GAMM2025

Session

Young Researchers’ Minisymposia

YRMS

7 Apr 2025, 16:30

Lecture and Conference Centre

Conveners

Young Researchers’ Minisymposia: YRMS4: Multi-scale phenomena in magnetic and elastic materials

• Leonard Kreutz
• Annika Bach

Young Researchers’ Minisymposia: YRMS2: Neural network-based constitutive modeling of elastic and inelastic materials

• Dominik K. Klein
• Karl A. Kalina

Young Researchers’ Minisymposia: YRMS6: Phase-Field Modeling of Multi-Physics Problems

• Vincent von Oertzen
• Martha Kalina

Young Researchers’ Minisymposia: YRMS1: New Perspectives on Classical Iterative Solvers in Numerical Linear Algebra

• Eda Oktay
• Kathryn Lund

Young Researchers’ Minisymposia: YRMS5: Mathematical analysis for systems of interacting particles

• Iulia Cristian
• Florian Oschmann

Young Researchers’ Minisymposia: YRMS3: Discretization of (port-)Hamiltonian systems

• Dorothea Hinsen
• Philipp L. Kinon

667. Constitutive Kolmogorov–Arnold Networks (CKANs): Combining Accuracy and Interpretability in Data-Driven Material Modeling

Kian Abdolazizi

07/04/2025, 16:30

Hybrid constitutive modeling combines two complementary approaches for describing and predicting a material’s mechanical behavior: data-driven black-box methods and physically constrained, theory-based models [1,2]. While black-box methods can achieve high accuracy, they often lack interpretability and extrapolation capabilities. In contrast, physics-based models offer theoretical insight and...

685. Derivation of the Vlasov-Stokes equation

Richard Höfer

07/04/2025, 16:30

We consider the N spherical particles suspended in a Stokes flow in R³. The particles satisfy a no-slip boundary condition and are subject to constant gravity with a mean-field scaling. The dynamics of the particles is modeled by Newton's laws. We discuss the rigorous derivation of the Vlasov-Stokes equation in the limit N →∞. The main difficulty arises from the implicit and singular particle...

679. Local boundary conditions in nonlocal hyperelasticity via heterogeneous horizons

Hidde Schönberger

07/04/2025, 16:30

In this talk, we consider a class of variational problems with integral functionals involving nonlocal gradients. These models have been recently proposed as refinements of classical hyperelasticity, aiming for an effective framework to capture discontinuous and singular material effects, such as fracture. Specific to our set-up is that the nonlocal gradient has a space-dependent interaction...

663. Mixed precision preconditioning strategies for GMRES

Bastien Vieublé

07/04/2025, 16:30

The Generalized Minimal Residual methods (GMRES) for the solution of general square linear systems Ax=b is often combined with a preconditioner to improve the convergence speed and the overall computing performance of the method. Successful mixed precision implementations for the application of the preconditioner inside GMRES have been previously proposed: certain strategy prescribes to apply...

673. Structure-preserving splitting methods for closed port-Hamiltonian systems

Marius Mönch

07/04/2025, 16:30

In this talk, we present splitting methods for closed port-Hamiltonian systems, focusing on preserving their internal structure, particularly the dissipation inequality. Port-Hamiltonian systems are characterized by their ability to describe energy-conserving and dissipative processes. The physical properties are encoded in the algebraic structure of the system. Operator splitting takes...

690. Towards a multi-phasefield model to analyze residual stresses

Sonja Hellebrand

07/04/2025, 16:30

Current research is shifting from minimizing or eliminating residual stresses in components to intentionally introducing them during the manufacturing process. Hot bulk forming processing enables the controlled modification of residual stresses by leveraging thermal, mechanical, and metallurgical interactions in order to evoke e.g. improved durabilty. Typically, hot bulk forming involves...

