Elastoplasticity

Elastoplasticity is the field of continuum mechanics that studies materials whose response combines elastic and plastic deformation under applied loads. Elastic deformation is reversible, while plastic deformation persists after unloading. Elastoplastic behavior is important for metals and other crystalline materials, especially under large strains, cyclic loading, or complex stress states.

Constitutive models describe how stress evolves with strain and internal state variables. A common framework splits strain into elastic and plastic parts: ε = ε^e + ε^p. The material yields when the stress reaches a yield surface in stress space, with classical criteria such as von Mises or Tresca for metals, and Drucker–Prager for soils. Plastic flow is described by a flow rule, frequently associative, linking the plastic strain increment to the gradient of the yield function. Hardening laws govern how the yield surface changes with plastic deformation; isotropic hardening enlarges the surface uniformly, while kinematic hardening translates it in stress space. In finite strains, elastoplasticity uses a multiplicative decomposition of the deformation gradient into elastic and plastic parts, with evolution laws for the internal variables.

Numerical integration relies on return-mapping algorithms that enforce the yield condition and update internal variables at each increment. Rate-independent models capture path dependence but require careful treatment of instabilities; rate-dependent (viscoplastic) models include time-rate effects to describe creep and rate effects.

Applications span metal forming, structural analysis under large loads, geotechnical engineering, and earthquake-resistant design. Limitations include model calibration from experiments, issues near localization, and the trade-off between physical realism and computational efficiency.