Bob Svendsen

• Professor (Full) at RWTH Aachen University

Phase-field approaches have gained increasing popularity as a consequence of their ability to model complex coupled multi-physical problems. The efficient modeling of migrating diffuse phase boundaries is a fundamental characteristic. A notable advantage of phase-field methods is their ability to account for diverse physical driving forces for inte...

Tungsten heavy alloy (WHA) is a typical multiphase alloy material consisting of hard tungsten (W) and soft matrix (γ) phases. When loaded, the two phases deform quite differently due to the large difference in their mechanical properties. At present, our understanding of phase deformation and behavior in the multiphase context is relatively poor co...

The purpose of the current work is the development of a so-called physics-encoded Fourier neural operator (PeFNO) for surrogate modeling of the quasi-static equilibrium stress field in solids. Rather than accounting for constraints from physics in the loss function as done in the (now standard) physics-informed approach, the physics-encoded approac...

In general, the overall macroscopic material behavior of any structural component is directly dependent on its underlying microstructure. For metal components, the associated microstructure is given in terms of a polycrystal. To enable the simulation of the related microstructural and overall elasto‐viscoplastic material behavior, a two‐scale simul...

The mechanical behavior of a periodic heterogeneous microstructure may be predicted by using a fast Fourier transform (FFT) based simulation approach. To reduce the computational effort of this method, we introduced a model order reduction (MOR) technique utilizing a reduced set of Fourier modes for the computations in Fourier space. To increase th...

Due to the general pursuit of technological advancement, structural components need to meet increasingly higher standards. In order to optimize the performance behavior of the used materials, detailed knowledge of the overall as well as microscopic material behavior under certain mechanical and thermal loading conditions is required. Hence, we pres...

The purpose of this work is the development of a trained artificial neural network for surrogate modeling of the mechanical response of elasto-viscoplastic grain microstructures. To this end, a U-Net-based convolutional neural network (CNN) is trained using results for the von Mises stress field from the numerical solution of initial-boundary-value...

Phase-field-based models have become common in material science, mechanics, physics, biology, chemistry, and engineering for the simulation of microstructure evolution. Yet, they suffer from the drawback of being computationally very costly when applied to large, complex systems. To reduce such computational costs, a Unet-based artificial neural ne...

The purpose of this work is the systematic comparison of the application of two artificial neural networks (ANNs) to the surrogate modeling of the stress field in materially heterogeneous periodic polycrystalline microstructures. The first ANN is a UNet-based convolutional neural network (CNN) for periodic data, and the second is based on Fourier n...

The purpose of this work is the development of an artificial neural network (ANN) for surrogate modeling of the mechanical response of viscoplastic grain microstructures. To this end, a U-Net-based convolutional neural network (CNN) is trained to account for the history dependence of the material behavior. The training data take the form of numeric...

Processes, such as deep rolling or induction hardening, have a remarkable influence on the material properties within the surface layer of a work piece. Our overall goal is to develop efficient two-scale methods, which are able to show the microstructural evolution of the machined material. The calculation of a spatially resolved microstructure com...

Mn enrichment at dislocations in Fe-Mn alloys due to segregation and spinodal decomposition along the dislocation line is studied via modeling and experimental characterization. To model these phenomena, both finite-deformation microscopic phase-field chemomechanics (MPFCM) and Monte Carlo molecular dynamics (MCMD) are employed. MPFCM calibration i...

Phase-field-based models have become common in material science, mechanics, physics, biology, chemistry, and engineering for the simulation of microstructure evolution. Yet, they suffer from the drawback of being computationally very costly when applied to large, complex systems. To reduce such computational costs, a Unet-based artificial neural ne...

The purpose of this work is the development and determination of higher-order continuum-like kinematic measures which characterize discrete kinematic data obtained from experimental measurement (e.g., digital image correlation) or kinematic results from discrete modeling and simulation (e.g., molecular statics, molecular dynamics, or quantum DFT)....

The overall, macroscopic constitutive behavior of most materials of technological importance such as fiber-reinforced composites or polycrystals is very much influenced by the underlying microstructure. The latter is usually complex and heterogeneous in nature, where each phase constituent is governed by non-linear constitutive relations. In order...

The purpose of the current work is the formulation of finite-deformation phase-field microelasticity (FDPFM) and its application to the modeling of (i) the dislocation core and (ii) dislocation interaction/reaction on intersecting glide planes in fcc crystals. The corresponding model formulation is carried out in the context of continuum thermodyna...

The complex interplay between chemistry, microstructure, and behavior of many engineering materials has been investigated predominantly by experimental methods. Parallel to the increase in computer power, advances in computational modeling methods have resulted in a level of sophistication which is comparable to that of experiments. At the continuu...

