GAMM2025

Session

S08: Multiscales and homogenization

S08

8 Apr 2025, 08:30

Lecture and Conference Centre

Conveners

S08: Multiscales and homogenization: S08.01

• Michał Wichrowski
• Jan Hauck

S08: Multiscales and homogenization: S08.02

• Vincent von Oertzen
• Mohammad Sarhil

S08: Multiscales and homogenization: S08.03

• Yousef Heider
• Tobias Kaiser

S08: Multiscales and homogenization: S08.04

• Christian Gierden
• Johannes Neumann

S08: Multiscales and homogenization: S08.05

• Katarzyna Kowalczyk-Gajewska
• Geralf Hütter

S08: Multiscales and homogenization: S08.06

• Christian Gierden
• Tobias Kaiser

Description

This section is dedicated to discuss recent advances in multiscale and homogenization techniques for static and dynamic problems. Topics of particular interest are nonlinear homogenization techniques, multiscale modelling of failure processes and localization phenomena, FE2 methods, atomistic to continuum coupling, contact homogenization, model reduction techniques and furthermore homogenization schemes incorporating experimentally determined microstructure data.

209. Micromechanical modelling of void growth in metals and alloys deforming by slip and twinning

Saketh Virupakshi, Katarzyna Kowalczyk-Gajewska

08/04/2025, 08:30

The lecture focuses on understanding and describing within the multiscale modelling frameworks the void growth and coalescence leading to the ductile damage of polycrystalline metals and alloys deforming by slip and twinning. Our motivation stems from solids with a high plastic anisotropy, like magnesium with hexagonal close packed (HCP) lattice, which are known to suffer from reduced...

210. On the efficient solution of cell problems by means of wavelet-enhanced FFT-approaches

Tobias Kaiser

08/04/2025, 09:10

The predictive accuracy of computational multiscale methods depends on detailed microstructural representations and sophisticated material models for microscale constituents. However, with increasing (physical) complexity of the cell problem, the computational cost keeps increasing as well. This stipulates the development of tailored solution approaches among which FFT-based spectral methods...

211. Analysis of an X-FFT solver for two-dimensional thermal homogenization problems

Flavia Gehrig

08/04/2025, 09:30

FFT-based computational homogenization methods [1, 2] have been shown to efficiently solve multi-scale problems that are discretized on a regular grid. However, due to the grid-like structure, the obtained local solution fields lack accuracy in the vicinity of material interfaces that are not parallel to the grid. Simple workarounds typically comprise the numerical efficiency of the solver. In...

212. Modeling of porous materials on multiple length scales using FE and FFT approaches

Julian Dahler

08/04/2025, 09:50

Within the framework of the project “Multifunctional High-Performace Components made of hybrid porous materials” (HyPo, TRR375) an efficient numerical multiscale model is being developed to describe the microscopic and macroscopic behavior of hybrid porous materials using a Finite Element - Fast Fourier Transform (FE-FFT) approach. The influence of different microstructural morphologies, e.g....

213. Thermo-mechanically coupled FE-FFT-based simulation of polycrystalline materials

Christian Gierden

08/04/2025, 10:10

In order to meet the high demands on usability, structural components in the aerospace and automotive industries are typically made from high performance metals. Throughout the life-cycle of a component, from its manufacturing to its application, the respective material behavior is strongly influenced not only by mechanical but also by thermal loads, which may for example lead to phase...

214. Generalized Criteria for Hyperintegration in Reduced-Order Multiscale Simulations

Geralf Hütter

08/04/2025, 16:30

Model order reduction has become an established tool to reduce costs in computational engineering. It is based on the idea that potential solutions to parameterized problems possess a certain kind of similarity, i.e. that the actual solution vectors reside in a lower-dimensional solution manifold. Vice versa, a certain solution can represented in terms of a low-dimensional solution...

