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 plane algorithms).

Simo, J.C. and Hughes, T.J.R., 2006. Computational Inelasticity. Springer Science & Business Media.