The reduction of iron ore with carbon-carriers is one of the largest sources of greenhouse gas emissions in the industry, motivating global activities to replace the coke-based blast furnace reduction by hydrogen-based direct reduction (HyDR). Iron oxide reduction with hydrogen has been widely investigated both experimentally and theoretically. The...

The purpose of this work is the development and determination of higher-order continuum-like kinematic measures which characterize discrete kinematic data obtained from experimental measurement (e.g., digital image correlation) or kinematic results from discrete modeling and simulation (e.g., molecular statics, molecular dynamics, or quantum DFT)....

We present a modified model order reduction (MOR) technique for the FFT-based simulation of composite microstructures. It utilizes the earlier introduced MOR technique (Kochmann et al., 2019), which is based on solving the Lippmann–Schwinger equation in Fourier space by a reduced set of frequencies. Crucial for the accuracy of this MOR technique is...

To capture the material behavior of composite microstructures, Moulinec and Suquet [5] proposed a homogenization scheme making use of fast Fourier transforms (FFT) and fixed-point iterations. To reduce the computational effort of this spectral method, Kochmann et al. [3] introduced a model order reduction technique, which is based on using a fixed...

The FFT-based method introduced by Moulinec and Suquet [9] serves as an alternative for the classical finite element based simulation of periodic microstructures. This simulation approach makes use of fast Fourier transforms (FFT) as well as fixed-point iterations to solve the microscopic boundary value problem which is captured by the Lippmann-Sch...

The reduction of iron ore with carbon-carriers is one of the largest sources of greenhouse gas emissions in the industry, motivating global activities to replace the coke-based blast furnace reduction by hydrogen-based direct reduction (HyDR). Iron oxide reduction with hydrogen has been widely investigated both experimentally and theoretically. The...

Dislocations are one-dimensional defects in crystals, enabling their deformation, mechanical response, and transport properties. Less well known is their influence on material chemistry. The severe lattice distortion at these defects drives solute segregation to them, resulting in strong, localized spatial variations in chemistry that determine mic...

Microscopic phase-field chemomechanics (MPFCM) is employed in the current work to model solute segregation, dislocation-solute interaction, spinodal decomposition, and precipitate formation, at straight dislocations and configurations of these in a model binary solid alloy. In particular, (i) a single static edge dipole, (ii) arrays of static dipol...

We present a modified model order reduction (MOR) technique for the FFT-based simulation of composite microstructures. It utilizes the earlier introduced MOR technique (Kochmann et al. [2019]), which is based on solving the Lippmann-Schwinger equation in Fourier space by a reduced set of frequencies. Crucial for the accuracy of this MOR technique i...

The purpose of this work is the development of an efficient two-scale numerical scheme for the prediction of the local and overall mechanical behavior of polycrystalline materials with elasto-viscoplastic constitutive behavior at finite strains. Assuming scale separation, the microstructural deformations are prescribed by the kinematics of the macr...

To capture all the individual microstructural effects of complex and heterogeneous materials in structural finite element simulations, a two‐scale simulation approach is necessary. Since the computational effort of such two‐scale simulations is extremely high, different methods exist to overcome this problem. In terms of a FFT‐based microscale simu...

In the current work, a number of algorithms are developed and compared for the numerical solution of periodic (quasi-static) linear elastic mechanical boundary-value problems (BVPs) based on two different discretizations of Fourier series. The first is standard and based on the trapezoidal approximation of the Fourier mode integral, resulting in tr...

open access: https://www.sciencedirect.com/science/article/pii/S0045782520302139 A chemo-mechanical model for a finite-strain elasto-viscoplastic material containing multiple chemical components is formulated and an efficient numerical implementation is developed to solve the resulting transport relations. The numerical solution relies on inverti...

The interplay of interface and bulk dislocation nucleation and glide in determining the motion of twin boundaries, slip-twin interaction, and the mechanical (i.e., stress-strain) behavior of fcc metals is investigated in the current work with the help of molecular dynamics simulations. To this end, simulation cells containing twin boundaries are su...

The purpose of this work is the formulation of energetic constitutive relations for thermoelasticity of non-simple materials based on atomistic considerations and equilibrium statistical thermodynamics (EST). In particular, both (unrestricted) canonical, and (restricted) quasi-harmonic, formulations are considered. In the canonical case, (spatial)...

The main goal of the current work is to present a grain boundary model based on the mis- match between adjacent grains in a geometrically nonlinear crystal viscoplasticity framework including the effect of the dislocation density tensor. To this end, the geometrically nonlinear crystal viscoplasticity theory by Alipour et al. (2019) is extended by...

