김경종
66 lines
2.7 KiB
Markdown
66 lines
2.7 KiB
Markdown
---
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type: concept
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title: "Incremental Elasto-Plastic Solution Methods"
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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-000133
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aliases:
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- elasto-plastic iteration methods
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- plasticity Newton iteration
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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 Element Plasticity]]"
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- "[[Nonlinear Finite Element Analysis]]"
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- "[[Static Equilibrium Equation Solvers]]"
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- "[[Abaqus Nonlinear Solution Control]]"
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- "[[Abaqus Constitutive Integration]]"
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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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---
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# Incremental Elasto-Plastic Solution Methods
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## Definition
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Incremental elasto-plastic solution methods are nonlinear finite element procedures that advance a path-dependent plastic response through load increments and equilibrium iterations.
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## Main Methods
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[[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]] presents the standard one-dimensional nonlinear methods before extending them to plasticity applications:
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- Direct iteration or successive approximation updates the nonlinear response with a repeated approximate solve.
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- Newton-Raphson iteration repeatedly linearizes the residual about the current state.
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- Tangential stiffness methods update the stiffness according to the current tangent response.
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- Initial stiffness methods reuse an earlier stiffness while moving nonlinear effects into residual or pseudo-load corrections.
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## FE Plasticity Loop
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1. Apply a load or time increment.
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2. Predict displacement or strain increments.
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3. Update stresses and internal variables at integration points.
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4. Assemble internal forces and tangent or secant stiffness terms.
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5. Solve for a correction and test convergence.
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6. Commit the plastic state only when the increment is accepted.
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## Why It Matters
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Plasticity makes equilibrium path-dependent. Large increments can cross yield surfaces poorly, inconsistent tangents can slow or prevent convergence, and initial-stiffness schemes can be robust but inefficient when the plastic zone changes quickly.
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## Connections
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- [[Abaqus Nonlinear Solution Control]] is the production Abaqus counterpart: increments, Newton iterations, cutbacks, stabilization, and convergence checks.
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- [[Abaqus Constitutive Integration]] supplies the material-point update that each global iteration relies on.
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- [[Static Equilibrium Equation Solvers]] covers the global equation solution layer beneath each nonlinear iteration.
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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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