김경종
75 lines
3.0 KiB
Markdown
75 lines
3.0 KiB
Markdown
---
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type: concept
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title: "Plastic Flow Rules and Hardening"
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complexity: advanced
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domain: computational-mechanics
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created: 2026-06-02
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updated: 2026-06-02
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address: c-000135
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aliases:
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- associated plasticity
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- non-associated plasticity
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- isotropic hardening
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- kinematic hardening
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tags:
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- concept
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- finite-element-method
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- plasticity
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- constitutive-modeling
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status: current
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related:
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- "[[Finite Element Plasticity]]"
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- "[[Plasticity Yield Criteria]]"
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- "[[Abaqus Constitutive Integration]]"
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- "[[Abaqus Metal Plasticity Models]]"
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- "[[Abaqus Geomaterial and Concrete Plasticity]]"
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sources:
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- "[[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]"
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source_refs:
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- source: "[[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]"
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raw_path: ".raw/FiniteElementsinPlasticityTheoryandPractice/"
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raw_files:
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- "FiniteElementsinPlasticityTheoryandPractice_024.md"
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- "FiniteElementsinPlasticityTheoryandPractice_029.md"
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- "FiniteElementsinPlasticityTheoryandPractice_050.md"
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- "FiniteElementsinPlasticityTheoryandPractice_001.md"
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md_indices:
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- 24
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- 29
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- 50
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- 1
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match: "heuristic-heading-keyword"
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confidence: high
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---
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# Plastic Flow Rules and Hardening
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## Definition
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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.
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## Flow Rules
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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.
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## Hardening
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The source distinguishes hardening ideas that are central to implementation:
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- Isotropic hardening expands or contracts the yield surface.
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- Kinematic hardening translates the yield surface and is important for reversed or cyclic loading.
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- Work hardening links yield evolution to accumulated plastic work or equivalent plastic strain.
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## Solver Consequences
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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.
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## Connections
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[[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.
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## Sources
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- [[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]
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