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Many elementary deformation processes in metals involve the motion of dislocations. The planes of glide and specific processes dislocations prefer depend heavily on their atomic core structures. Atomistic simulations are desirable for dislocation modeling but their application to even sub-micron scale problems is in general computationally costly....

The purpose of the current work is the formulation of macroscopic constitutive relations, and in particular continuum flux densities, for polar continua from the underlying mass point dynamics. To this end, generic microscopic continuum field and balance relations are derived from phase space transport relations for expectation values of point fiel...

Single crystal Ni-based superalloys have long been an essential material for gas turbines in aero engines and power plants due to their outstanding high temperature creep, fatigue and oxidation resistance. A turning point was the addition of only 3 wt.% Re in the second generation of single crystal Ni-based superalloys which almost doubled the cree...

We present a model order reduction (MOR) method for finite strain FFT solvers to reduce the computational costs of the FFT simulation scheme of a two‐scale FE‐FFT simulation. The underlying method is based on a reduced set of frequencies which leads to a reduced fixed‐point scheme. The reduced set of frequencies is determined offline, based on the...

We present an efficient and accurate solution scheme for a FE-FFT-based two-scale simulation which is based on a microstructural convergence analysis leading to a minimal number of grid points, which needs to be considered in terms of the two-scale simulation. While performing the entire simulation with this coarse discretized microstructure, the m...

Mixed-type dislocations are prevalent in metals and play an important role in their plastic deformation. Key characteristics of mixed-type dislocations cannot simply be extrapolated from those of dislocations with pure edge or pure screw characters. However, mixed-type dislocations traditionally received disproportionately less attention in the mod...

A chemo-mechanical model for a finite-strain elasto-viscoplastic material containing multiple chemical components is formulated and an efficient numerical implementation is developed to solve the resulting transport relations. The numerical solution relies on inverting the model relations in terms of the chemical potential. In this work, a semi-ana...

This contribution deals with investigations on enhanced Fischer–Burmeister nonlinear complementarity problem (NCP) functions applied to a rate-dependent laminate-based material model for ferroelectrics. The framework is based on the modelling and parametrisation of the material’s microstructure via laminates together with the respective volume frac...

Dislocation-precipitate interaction and solute segregation play important roles in controlling the mechanical behavior of Ni-based superalloys at high temperature. In particular, the increased mobility of solutes at high temperature leads to increased dislocation-solute interaction. For example, atom probe tomography (APT) results [1] for single cr...

To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For this purpose a 2D semi-discrete model is proposed in this paper. It consists of two distinct phases, each with...

Predicting the structural response of advanced multiphase alloys and understanding the underlying microscopic mechanisms that are responsible for it are two critically important roles modeling plays in alloy development. An alloys demonstration of superior properties, such as high strength, creep resistance, high ductility, and fracture toughness,...

Predicting the structural response of advanced multiphase alloys and understanding the underlying microscopic mechanisms that are responsible for it are two critically important roles that modeling plays in alloy development. The demonstration of superior properties of an alloy, such as high strength, creep resistance, high ductility, and fracture...

In the continuum context, the displacements of atoms induced by a dislocation can be approximated by a continuum disregistry field. In this work, two phase-field (PF)-based approaches and their variants are employed to calculate the disregistry fields of static, extended dislocations of pure edge and pure screw character in two face-centred cubic m...

Different selected approaches of Fischer‐Burmeister (FB) nonlinear complementarity problem (NCP) functions are investigated towards the local convergence properties and the possible parameter influences. The Fischer‐Burmeister functions are applied to a micromechanically motivated material model for ferroelectric materials. The particular model emp...

The purpose of this work is the derivation of a numerically robust algorithmic formulation for the computation of the overall consistent algorithmic tangent moduli for the two‐scale modeling of heterogeneous materials with non‐linear constitutive behavior at finite strains. The underlying concept is a perturbation method. In contrast to existing nu...

This work is concerned with the development of a novel model order reduction technique for FFT solvers. The underlying concept is a compressed sensing technique which allows the reconstruction of highly incomplete data using non-linear recovery algorithms based on convex optimization, provided the data is sparse or has a sparse representation in a...

To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For this purpose a 2D semi-discrete model is proposed in this paper. It consists of two distinct phases, each with...

The purpose of this work is the development of a two-scale, FE-FFT-and phase-field-based computational model to link macro-scopic deformation processes to microstructural modifications and peripheral and surface zone properties of polycrystalline materials. The macroscopic BVP is solved using finite element (FE) methods and the solution of the micr...

