Material rate dependence and mesh-sensitivity in localization problems (Q1089170)

The role of material rate dependence in setting the character of governing equations is illustrated in the context of a simple one- dimensional problem. For rate dependent solids, the incremental equilibrium equations for quasi-static problems remain elliptic and wave speeds for dynamic problems remain real, even in the presence of strain- softening. The pathological mesh sensitivity associated with numerical solutions of localization problems for rate-independent solids is eliminated. In effect, material rate dependence implicitly introduces a length scale into the governing equations, although the constitutive does not contain a parameter with the dimensions of length. Numerical results are presented that illustrate the localization behavior of slightly rate- dependent solids under both quasi-static and dynamic loading conditions.