Computational Plasticity

All information regarding the lecture and the exercise of the current semester can be found in the respective courses in moodle and TUCaN.

• Part I: One-dimensional plasticity: formulation and numerical implementation
  • Derivation of one-dimensional constitutive equations, building on the phenomenological interpretation of plasticity
  • Strong and weak forms of the initial boundary value problem (IBVP), its discretization and linearization
  • Integration algorithms (return map algorithms) for one-dimensional constitutive equations
• Part II: Three-dimensional classical rate-independent plasticity
  • Review of classical governing equations within continuum mechanics and thermodynamics
  • Theory of yield surfaces and classical small-strain plasticity models
  • Maximum plastic dissipation principle and its interpretation as a constrained convex optimization problem
  • Derivation of constitutive equations from convex optimization principles
• Part III: Integration algorithms for plasticity
  • Incremental form of constitutive equations and geometric interpretation as closest point projection
  • Radial return map algorithm for J2 plasticity
  • General return map algorithms (closest point projection algorithms, cutting plain algorithms)

Students develop a rigorous understanding of integration algorithms for elastoplastic constitutive problems and their mathematical foundations from a convex optimization perspective. They are able to solve and implement multidimensional problems for inelastic solids focusing on return map algorithms for rate-independent plasticity models, linearization of nonlinear global governing equations, and discretization and solution in the context of the finite element method.

Grundlagen der Finite-Elemente-Methode (13-E1-M001) is recommended.