  Strain localization is an instability phenomenon occurring in deformable
solid materials which undergo dissipative deformation mechanisms. Such
instability is characterized by the localization of the displacement or
velocity fields in a zone of finite thickness and is generally associated with
the failure of materials. In several fields of material engineering and natural
sciences, estimating the thickness of localized deformation is required to make
accurate predictions of the evolution of the physical properties within
localized strain regions and of the material strength. In this context,
scientists and engineers often rely on numerical modeling techniques to study
strain localization in solid materials. However, classical continuum theory for
elasto-plastic materials fails at estimating strain localization thicknesses
due to the lack of an internal length in the model constitutive laws. In this
study, we investigate at which conditions multiphysics coupling enables to
regularize the problem of strain localization using rate-dependent plasticity.
We show that coupling the constitutive laws for deformation to a single generic
diffusion-reaction equation representing a dissipative state variable can be
sufficient to regularize the ill-posed problem under some conditions on the
softening parameters in the plastic potential. We demonstrate in these cases
how rate-dependent plasticity and multiphysics coupling can lead to material
instabilities depicting one or several internal length scales controlled by the
physical parameters resulting in the formation of regular or erratic patterns.
As we consider a general form of the equations, the results presented in this
study can be applied to a large panel of examples in the material engineering
and geosciences communities.