This work is concerned with the development of a numerically robust two-scale computational approach for the prediction of the local and overall mechanical behavior of heterogeneous materials with non-linear constitutive behavior at finite strains. Assuming scale separation, the macroscopic constitutive behavior is determined by the mean response o...

Recently, two-scale FE-FFT-based methods (e.g., Spahn et al. in Comput Methods Appl Mech Eng 268:871–883, 2014; Kochmann et al. in Comput Methods Appl Mech Eng 305:89–110, 2016) have been proposed to predict the microscopic and overall mechanical behavior of heterogeneous materials. The purpose of this work is the extension to elasto-viscoplastic p...

The purpose of this work is the development of a framework for the formulation of geometrically non-linear inelastic chemomechanical models for a mixture of multiple chemical components diffusing among multiple transforming solid phases. The focus here is on general model formulation. No specific model or application is pursued in this work. To thi...

The purpose of this work is the prediction of micromechanical fields and the overall material behavior of heterogeneous materials using an efficient and robust two-scale FE-FFT-based computational approach. The macroscopic boundary value problem is solved using the finite element (FE) method. The constitutively dependent quantities such as the stre...

A new concept for hybrid discontinuous Galerkin methods is presented: control points. These are defined on the inter-element boundaries. The concept makes it possible to formulate element shape functions without nodes. Moreover, the theory is not restricted to certain element shapes. Furthermore, one can formulate the discrete model such that the d...

This work is concerned with the development of an efficient two-scale numerical scheme for the prediction of the local and effective mechanical response of heterogeneous materials with non-linear constitutive behavior. In order to ensure both, accurate micromechanical fields and feasible overall CPU-times, an efficient but rather simple solution sc...

The present contribution deals with the development of a laminate-based model designed to study the single and polycrystalline tetragonal ferroelectric material behaviour. Laminate-based models are micromechanically motivated and consider the volume fraction of the distinct ferroelectric variants directly in their formulation. At first, a single cr...

Crystal nucleation is among the most important processes in the synthesis of materials. Here we study the competitive and multistep nucleation process of body centered cubic (bcc) and face centered cubic (fcc) crystals using phase-field crystal simulations. The initial state is a non-equilibrium liquid. This transforms into an amorphous phase compo...

The purpose of the current work is the formulation of models for conservative and non-conservative dynamics in solid systems with the help of the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC: e.g., Grmela and Öttinger, Phys. Rev. E 56(6), 6620 (1997); Öttinger and Grmela, Phys. Rev. E 56(6), 6633 (1997)). In th...

A finite-strain anisotropic phase field method is developed to model the localisation of damage on a defined family of crystallographic planes, characteristic of cleavage fracture in metals. The approach is based on the introduction of an undamaged configuration, and the inelastic deformation gradient mapping this configuration to a damaged configu...

The purpose of this work is the multiscale FE-FFT-based prediction of macroscopic material behavior, micromechanical fields and bulk microstructure evolution in polycrystalline materials subjected to macroscopic mechanical loading. The macroscopic boundary value problem (BVP) is solved using implicit finite element (FE) methods. In each macroscopic...

This contribution deals with the numerical modelling of polycrystalline ferroelectric materials considering a sequential laminate-based approach established for tetragonal single-crystal ferroelectrics. The particular model [1] is considered and extended to predict the material behaviour of poly-crystal tetragonal ferroelectric ceramics. The derive...

We investigate non-linear elastic deformations in the phase field crystal model and derived amplitude equations formulations. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite strain tensor. It reflects the Eulerian structure of the continuum models and correctly describes the strain dep...

A phase field method for brittle fracture is formulated for a finite strain elasto-viscoplastic material using a novel obstacle phase field energy model. The obstacle energy model results in a crack profile with compact support, and thus gives a physically realistic description of the material behaviour at the vicinity of the crack tip. The resulti...

The purpose of the current work is the theoretical and computational comparison of selected models for the energetics of dislocation dissociation resulting in stacking fault and partial dislocation (core) formation in fcc crystals as based on the (generalized) Peierls-Nabarro (GPN: e.g., Xiang et al., 2008; Shen et al., 2014), and phase-field (PF:...

Purpose is the formulation, numerical implementation, identification and application of a material model for ductile damage and failure during cyclic and non-proportional loading. The authors combined a hyperelasticity-based elasto-plastic model for non-linear isotropic as well as kinematic hardening with a modified Gurson model. Evolution strategy...

