Computational Plasticity

Alle Informationen zur Vorlesung und den Übungen eines aktuellen Semesters entnehmen Sie bitte den entsprechenden Kursen in moodle und TUCaN.

Da die Vorlesung auf Englisch ist, ist das Inhaltsverzeichnis nur auf dieser Sprache vorhanden.

• 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)

Da die Vorlesung auf Englisch ist, sind die Qualifikationsziele nur auf dieser Sprache vorhanden.

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) ist empfehlenswert.