whole structure. We investigate, how the optimization of...

In this paper, we propose a novel, semi-analytic approach for the two-scale, computational modeling of concentration transport in packed bed reactors. Within the reactor, catalytic pellets are stacked, which alter the concentration evolution. Firstly, the considered experimental setup is discussed and a naive one-scale approach is presented. This o...

In our previous works, we established the method of thermodynamic topology optimization based on Hamilton’s principle. With the use of a gradient-enhanced regularization and the formulation of the resulting differential equation in the strong form, it is necessary to calculate the Laplacian of the design function. Also, a Neumann boundary condition...

Anisotropic materials are often used for high-performance components and thus the optimization of structures produced with those materials is of major interest. To optimize such structures, the topology as well as the material orientation should be considered as design variables for maximum performance. Most common production processes of anisotrop...

In order to find optimal structures for realistic applications, it is essential to include the real material behavior in the optimization process. For this purpose, this research focuses on thermodynamic topology optimization accounting for plasticity for which a surrogate material model is developed. Characteristically, the stress/strain diagram r...

We present our work on a new variational approach for thermodynamic topology optimization of hyperelastic structures: building upon our previous works, we follow a thermodynamic approach for deriving a field equation that describes the evolution of the density. The problem of topology optimization is consequently solved without the need of expensiv...

In this contribution we present a gradient damage formulation (cf. [1]) for hyperelastic materials undergoing large deformations, which is based on the small strain formulation of [2]. Through discretizing the gradient extended damage field with the neighbored element method the damage update can be performed at the element level. Although local up...

The modeling of damage processes in materials constitutes an ill‐posed mathematical problem which manifests in mesh‐dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by regularization schemes of which the gradient enhancement of the strain energy density is often used. In this contribution...

An established strategy for material modeling is provided by energy-based principles such that evolution equations in terms of ordinary differential equations can be derived. However, there exist a variety of material models that also need to take into account non-local effects to capture microstructure evolution. In this case, the evolution of mic...

In this contribution, we present an extension of the thermodynamic topology optimization that accounts for a non-linear material behavior due to the evolution of plastic strains. In contrast to physical loading and unloading processes, a virtual unloading due to stiffness evolution during the optimization process must not result in a hysteresis in...

The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by regularization schemes of which the gradient enhancement of the strain energy density is often used. In this contribution...

We present a novel approach to topology optimization based on thermodynamic extremal principles. This approach comprises three advantages: (1) it is valid for arbitrary hyperelastic material formulations while avoiding artificial procedures that were necessary in our previous approaches for topology optimization based on thermodynamic principles; (...

A three‐dimensional topology optimization of anisotropic materials including the optimization of the local material orientation based on thermodynamic principles is presented. To this end, the topology is parameterized by a continuous density variable with penalization of intermediate densities (SIMP) [1]. The material orientation is defined by the...

In this contribution, we present a novel modeling approach for mass transport problems that connects the microscale with the macroscale. It is based on a proper investigation of the diffusion process in the catalytic pellets from which, after semi‐analytic considerations, a source term for the macroscopic advection‐diffusion process can be identifi...

In a series of papers, we investigated the problem of efficiently analyzing visco‐elastic materials with stochastic material properties. The related evolution equation could be solved analytically which allowed for a stochastic series expansion around the mean for the internal variable. This, in turn, gave access to analytical expressions for the s...

Material models exhibiting softening effects due to damage or localization share the problem of leading to ill-posed boundary value problems that lead to physically meaningless, mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior, described, e.g., by internal variables, at a spat...

The benefit of adaptive meshing strategies for a recently introduced thermodynamic topology optimization is presented. Employing an elementwise gradient penalization, stability is obtained and checkerboarding prevented while very fine structures can be resolved sharply using adaptive meshing at material-void interfaces. The usage of coarse elements...

An established strategy for material modeling is provided by energy-based principles such that evolution equations in terms of ordinary differential equations can be derived. However, there exist a variety of material models that also need to take into account non-local effects to capture microstructure evolution. In this case, the evolution of mic...

In a recent publication, an approach to optimize the orientation of anisotropic materials was presented. This strategy was embedded into the thermodynamic topology optimization based on growth. In this paper, we show that the thermodynamic orientation optimization can also be used in more classical approaches to topology optimization. We furthermor...