215. Statistically compatible hyper-reduction for variationally consistent homogenization and its application to diffusion

Jan Hauck

08/04/2025, 17:10

We present a statistically compatible hyper-reduction method and its application to time dependent diffusion processes in a homogenized two-phase materials consisting of inclusions in a matrix. We use a variationally consistent homogenization. The hyper-reduction method introduces generalized integration points which ensure the consistency with the first and second statistical moment of the...

216. Nonlinear reduced order modeling for computational homogenization using manifold learning and hyperreduction techniques

Erik Faust

08/04/2025, 17:30

Fully coupled high-fidelity simulations using the multiscale finite element (FE2) method are prohibitively expensive for many relevant multiscale problems. The computational cost of FE2 simulations is dominated by the assembly and solution of large linear equation systems which are required by a nonlinear solver on the microscale [1,2]. Additionally, obtaining homogenised macroscopic stresses...

217. An efficient multiscale finite element approach for ferroelectric continua

Reschad Wakili

08/04/2025, 17:50

Ferroelectric as well as ferromagnetic materials are widely used in smart structures and devices as actuators, sensors etc. Regarding their nonlinear behavior, a variety of models has been established in the past decades. Investigating hysteresis loops or electromechanical/magnetoelectric coupling effects, only simple boundary value problems (BVP) are considered. In [1] a new scale–bridging...

218. Hyper-reduction through empirically corrected clustering

Stephan Wulfinghoff

08/04/2025, 18:10

A novel hyper-reduction technique is proposed and applied to nonlinear magnetostatic and mechanical computational homogenization. The method combines the ideas of microstructural clustering with the empirical identification of a reduced set of integration points. The macroscopic magnetic response (2D) is hardly distinguishable from the finite element results already for 12 integration points...

219. Neural network enhanced computational polyconvexification

Loïc Balazi

09/04/2025, 16:30

Many applications in the field of nonlinear elasticity aim at finding a global minimizer of functionals of the form
I(u) = ∫_Ω W(∇u(x))dx
over a domain Ω ⊂ ℝᵈ in spatial dimension d ∈ {2, 3} for a suitable weak class of deformations u : Ω → ℝᵈ. In many relevant cases, the density W : ℝᵈ × ᵈ → ℝ̅ ≔ ℝ ∪ {∞} does not satisfy a suitable notion of convexity, and the existence of minimizers cannot...

220. Deep Eshelby Network: An AI Framework for Multiscale Mean-Field Homogenization

Michael Schwaighofer

09/04/2025, 16:50

Mean-field homogenization theories mainly rely on the Eshelby problem, which provides solutions for eigenstrain concentration in an ellipsoidal inclusion embedded within an infinite matrix. In nature, however, microstructures often feature inclusions with non-ellipsoidal shapes for which no analytical Eshelby solutions exist [1]. To address this limitation, we aim to develop a generalizable...

221. Digital physics of 3D-printed sand cores

Elodie Donval

09/04/2025, 17:10

3D printing of sand cores enables the design of complex casted parts and an easier prototyping approach. However, the 3D printed materials behave differently from the traditional, core-blown sand core materials. In particular, the layer-by-layer printing process may introduce some anisotropy in the macroscopic thermal, mechanical and flow properties. These macroscopic properties directly...

222. Model discovery in multiscale simulations for anisotropic materials

Jorge-Humberto Urrea-Quintero

09/04/2025, 17:30

Composite materials often exhibit complex anisotropic mechanical responses governed by their microstructural geometry and material phase distributions. Capturing these responses and their dependence on microstructural parameters is thus a critical challenge. In this work, we address this problem through a data-driven model-discovery framework that infers interpretable constitutive...

223. Deep-Learning-Based Numerical Homogenization of Heterogeneous Media

Fabian Kröpfl

09/04/2025, 17:50

We present a deep-learning-based approach to the compression of multi-scale partial differential operators characterized by highly heterogeneous coefficients. Such operators naturally appear in many science and engineering disciplines when modeling processes in heterogeneous media, that are marked by the interaction of effects on multiple scales. In order to simulate the effective behaviour of...

