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+---
+type: concept
+title: "Finite Element Plasticity"
+complexity: advanced
+domain: computational-mechanics
+created: 2026-06-02
+updated: 2026-06-02
+address: c-000132
+aliases:
+  - elasto-plastic finite element analysis
+  - FE plasticity
+tags:
+  - concept
+  - finite-element-method
+  - plasticity
+  - nonlinear-analysis
+status: current
+related:
+  - "[[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]"
+  - "[[Nonlinear Finite Element Analysis]]"
+  - "[[Abaqus Constitutive Integration]]"
+  - "[[Abaqus Metal Plasticity Models]]"
+  - "[[Abaqus Geomaterial and Concrete Plasticity]]"
+  - "[[Incremental Elasto-Plastic Solution Methods]]"
+  - "[[Plasticity Yield Criteria]]"
+  - "[[Plastic Flow Rules and Hardening]]"
+  - "[[Midas FEA Concrete Cracking and Material Models]]"
+sources:
+  - "[[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]"
+  - "[[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]]"
+---
+
+# Finite Element Plasticity
+
+## Definition
+
+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.
+
+## How It Works
+
+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.
+
+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.
+
+[[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.
+
+## Why It Matters
+
+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.
+
+## Solver Implementation View
+
+- Store state variables at integration points, not just at nodes.
+- Separate elastic trial response from plastic correction or viscoplastic update.
+- Assemble internal force from the updated stress field.
+- Provide a tangent stiffness or iterative update strategy consistent with the selected plasticity algorithm.
+- Verify with element-level and structure-level cases before trusting production simulations.
+
+## Sources
+
+- [[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]
+- [[Midas-FEA-Analysis-Manual|Midas FEA Analysis Manual]]