We present an adaptive numerical treatment for a recently published model for brittle damage with gradient enhancement. We employ adaptive strategies both in time and space, yielding detailed investigations of the convergence behavior: the damage distribution can be resolved with very high accuracy, turning the damage behavior into cracks known fro...

Based on our previous works, we present the finite-element implementation of an energy-based material model that displays the effect of functional fatigue of shape memory alloys during cyclic loading. The functional degradation is included in our model by taking account of irreversible martensitic volume fractions. Three internal variables are used...

In our previous work, we developed a variational approach for topology optimization based on thermodynamic principles, i.e. Hamilton's principle for dissipative processes. Hamilton's principle yields a closed set of differential equations for a variety of problems in continuum mechanics, which include microstructural processes described by internal...

Due to their special material behavior– namely the superelasticity as well as the one‐way and two‐way effect– shape memory alloys are very attractive materials for industrial applications. The solid/solid phase transformation between austenite and martensite is however accompanied by a formation of dislocations which influence the cyclic behavior o...

As is well‐known, softening effects that are characteristic for damage models are accompanied by ill‐posed boundary value problems. This arises from non‐convex and non‐coercive energies and results in mesh‐dependent finite element results. For that reason, regularization strategies, which somehow take into account the non‐local behavior, have to be...

The prediction of failure mechanism in structures are always an important topic in the field of computational mechanics. Finite element computations of an inelastic material involving softening behavior (e.g. softening plasticity or damage) can suffer from strongly mesh‐dependent results. Therefore, such continuum models should be equipped with a r...

Modeling and simulation of materials with stochastic properties is an emerging field in both mathematics and mechanics. The most important goal is to compute the stochastic characteristics of the random stress, such as the expectation value and the standard deviation. An accurate approach are Monte Carlo simulations; however, they consume drastic c...

Micromechanical modeling of material behavior has become an accepted approach to describe the macroscopic mechanical properties of polycrystalline materials in a microstructure-sensitive way. The microstructure is modeled by a representative volume element (RVE), and the anisotropic mechanical behavior of individual grains is described by a crystal...

A strategy for tension/compression anisotropy enhancement of topology optimization approaches is presented. To this end, a spectral decomposition of stresses and strains into tension and compression contributions allows for a multi-material optimization that favors tension or compression affine materials, dependent on the predominant local state. N...

Computationally efficient approaches to topology optimization usually include heuristic update and/or filtering schemes to overcome numerical problems such as the well-known checkerboarding phenomenon, local minima, and the associated mesh dependency. In a series of papers, Hamilton’s principle, which originates from thermodynamic material modeling...

Even in the simple linear elastic range, the material behavior is not deterministic, but fluctuates randomly around some expectation values. The knowledge about this characteristic is obviously trivial from an experimentalist's point of view. However, it is not considered in the vast majority of material models in which “only” deterministic behavio...

As damage occurs in the context of high stresses that are also related to the presence of plastic strains, it is natural to investigate the effect of plasticity on damage evolution and to thus achieve a more realistic model. In this work, the existing and new damage model presented in [Junker P, Schwarz S, Makowski J, Hackl K. Continuum Mech. Therm...

In our previous works [1–3], we introduced a variational approach derived from thermodynamical principles, i.e. Hamilton's principle for dissipative processes. The Hamilton principle directly yields evolution equations providing an iterative update scheme for the design variables of the problem, requiring no additional (mathematical) minimization a...

This paper presents a mathematically accurate and numerically very fast procedure to compute both expectation and variance (and standard deviation) of the stresses in a visco‐elastic material with stochastically fluctuating elastic properties. The stochastic material properties turn the evolution equation for the viscous strain components into a st...

Shape memory alloys show the effect of functional fatigue under cyclically loading. This fatigue comes along with a decrease of the stress plateaus in the characteristic hysteresis curve which is also accompanied by an accumulated permanent strain. Cyclic experiments detected that a formation of dislocations trigger a stabilization of martensite an...

A model framework for the analysis of isotropic quasi‐brittle damage, was recently presented in [1]. Within this paper, the model in [1] is significantly improved. To be more precise, and in contrast to [1], the novel model: (i) eliminates unnecessary model parameters, (ii) can be better interpreted from a physics point of view, (iii) can capture a...