224. Digital process and functional design for PUR foam components based on multiscale simulations

Sarah Staub

09/04/2025, 18:10

The presented complete simulation chain connects the simulation of the reactive injection molding process with the structural mechanical properties based on computational homogenization.

The simulation of the foam expansion is carried out macroscopically with ITWMs FOAM solver. The rheology is calibrated in terms of rising pipe experiments for different pipe diameters and reaction masses,...

225. Microstructure-Property Relationships in Solid Oxide Fuel Cell Electrodes

Eric Langner

10/04/2025, 08:30

Solid oxide fuel cells (SOFCs) are among the most promising energy conversion technologies, as they (i) enable a significant reduction in emissions of air-polluting gases and of carbon dioxide and (ii) simultaneously achieve high energy efficiencies. The overall performance of the fuel cell strongly depends on the porous electrodes - anode and cathode - at which the electrochemical reactions...

226. A Homogenization Approach for Modeling Ion Transport in Solid Oxide Fuel Cells

Janna Puderbach

10/04/2025, 08:50

We present an approach to simulate electrochemical processes in solid oxide fuel cells porous electrodes, focusing on the interplay of diffusion and ion exchange in their complex material structure. The ion exchange that takes place at the material interfaces leads to discontinuities that pose a challenge for numerical modeling. Solving diffusion problems within these domains leads to strongly...

227. FExMS - Coupling Finite Elements with Molecular Statics by Homogenization

Aagashram Neelakandan

10/04/2025, 09:10

The aim of this work is to develop and implement an advanced two-scale simulation framework that links the nanoscale to the length scale of microns via computational homogenization. We propose a novel framework that integrates the LAMMPS molecular statics solver with a finite element method (FEM). The core objective of this work is to reduce computation time by enabling parallel execution of...

228. Multiscale modeling of lamellar materials accounting for size effects

Claudius Klein

10/04/2025, 09:30

The quantitative prediction of macroscopic mechanical properties of materials requires the consideration of the material microstructure. The focus of this talk is on metallic material systems with lamellar microstructures, such as NiAl-Cr(Mo) [1] or binary Fe-Al [2]. These consist of individual domains in which the materials constituents are arranged in fine layers (thickness in the micrometre...

229. The influence of microstructure model parameters on the prediction of effective elastic properties of cement paste

Tadeusz Burczyński

10/04/2025, 09:50

Cement paste serves as a binder for cementitious materials, playing a crucial role in the development of construction materials. Its composition and constituent ratios can be adjusted to meet specific requirements. The microstructure of cement paste, formed during the hydration process, typically comprises a combination of various hydration products, unreacted clinker particles and pores....

230. FE² method to model rod- and beam-like carbon-based nanostructures

Julian Ochs

10/04/2025, 10:10

Nanostructures are at the forefront of research due to their extraordinary mechanical, thermal, and chemical properties. Slender atomic arrangements, such as nanorods and nanobeams, open up possibilities for developing highly sensitive sensors. This contribution investigates these specific structures. If local effects such as vacancy defects and bond breaking or making scenarios play a role in...

231. Towards a digital twin for pavements: A viscoplastic enhancement of the Microlayer framework for asphalt modeling

Marcel May

10/04/2025, 14:00

The numerical modeling of asphalt's mechanical behavior poses significant challenges due to its anisotropic and nonlinear viscoplastic characteristics. This paper presents a thermodynamically consistent multiscale material model based on the Microlayer framework (ML). In contrast to conventional approaches, the ML model dispenses with discrete modeling of the microstructure and instead uses...

232. Inverse design of architected materials: spinodoids vs TPMS

Alexandra Otto

10/04/2025, 14:20

Mechanical metamaterials are architected materials whose mechanical properties are determined by the combination of a bulk material and a designed microstructure. Therefore, these materials are ideally suited for inverse design tasks, i.e., for finding a specific metamaterial for a given property. Within this contribution, we present a neural network (NN)-based inverse design approach and...

