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

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

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 plane algorithms)

• J.C. Simo, T.J.R. Hughes (1998) Computational Inelasticity. Springer New York, NY, 1st Edition. DOI: 10.1007/b98904