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type, title, complexity, domain, created, updated, address, aliases, tags, status, related, sources
| type | title | complexity | domain | created | updated | address | aliases | tags | status | related | sources | ||||||||
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| concept | Finite Element Plasticity | advanced | computational-mechanics | 2026-06-02 | 2026-06-02 | c-000132 |
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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 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.