233. Variable Scale Separations in Homogenization of Phase Transforming Materials

Vincent von Oertzen

10/04/2025, 14:40

The homogenization of solids with a fixed microstructure has been extensively studied over the last decades for a variety of material systems. However, homogenizing phase-transforming materials with an evolving microstructure still remains an unresolved challenge, even from a methodological perspective. Specifically, the conventional definition of a microscopic length scale is based on the...

234. Development and Implementation of a New Algorithm for Periodic Boundary Conditions in 3D RVE Models

Reza Sadeghpour

10/04/2025, 15:00

Fused Filament Fabrication (FFF), a widely used additive manufacturing method, is widely recognized for its cost-effectiveness and ability to produce complex geometries with high design flexibility. Despite these advantages, the layer-by-layer deposition process introduces inherent challenges, including anisotropic mechanical properties, internal voids, and weak interlayer bonding, all of...

235. Experiments on the energy absorption of open cellular structures under static and dynamic loading

Kerstin Weinberg

10/04/2025, 15:20

Cellular materials, with their unique combination of lightweight, high strength, and good deformability, are promising for engineering applications. They may initially be divided into irregular structures and regularly repeating arrangements. Both categories can be open-celled or closed-celled. This contribution investigates the energy-absorbing properties of foamy and lattice-like structures...

236. Generating microstructures for long fiber reinforced composites with fiber curvature control

Celine Lauff

10/04/2025, 15:40

Discontinuous fiber-reinforced composites offer a high potential for lightweight applications due to their favorable specific stiffness and design freedom. Micro-CT imaging reveals that their microstructure is highly anisotropic, random and heterogeneous, which needs to be considered to predict their mechanical properties properly. For such materials, computational multiscale methods are...

237. Continuum Modeling of Dislocation Microstructures under Contact Mechanics

Sing-Huei Lee

10/04/2025, 16:30

Dislocation-mediated plastic deformation plays a crucial role in determining the mechanical behavior and microstructural evolution in contact mechanics, yet establishing a robust multiscale linkage remains a challenge. Here, we introduce a crystal plasticity model based on continuum dislocation dynamics that integrates microscale dislocation behavior with \linebreak macroscale plastic...

238. Empirically Corrected Cluster Cubature for Reduced Order Models

Hauke Goldbeck

10/04/2025, 16:50

We present a hyper-reduction technique applied to the computational homogenization in (nonlinear) magneto statics. Within the method a reduced set of integration points is identified by clustering and empirically corrected. The presented method is applied to a computationally homogenized (nonlinear) 3D magnetostatics model, which contains multiple phases showing different material behavior...

239. A generic software framework for adaptively solving two-scale coupled problems

Ishaan Desai

10/04/2025, 17:10

A major roadblock in the widespread adoption of multiscale modeling as a simulation technique is the complexity in implementing the coupling of existing softwares seamlessly at different physical and computational scales. In this work, we present a software framework which couples a hierarchy of surrogate models on the micro-scale, to a macro-scale model. The framework consists of two software...

240. Upscaling Paper Microstructures: A Statistical Approach Utilizing Mechanical and Image Data

Johannes Neumann

10/04/2025, 17:30

The function of paper has expanded considerably beyond its original role as a pure information carrier. Paper is now used in a wide range of modern applications, including packaging, furniture and insulation materials. As a result, paper has established itself as a sustainable alternative to carbon-based materials in a variety of areas.

Despite the high demand for paper and paperboard...

242. Identification of material parameters in the relaxed micromorphic model

Mohammad Sarhil

10/04/2025, 17:50

The relaxed micromorphic model (RMM) is an enriched model that uses the kinematics of the classical micromorphic theory but employs a relaxed curvature in terms of the Curl of the microdistortion field instead of the full gradient [1]. This leads to many advantages that other higher-order continua do not exhibit [2,3]. The most important feature is that the RMM operates as a two-scale linear...

241. Quantifying the error of non-representative volume elements in stochastic homogenization of elastic composites

Shreyas Karthik Ravichandran