691. A Phase-Field Framework for the Modeling of Rate-(In)Dependent Hysteretic Behavior of Phase-Transforming Solids

El Khatib Omar

07/04/2025, 16:50

Phase-transforming solids, including shape memory alloys (SMAs), represent a class of multifunctional materials renowned for their remarkable thermo-mechanical properties, such as superelasticity and shape recovery. These materials undergo microstructure evolution during stress- and temperature-induced phase transformations between austenite and multi-variant martensite. The energy...

674. Discrete gradient methods for semi-explicit port-Hamiltonian DAEs

Riccardo Morandin

07/04/2025, 16:50

Port-Hamiltonian systems are an extension of Hamiltonian systems that incorporate network structure and energy exchanges through ports, enabling the modeling of open, interconnected physical systems from various domains. The interconnection of network components often leads to differential-algebraic equations, which also include algebraic constraints, like in the case of Kirchhoff's laws. To...

686. Homogenization of the compressible Navier–Stokes equations in critically perforated domains

Friederike Lemming

07/04/2025, 16:50

We consider the homogenization of the time-dependent compressible Navier–Stokes equations in the low Mach number regime in domains with critically scaled perforations. In analogy to a classical result of Allaire (ARMA90) for the incompressible fluids, we obtain in the limit the incompressible Navier–Stokes system with an additional Brinkman friction term.

664. Mixed Precision Iterative Refinement for Linear Inverse Problems

Lucas Onisk

07/04/2025, 16:50

We investigate the iterative refinement method applied to the solution of linear discrete inverse problems by considering its application to the Tikhonov problem in mixed precision. Previous works on mixed precision iterative refinement methods for the solution of symmetric positive definite linear systems and least-squares problems have shown regularization to be a key requirement when...

668. Physics-augmented neural networks meet data-driven identificaton - A dual-stage constitutive modeling framework

Lennart Linden

07/04/2025, 16:50

The formulation and calibration of constitutive models remain challenging for materials exhibiting complex nonlinear elastic or inelastic behavior. In recent years, data-based or data-driven approaches have gained significant attention within the computational mechanics community to address these challenges. However, these methods typically require extensive datasets, often consisting of...

680. Three dimensional gradient plasticity, a Gamma-Convergence approach

Martino Fortuna

07/04/2025, 16:50

We present some recent developments in the derivation of a model for three-dimensional crystal plasticity via a Gamma convergence approach. It has long been understood that, in crystalline materials such as metals, a major role in the mechanisms involved in plastic deformations is played by a particular kind of defects of the underlying crystal lattice called dislocations. In the...

665. Inner product free Krylov methods for large-scale inverse problems

Malena Sabaté Landman

07/04/2025, 17:10

Inverse problems focus on reconstructing hidden objects from indirect and often noisy measurements and are prevalent in numerous scientific and engineering disciplines. However, these reconstructions are typically highly sensitive to perturbations such as measurement errors, making regularization essential to obtain meaningful approximations.

Krylov subspace methods are a class of very...

669. Material Model Discovery from Physics-Enforced Neural Networks

Knut Andreas Meyer

07/04/2025, 17:10

Physics-enforced neural-network inelastic material models guarantee adherence to the laws of physics, even before training. There are currently two main approaches to enforce this, either by using neural networks with convexity restrictions to model thermodynamical potentials (known as Physics-Augmented Neural Networks, cf. [1]), or by embedding neural networks in the evolution laws such that...

687. Non-existence of mean-field models for particle orientations in suspensions

Richard Schubert

07/04/2025, 17:10

Recent years have seen the derivation of different kinds of mean-field models for the behaviour of particles in suspensions. This is typically based on the relatively mild singularity of the interaction. However, in models, where the orientation of the particles interact to leading order, the typical strategy runs into problems. We present here a negative result that suggests that no...

