This research will develop algorithms which estimate and control the error in numerical approximations of initial/boundary-value problems in nonlinear path-dependent continua. The research will focus on the development and implementation of adaptive finite- element methods for the analysis of strain localization and failure in viscoplastic solids. Specific applications will be implemented for the case of porous ductile solids under conditions which include the generation of new surfaces due to local material failure by void coalescence. The development of such adaptive finite-element models could have a major impact on the numerical simulation of many phenomena which include progressive failure through localization of plastic flow such as the ballistic impact, the perforation and penetration of solids, crashworthiness, metal forming and manufacturing processes.
