---
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]]