Multiplicative decomposition of the deformation gradient

Summary

The multiplicative decomposition writes the deformation gradient of an elastic–plastic body as a product $F = F^e F^p$ of an elastic part $F^e$ and a plastic part $F^p$. The plastic part maps the reference configuration to a local, stress-free intermediate configuration, and the elastic part maps this to the current configuration. It is the standard kinematic basis of finite strain plasticity and of crystal plasticity, and it is often called the Kröner–Lee decomposition. At small strains it reduces to the familiar additive split of the strain into elastic and plastic parts.