Finite plasticity in P⊤P. Part II: quasistatic evolution and linearization

We address a finite-plasticity model based on the symmetric tensor P^T P instead of the classical plastic strain P. Such a structure arises by assuming that the material behavior is invariant with respect to frame transformations of the intermediate configuration. The resulting variational model is lower-dimensional, symmetric, and based solely on the reference configuration. The constitutive model has been introduced in Part I [24] where the corresponding analysis at the material-point level has also been developed. Here, we combine the constitutive relation with the equilibrium system and prove the existence of quasistatic evolutions and convergence of time-discretizations. Secondly, we investigate the linearization limit for small deformations via a rigorous evolution Γ-convergence argument.