This text is an examination of the nonlinear phenomena created when fractures develop in structural materials upon application of static, cyclic or dynamic external loads. Incorporated in the volume are the mathematical models aimed at the quantative prediction of ductile failure in strain-hardening metallic alloys, or quasi-brittle fracture in strain-softening materials such as rock, concrete and cementitious composites. By scrutinizing the microstructure (mesomechanics) involved, the text incorporates certain recommendations concerning new technologies and procedures required in the manufacture of high performance materials with enhanced resistance to crack propagation and superior mechanical properties.