MultiPhysicsVault/wiki/concepts/Plastic Flow Rules and Hardening.md

type, title, complexity, domain, created, updated, address, aliases, tags, status, related, sources, source_refs

type	title	complexity	domain	created	updated	address	aliases	tags	status	related	sources	source_refs
concept	Plastic Flow Rules and Hardening	advanced	computational-mechanics	2026-06-02	2026-06-02	c-000135	associated plasticity non-associated plasticity isotropic hardening kinematic hardening	concept finite-element-method plasticity constitutive-modeling	current	Finite Element Plasticity Plasticity Yield Criteria Abaqus Constitutive Integration Abaqus Metal Plasticity Models Abaqus Geomaterial and Concrete Plasticity	Finite-Elements-in-Plasticity-Theory-and-Practice	source raw_path raw_files md_indices match confidence Finite-Elements-in-Plasticity-Theory-and-Practice .raw/FiniteElementsinPlasticityTheoryandPractice/ FiniteElementsinPlasticityTheoryandPractice_024.md FiniteElementsinPlasticityTheoryandPractice_029.md FiniteElementsinPlasticityTheoryandPractice_050.md FiniteElementsinPlasticityTheoryandPractice_001.md 24 29 50 1 heuristic-heading-keyword high

Plastic Flow Rules and Hardening

Definition

Plastic flow rules and hardening laws define what happens after a stress state reaches a yield surface. The flow rule gives the direction of plastic strain increment, and the hardening law evolves the yield condition as plastic deformation accumulates.

Flow Rules

In associated plasticity, the plastic potential is the same as the yield function, so the plastic strain increment is normal to the yield surface. In non-associated plasticity, the plastic potential differs from the yield function, which is often important for pressure-dependent frictional materials where dilatancy must be controlled separately from yield.

Hardening

The source distinguishes hardening ideas that are central to implementation:

• Isotropic hardening expands or contracts the yield surface.
• Kinematic hardening translates the yield surface and is important for reversed or cyclic loading.
• Work hardening links yield evolution to accumulated plastic work or equivalent plastic strain.

Solver Consequences

Flow and hardening choices determine which internal variables must be stored at integration points. They also determine the material tangent used by implicit global iteration and the pseudo-load corrections used by simpler incremental schemes.

Connections

Plasticity Yield Criteria gives the elastic/plastic boundary. Abaqus Constitutive Integration is the production stress-update layer that turns flow and hardening rules into state updates and tangent terms. Abaqus Metal Plasticity Models and Abaqus Geomaterial and Concrete Plasticity are user-facing model families built from these ideas.

Sources

• Finite-Elements-in-Plasticity-Theory-and-Practice