김경종
63 lines
3.2 KiB
Markdown
63 lines
3.2 KiB
Markdown
---
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type: concept
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title: "Finite Element Plasticity"
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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-000132
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aliases:
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- elasto-plastic finite element analysis
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- FE plasticity
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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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- nonlinear-analysis
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status: current
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related:
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- "[[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]"
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- "[[Nonlinear Finite Element Analysis]]"
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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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- "[[Incremental Elasto-Plastic Solution Methods]]"
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- "[[Plasticity Yield Criteria]]"
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- "[[Plastic Flow Rules and Hardening]]"
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- "[[Midas FEA Concrete Cracking and Material Models]]"
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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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- "[[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]]"
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---
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# Finite Element Plasticity
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## Definition
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Finite element plasticity is the finite element treatment of irreversible material deformation. The global problem remains an equilibrium or momentum balance problem, but the element integration points carry history-dependent stress, plastic strain, hardening variables, and yield-state information.
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## How It Works
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The analysis advances by load or time increments. Within each increment, element strains are computed from nodal unknowns, material states are updated at integration points, internal forces are assembled, and a linearized global system is solved until the residual and state updates are acceptable.
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The central algorithmic pieces are [[Plasticity Yield Criteria]], [[Plastic Flow Rules and Hardening]], and [[Incremental Elasto-Plastic Solution Methods]]. A yield function decides whether a stress state remains elastic. A flow rule maps yield-surface information into plastic strain increments. A hardening law evolves the yield condition after plastic work.
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[[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]] adds a production material-model perspective: associated and non-associated flow, isotropic strain hardening, explicit and implicit rate-form integration, Rankine and Tresca criteria, total strain cracking, and interface material laws are tied directly to concrete and civil structural nonlinear analysis.
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## Why It Matters
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Plasticity is one of the main reasons a finite element solver must be incremental and path-dependent. The same mesh can produce different results depending on increment size, tangent consistency, stress return/update method, hardening law, and convergence tolerance.
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## Solver Implementation View
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- Store state variables at integration points, not just at nodes.
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- Separate elastic trial response from plastic correction or viscoplastic update.
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- Assemble internal force from the updated stress field.
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- Provide a tangent stiffness or iterative update strategy consistent with the selected plasticity algorithm.
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- Verify with element-level and structure-level cases before trusting production simulations.
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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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- [[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]]
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