The purpose of the research is to investigate the complete failure of structures composed of materials which fail by progressive distributed damage and cracking as found in materials such as concrete, wood, and rocks. The proposed theory is an extension of the nonlocal continuum approach in such a way that the nonlocal concept is applied only to those variables which cause strain-softening, so that the response is local when the damage does not grow. The proposed research includes verification of the proposed theory by numerical analysis as well as experimental results.