692. Phase-field modeling of deformation twinning and its interaction with plastic slip in magnesium during nano-indentation

Mohsen Rezaee-Hajidehi

07/04/2025, 17:10

Magnesium is distinguished by a highly anisotropic inelastic deformation involving a profuse activity of deformation twinning. Modeling deformation twinning poses additional challenges in comparison to plastic slip due to the critical dissimilarities in the underlying mechanisms and characteristics. A finite-strain model of coupled twinning and plastic slip is formulated by combining the...

675. Structure-preserving finite element method for port-Hamiltonian systems with implicit or differential constitutive relations

Antoine Bendimerad-Hohl

07/04/2025, 17:10

In this work we study the structure-preserving space discretization of port-Hamiltonian (pH) systems defined with implicit or differential constitutive relations. Using the concept of Stokes-Lagrange structure to describe these relations, we show how these can be reduced to a finite-dimensional Lagrange subspace of a pH system thanks to a structure-preserving Finite Element Method. As an...

681. Variational methods applied to discrete models in brittle damage

Elise Bonhomme

07/04/2025, 17:10

In this talk, I will study a discrete model of brittle damage in different regimes where the damaged zone concentrates on vanishingly small sets. We will identify the nature of the effective limit models obtained by means of an asymptotic analysis based on the Gamma-convergence of the total energies. I will recall the mechanical model of brittle damage introduced by Francfort and Marigo...

693. A Geometrical Approach to Modeling Wetting on Structured Surfaces

Jana Kunz

07/04/2025, 17:30

Technical surfaces are rarely perfectly smooth; instead, they typically exhibit some degree of roughness. Furthermore, as micro-production techniques continue to advance, it has become possible to manufacture geometrical surface structures at the microscale, posing challenges for wetting models, which are often designed for smooth surfaces. In [1, 2], a phase-field model for surface wetting...

666. A stable one-synchronization variant of reorthogonalized BCGS and its application in s-step GMRES

Yuxin Ma

07/04/2025, 17:30

The block classical Gram--Schmidt (BCGS) algorithm and its reorthogonalized variant are widely used methods for computing the economic QR factorization of block columns X due to their lower communication cost compared to other approaches such as modified Gram--Schmidt and Householder QR. To further reduce communication, i.e., synchronization, there has been a long ongoing search for a variant...

670. From Food Science to Engineering: Unveiling Tofu’s Mechanics using iCANNs

Birte Boes

07/04/2025, 17:30

The characterization of mechanical properties is essential not only in traditional engineering applications but also in food science, where it serves as a powerful tool for texture profile analysis (TPA) of food. Standardized TPA is commonly used to extract properties such as hardness and springiness [1]. To modify food texture, additional ingredients, such as thickeners, are often introduced...

682. On Scaling Properties For A Class Of Two-Well Problems For Higher Order Homogeneous Linear Differential Operators

Camillo Tissot

07/04/2025, 17:30

We study the (lower) scaling behavior of a class of compatible two-well problems for higher order, homogeneous linear differential operators. To this end, we first deduce general lower scaling bounds which are determined by the vanishing order of the symbol of the operator on the unit sphere in the direction of the associated element in the wave cone. We complement the lower bound estimates by...

676. Structure-preserving discretization of geometrically exact beams in the framework of Lie group variational integrators

Maximilian Herrmann

07/04/2025, 17:30

Geometrically exact beam models provide a powerful way to accurately model slender elastic elements undergoing large deformations, which is essential in many applications such as medical or soft robotics, cable and pipe modeling, or even biophysics. Due to the underlying kinematic description based on a Cosserat continuum, these models possess an inherent geometric structure, as their...

688. Understanding the Phase Transition in the 2D Becker-Döring Model

Jens Scholten

07/04/2025, 17:30

The Becker-Döring equations are the simplest discrete coagulation-fragmentation model, where the cluster interaction only occurs through the monomers. Nonetheless, they are able to describe the phase transition of the underlying physical system and offer a rich mathematical study. We consider a straightforward extension, where clusters are build from two different types of monomers. The added...

