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type, title, complexity, domain, created, updated, address, aliases, tags, status, related, sources
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| concept | Plastic Flow Rules and Hardening | advanced | computational-mechanics | 2026-06-02 | 2026-06-02 | c-000135 |
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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.