GAMM2025

Session

PP03: Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials

PP03

8 Apr 2025, 14:00

Lecture and Conference Centre

Conveners

PP03: Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials: PP03.01

• Klaus Hackl
• Dorothee Knees

731. Material Design for Multiple Loads

Lorenzo Sommella

08/04/2025, 14:00

We consider the optimization of the topology and geometry of an elastic structure subjected to a set of boundary loads. Specifically, we aim to minimize the energy, which is the sum of the material volume and the structure's compliance (defined as the work done by the load). This theory has been extensively developed by many authors, such as Allaire, Murat, and Kohn, in the case of a single...

732. Predicting plastic activity in disordered solids via geometric measures

Somar Shekh Alshabab

08/04/2025, 14:20

Unlike their crystalline counterparts, glasses have a complex structure that lacks any long-range order, resulting in the system possessing a large number of metastable states. The system transitions between these metastable states, giving rise to a complex mechanical response when subjected to mechanical deformation. These transitions manifest as localized atomic rearrangements also known as...

733. A dimensionally reduced capillary problem and its phase-field approximation

Luciano Sciaraffia, Yizhen Wang

08/04/2025, 14:40

We study the behaviour of a given volume of liquid confined between two rough solid plates. When the separation between the plates is small relative to the liquid volume, capillary bridges are expected to form, which minimise Gauss' capillary energy locally. We derive aΓ-expansion for the energy as the plate separation approaches zero, yielding a dimensionally reduced problem in terms of the...

734. Arclength methods and dissipative processes – Analysis and numerical experiments

Felix Rörentrop

08/04/2025, 15:00

The talk is concerned with rate-independent dissipative processes and their approximations by means of balanced-viscosity solutions.

Within the first part of the talk, algorithms for approximating balanced-viscosity solutions by means of arclength-methods are discussed. The focus is on the modeling of brittle fracture, cf. [1]. It is shown that balanced-viscosity solutions indeed capture...

735. Towards dynamic phase-field fracture in finite strains

Sven Tornquist

08/04/2025, 15:20

We give a brief overview of our previous work analyzing models for dynamic phase-field fracture in viscoelastic materials under small strains [1]. Building on this, the initial steps towards an extension of the framework to finite strains are addressed. In this context, we adopt a first-order formulation for the momentum balance to describe the dynamics of the elastic solid. To model the...

736. Computational Semiconvexification for Relaxation in Isotropic Damage

Timo Neumeier

08/04/2025, 15:40

The numerical simulation of finite strain damage models often faces challenges owing to the non-convexity of the underlying strain energy densities, such as mesh-dependent approximations and stability issues. In this talk, we focus on recent developments in computational relaxation by semiconvexification of a pseudo-time-incremental damage model, including the efficient approximation of...