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wiki/concepts/Plasticity Yield Criteria.md

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+---
+type: concept
+title: "Plasticity Yield Criteria"
+complexity: advanced
+domain: computational-mechanics
+created: 2026-06-02
+updated: 2026-06-02
+address: c-000134
+aliases:
+  - yield surface
+  - plastic yield functions
+  - Tresca yield criterion
+  - von Mises yield criterion
+  - Mohr-Coulomb yield criterion
+  - Drucker-Prager yield criterion
+tags:
+  - concept
+  - finite-element-method
+  - plasticity
+  - constitutive-modeling
+status: current
+related:
+  - "[[Finite Element Plasticity]]"
+  - "[[Plastic Flow Rules and Hardening]]"
+  - "[[Abaqus Metal Plasticity Models]]"
+  - "[[Abaqus Geomaterial and Concrete Plasticity]]"
+  - "[[Plane Stress and Plane Strain Elements]]"
+  - "[[Axisymmetric Finite Elements]]"
+sources:
+  - "[[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]"
+---
+
+# Plasticity Yield Criteria
+
+## Definition
+
+A plasticity yield criterion defines the stress states at which a material leaves elastic response and begins plastic flow. In finite element analysis, the yield function is evaluated at integration points during each increment.
+
+## Criteria In The Source
+
+[[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]] emphasizes four criteria for two-dimensional and axisymmetric plasticity programs:
+
+- Tresca: pressure-insensitive yielding based on maximum shear stress.
+- von Mises: pressure-insensitive yielding based on distortional energy or deviatoric stress invariant.
+- Mohr-Coulomb: pressure-dependent yielding commonly used for frictional geomaterials.
+- Drucker-Prager: smooth pressure-dependent approximation useful for soils, rocks, and other frictional media.
+
+## Solver Consequences
+
+The yield criterion affects:
+
+- how elastic trial stresses are tested;
+- where plastic corrections are projected;
+- whether the yield surface has corners or singular points;
+- whether pressure contributes to yielding;
+- which stress components and invariants must be computed in each element routine.
+
+## Connections
+
+Pressure-insensitive criteria connect directly to [[Abaqus Metal Plasticity Models]]. Pressure-dependent criteria connect to [[Abaqus Geomaterial and Concrete Plasticity]]. All criteria depend on [[Plastic Flow Rules and Hardening]] to define the post-yield strain increment and evolution of the yield surface.
+
+## Sources
+
+- [[Finite-Elements-in-Plasticity-Theory-and-Practice|Finite Elements in Plasticity: Theory and Practice]]
+