The purpose of this work is the continuum modelling of transport and pile-up of infinite discrete dislocation walls driven by non-local interaction and external loading. To this end, the underlying model for dislocation wall interaction is based on the non-singular Peierls–Nabarro (PN) model for the dislocation stress field. For simplicity, attenti...

The purpose of this work is the development of a two-scale phase-field-based computational model for coupled microstructure evolution and macroscopic mechanical material behavior. To this end, the mechanical behavior of the macroscopic continuum is based on a model for each of its material elements or points as a unit cell (UC) whose average proper...

The purpose of the current work is the comparison of thermodynamic model formulations for chemically and structurally inhomogeneous solids at finite deformation based on “standard” non-equilibrium thermodynamics [SNET: e. g. S. de Groot and P. Mazur, Non-equilibrium Thermodynamics, North Holland, 1962] and the general equation for non-equilibrium r...

We investigate non-linear elastic deformations in the phase field crystal model and derived amplitude equations formulations. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite strain tensor. It reflects the Eulerian structure of the continuum models and correctly describes the strain dep...

The purpose of this work is the phase-field modeling of fcc-to-bcc martensitic phase transformations in polycrystals and the coupling with crystal plasticity. Assuming microscopic periodic fields, Green-function-and fast Fourier transform (FFT)-methods are used to solve the quasi-static balance of linear momentum. The Allen-Cahn evolution equation...

This contribution focuses on the sequential laminate-based modelling approach for the numerical simulation of the complex electromechanical material behaviour of ferroelectric single crystals. The construction of engineered domain configurations by using the method of sequential lamination in order to study the domain evolution and polarisation swi...

In order to identify a method allowing for a fast solute assessment without lengthy ab initio calculations, we analyze correlations and anti-correlation between the stacking fault energies which were shown to be related to the macroscopic ductility in Mg alloys, and five material parameters of 18 different elemental solutes. Our analysis reveals th...

Using ab initio calculations and symmetrized plane waves, we analyze the basal-plane generalized stacking fault energies in pure Mg and Mg-Y alloys and show that the knowledge of energies of only five specific points is sufficient to accurately predict the core structures and Peierls stresses of ⟨a⟩-type edge dislocations in these alloys. Our five-...

The purpose of the current work is the investigation and comparison of aspects of the material behavior predicted by two models for anisotropic, and in particular cross, hardening in bcc sheet steels subject to non-proportional loading. The first model is the modified form (Wang et al., 2008) of that due to Teodosiu and Hu (1995) and Teodosiu and H...

In this work, thermodynamic models for the energetics and kinetics of inhomogeneous gradient materials with microstructure are formulated in the context of continuum thermodynamics and material theory. For simplicity, attention is restricted to isothermal conditions. The materials of interest here are characterized by (1) first- and second-order gr...

We present a two-scale, FE-FFT-and phase-field-based model of bulk microstructure evolution and macroscopic structural behavior. On the macro scale the finite element (FE) method is used to solve the macroscopic BVP. In each integration point a microscopic RVE is embedded. Assuming microscopic periodic fields, Green-function methods and fast Fourie...

The purpose of the current work is the comparison of a phenomenological and a laminate-based model for rate-dependent switching in ferroelectric single crystals. To this end, the phenomenological model formulation of [1] is considered. In this model, the polarization vector is treated as an internal variable. The evolution of the polarization deter...

An electro-mechanically coupled phase field model for ferroelectric domain evolution is introduced. Based on Gurtin's concept of a microforce balance, a generalized Ginzburg-Landau evolution equation is derived from the second law of thermodynamics. The thermodynamic potential is formulated for transversely isotropic material behavior by adopting a...

This paper deals with the application of the model presented in the first part Schrade et al. [1] to ferroelectric composites filled with electrically conducting inclusions as well as to ferroelectric polycrystals. Composites are analyzed through the use of a computational homogenization framework for phase field methods proposed in Zäh & Miehe [2]...

The purpose of the current work is the development of a phase field model for dislocation dissociation, slip and stacking fault formation in single crystals amenable to determination via atomistic or ab initio methods in the spirit of computational material design. The current approach is based in particular on periodic microelasticity (Wang and Ji...

Single crystal ferroelectric materials, e.g. BaTiO 3 , have recently been exploited to achieve large strain actuation through domain switching and material development; see Park and Shrout (1997) and Burcsu et al. (2004). When subjected to an electromechanical load, the strains obtained in single crystals were observed to be of higher magnitude tha...

A recent material model considering the evolution of plastic anisotropy in interstitial free steels is validated for the forming process of the channel die, a complex part. In the model the evolution of the intra-granular microstructure is represented by tensor-valued internal variables. The model accounts for the cross hardening behavior observed...