One-Dimensional Softening With Localization

The relationship between material softening and structural softening is investigated through the use of a model problem in one dimension. If the size of the softening zone is large the structural softening response is stable under displacement-prescribed loading. For a small size, the softening response is unstable and the loading regime is sensitive to imperfections in stiffness. A nonlocal constitutive equation in which the limit stress is a function of strain and strain gradient is introduced to provide an approach for simulating softening with localization. Implications for the numerical modeling of softening phenomena are given.