Damage models, which are characterized by softening effects, suffer from ill‐posed boundary value problems that result in mesh‐dependent finite‐element results. Regularization strategies counteract these problems by taking into account the non‐local behavior such as realized by the gradient‐enhanced formulation presented in [1]. Two variational equ...

In a series of previous works, we established a novel approach to topology optimization for compliance minimization based on thermodynamic principles known from the field of material modeling. Hamilton's principle for dissipative processes directly yields a partial differential equation (referred to as the evolution equation) as an update scheme fo...

This paper deals with a constitutive model suitable for the analysis of quasi-brittle damage in structures. The model is based on incremental energy relaxation combined with a viscous-type regularization. A similar approach—which also represents the inspiration for the improved model presented in this paper—was recently proposed in Junker et al. (C...

Modern high-performance materials have inherent anisotropic elastic properties. The local material orientation can thus be considered to be an additional design variable for the topology optimization of structures containing such materials. In our previous work, we introduced a variational growth approach to topology optimization for isotropic, lin...

Even in the simple linear elastic range, the material behavior is not deter-ministic, but fluctuates randomly around some expectation values. The knowledge about this characteristic is obviously trivial from an experimentalist's point of view. However, it is not considered in the vast majority of material models in which "only" deterministic behavi...

Stochastic fluctuations of material properties, i.e. the elastic constants, result in stochastic fluctuations of the material's response to mechanical loading, i.e. the stresses. In this contribution, we present an analytical approach to the time‐efficient and mathematically accurate modeling of the stochastic behavior of visco‐elastic materials. T...

Many modern high-performance materials have inherent anisotropic elastic properties and its local material orientation can be considered to be an additional design variable for the topology optimization [1–3]. We extend our previous model for topology optimization with variational controlled growth [4–6] for linear elastic anisotropic materials, fo...

The inclusion of information on the stochastic behavior of microstructures is a key issue for modeling materials with even higher precision. To this end, stochastic series expansions offer an elegant for accounting for randomness. A prominent example is the usage of the so-called Chaos Polynomial Expansion in the context of the Stochastic Finite El...

Due to the effects of pseudoelasticity and pseudoplasticity, shape memory alloys (SMAs) are very promising materials for the industrial usage. However, applications of SMA are still challenging due to the functional degradation during cyclic loading. The related effect of functional fatigue which occurs during pseudoelastic loading is modeled by su...

Since damage occurs in context of high stresses that are also related to the development of plastic strains, it is natural to couple damage and plasticity phenomena to achieve a more realistic model. Hereto, the new damage model presented in [2] was used and enhanced with plasticity and isotropic hardening, as first shown in [1]. Thereby, the damag...

It is well known that plastic deformations in shape memory alloys stabilize the martensitic phase. Furthermore, the knowledge concerning the plastic state is crucial for a reliable sustainability analysis of construction parts. Numerical simulations serve as a tool for the realistic investigation of the complex interactions between phase transforma...

In situ measurements are a pivotal extension of conventional transmission electron microscopy (TEM). By means of the shape memory alloy NiTi thin film Functional Grids were produced for in situ straining as alternative or at least complement of expensive commercial holders. Due to the martensite-austenite transition temperature straining effects ca...

The phenomenon of functional fatigue occurs during cyclic loading of pseudoelastic shape memory alloys. We model this effect by considering an irreversible martensitic volume fraction in addition to the reversible amounts of austenite and martensite based on variational principles. The inclusion of irreversible martensitic volume fractions coincide...

Material models, including softening effects due to, for example, damage and localizations, share the problem of ill-posed boundary value problems that yield mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior described, for example, by internal variables, at a spatial level. Thi...

The objective of topology optimization is to find a mechanical structure with maximum stiffness and minimal amount of used material for given boundary conditions [2]. There are different approaches. Either the structure mass is held constant and the structure stiffness is increased or the amount of used material is constantly reduced while specific...

Common material models that take into account softening effects due to damage have the problem of ill-posed boundary value problems if no regularization is applied. This condition leads to a non-unique solution for the resulting algebraic system and a strong mesh dependence of the numerical results. A possible solution approach to prevent this prob...

