Mesh Dependence and Nonlocal Regularization of One-Dimensional Strain Softening Plasticity

Finite-element analysis of strain localization based on classical theory of continuum mechanics suffers from pathological mesh dependence when strain softening models are used. For quasistatic problems, the mesh dependence is demonstrated through an analysis of the tangent stiffness matrix of a one-dimensional problem. To regularize the mesh dependence, a nonlocal strain softening model is proposed, which is based on the nonlocal plasticity theory and the representative line element. Both analytical and numerical solutions of strain localization with the proposed model are developed and compared with each other. The model is also applied in the numerical simulation of a direct tensile test of a concrete specimen in the existing literature, and reasonable agreement is achieved between numerical solutions and the experimental response.