677. Determination of ISS gain functions leveraging finite-dimensional approximations with applications to dissipative systems

Birgit Hillebrecht

07/04/2025, 17:50

The introduction of input-to-state stability (ISS) in control systems research has resulted in numerous investigations into its properties, particularly for finite-dimensional systems. While ISS for these finite-dimensional systems is well-established, its extension to infinite-dimensional systems still presents unresolved challenges. One of these challenges is the determination of ISS gain...

694. On the energy decomposition in variational phase-field models for brittle fracture under multi-axial stress states

Francesco Vicentini

07/04/2025, 17:50

Phase-field modelling of fracture is gaining popularity in the fracture mechanics community, particularly for its ability to generate cracks with arbitrarily complex geometries and topologies in two and three dimensions without the need for ad hoc criteria. The model first introduced in [1] has a clear connection with Griffith’s propagation criterion via Gamma convergence tools and recent...

683. Pattern Formation in Biomembranes: from Interpolation Inequalities to a Scaling Law result

Anastasija Pešić

07/04/2025, 17:50

In this talk, we explore a scaling law for the infimal energy of a one-dimensional nonlocal variant of the Canham-Helfrich functional in terms of problem parameters. This functional models the formation of periodic structures in cellular membranes, known as lipid rafts, by incorporating a coupling term between the order parameter and the local curvature of the membrane. A key tool in...

671. Physics-augmented neural networks for efficient multiscale beam simulations

Jasper O. Schommartz

07/04/2025, 17:50

Slender, beam-like structures with hyperelastic base materials and complex cross-sectional shapes exhibit highly nonlinear constitutive responses in terms of their effective strain measures and stress resultants. This behavior is determined by the base material as well as geometric nonlinearities on the cross-sectional scale. While classical constitutive models for beams are typically...

689. Sharp interface dynamics in viscous two-phase flows: stability and long-time behavior

Elena Salguero

07/04/2025, 17:50

We investigate the dynamics of two immiscible viscous fluids in a two-dimensional domain, governed by the Stokes-transport system. Our focus lies on the evolution of the free interface separating the fluids. Using a contour dynamics approach, we derive a nonlinear, nonlocal equation for the free boundary and exploit it to study the stability and long-time behavior of the system. This work is...

672. Effective material modeling of complex viscoelastic shell structures with artificial neural networks

Jeremy Geiger

07/04/2025, 18:10

The growing demand for high-performance materials has led to significant advancements in engineering composite structures, such as laminates, and fiber-reinforced materials, and novel developments such as voided slabs for reinforced concrete. While these materials optimize the structural performance by taking advantage of the unique properties of the different constituents, developing...

684. Energy barriers for boundary nucleation in solid solid phase transitions

Konstantinos Zemas

07/04/2025, 18:10

We discuss energy scaling laws for simplified, singularly perturbed, double-well nucleation problems confined in a half-space, for an inclusion of fixed volume. Motivated by models for boundary nucleation of a single-phase martensite inside a parental phase of austenite, our main focus in this nonlocal isoperimetric problem is how the relationship between the rank-1 direction and the...

678. Learning of Hamiltonians, variational principles, and symmetries from data

Christian Offen

07/04/2025, 18:10

I will show how techniques in Geometric Numerical Integration can be exploited for data-driven system identification. I will demonstrate that exploiting Hamiltonian or variational structure can lead to increased accuracy in system identification by machine learning. Moreover, an exploit of data-driven symmetries can improve the extrapolation performance of machine-learned models and enables to...

695. Neural networks meet fracture phase-field: Hybrid modelling of crack propagation

Franz Dammaß

07/04/2025, 18:10

In recent times, material models that rely on neural network-based methods become increasingly popular, with many applications to soft solids. Moreover, for the modelling of fracture phenomena, the phase-field approach has proven to be a powerful tool. In this contribution, we combine these two concepts.

We present a hybrid phase-field model of fracture at finite deformation and its...