Shape memory alloys show a very complex material behavior associated with a diffusionless solid/solid phase transformation between austenite and martensite. Due to the resulting (thermo‐)mechanical properties – namely the effect of pseudoelasticity and pseudoplasticity – they are very promising materials for the current and future technical develop...

Numerical instabilities cause the well-known problem of checkerboarding during topology optimization: elements that possess material are periodically neighbored to elements that are material-free. Furthermore, such numerical solutions depend on the finite element mesh and no reasonable processing techniques exist for manufacture. Thus, integral- or...

This work presents a variational material model for transformation-induced plasticity in steels. We will use the principle of the minimum of the dissipation potential to develop a coupled material model for plastic deformations and phase transformations that simultaneously accounts for the hardening effects that play an important role. We will use...

Due to the effect of transformation induced plasticity (TRIP) , TRIP-steels are very promising materials, e.g. for the automobile industry. The material behavior is characterized by very complex inner processes, namely phase transformation coupled with plastic deformation and kinematic hardening. We establish a micromechanical model which uses the...

Common material models that take into account softening effects due to damage encounter the problem of ill‐posed boundary value problems if no regularization is applied. This condition leads to a non‐unique solution for the resulting algebraic system and a strong mesh dependence of the numerical results. A possible solution approach to prevent this...

The pseudoelastic material behavior is one outstanding feature of shape memory alloys. This effect comes along with the forming of two plateaus in the stress/strain diagram of a tension test. Cyclic loading leads to a decrease particularly of the upper stress-plateau due to the evolution of plastic deformations which also implies fatigue of the mat...

A micromechanical model for finite single crystal plasticity was introduced by Kochmann & Hackl (2011 Contin.Mech. Thermodyn. 23, 63–85 (doi:10.1007/ s00161-010-0714-5)). This model is based on thermodynamic variational principles and leads to a non-convex variational problem. Based on the Lagrange functional, an incremental strategy was outlined t...

This paper presents a new approach to topology optimization that is based on observations of natural biological systems in which growth processes are initialized during high mechanical loading. A compliance parameter is introduced that serves as an internal variable and for which evolution equations are derived using the variational principle of th...

Too difficult, too abstract, too theoretical – many first-year engineering students complain about their mathematics courses. The project MathePraxis aims to resolve this disaffection. It links mathematical methods as they are taught in the first semesters with practical problems from engineering applications – and thereby shall give first-year eng...

Most modern wear resistant materials feature a multiphase microstructure and the macroscopic wear behavior is controlled by the local mechanical properties of the single phases. Indentation testing and in particular nanoindentation allows for the local mechanical characterization of materials and their phases. This paper addresses the determination...

Taking into account softening effects in connection with conventional inelastic material models can cause ill-posed boundary value problems. These problems can be established by obtaining no unique solution for the resulting algebraic system or by having a strong mesh dependence of the numerical results. This is the consequence of losing ellipticit...

Shape memory alloys show the well known effect of pseudo-elasticity associated with the formation of two stress plateaus in the stress/strain diagram for tension tests. Due to cyclic loading, the stress plateaus decrease with every load cycle, particularly the upper one. This important effect of functional fatigue results from plastic deformations...

The impressive properties of shape memory alloys are produced by means of solid-to-solid phase transformations where thermal effects play an important role. In this paper we present a model for polycrystalline shape memory alloys which takes full thermo-mechanical coupling into account. Starting from the equations of the first and the second law of...

Shape memory alloys possess several features that make them interesting for industrial applications. However, due to their complex and thermo-mechanically coupled behavior, direct use of shape memory alloys in engineering construction is problematic. There is thus a demand for tools to achieve realistic, predictive simulations that are numerically...

We propose a thermodynamically consistent model of static and dynamic recrystallization for metals during and after severe plastic deformations that is capable of predicting the evolution of dislocation density as well as mean grain size.

A micromechanical model for polycrystalline shape memory alloys (SMAs) was introduced in a series of papers by Hackl and co-authors. In order to model the polycrystalline aspect, they assumed a specific set of orientation distribution functions that had to be resolved with high numerical effort. Although this model displays interesting aspects, its...