Piolax Inc

In the case of finite deformations, the Piola–Kirchhoff stress tensors express the stress relative to the reference configuration. This is in contrast to the Cauchy stress tensor which expresses the stress relative to the present configuration. For infinitesimal deformations and rotations, the Cauchy and Piola–Kirchhoff tensors are identical. Whereas the Cauchy stress tensor relates stresses in the current configuration, the deformation gradient and strain tensors are described by relating the motion to the reference configuration; thus not all tensors describing the state of the material are in either the reference or current configuration. Describing the stress, strain and deformation either in the reference or current configuration would make it easier to define constitutive models. The 1st Piola–Kirchhoff stress tensor, is one possible solution to this problem. It defines a family of tensors, which describe the configuration of the body in either the current or the reference state.