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Variational Methods for Partial Differential Equations in Solid Mechanics and Materials Science

Description of the research Group

The research focuses on the study  of a class of  nonlinear evolutionary PDEs by variational methods. These PDEs arise in various models for solid mechanics and materials science, including phase transition and separation, damage, fracture, and plasticity systems. On the one hand, their analytical study from the viewpoint of  existence and  qualitative properties of solutions contributes to the theoretical validation of the associated models, and it is sometimes the starting point for numerics. On the other hand, this investigation often has a more general theoretical character, transcending the original applicative problem and leading to results for evolution equations in metric spaces.

esearch activities
  • Well-posedness for PDE systems modeling phase transition, phase separation, delamination.
  • Analysis of rate-independent processes in damage, fracture, plasticity.
  • Dimensional reduction problems.
  • Singular perturbation problems.
  • Gradient flows in metric spaces.
  • Weak solution concepts for rate-independent systems.
Keywords

Damage; Plasticity; Delamination; Rate-Independent Systems; Gradient Flows in Metric Spaces.

Group members