The Failure Theory for Isotropic Materials: Proof and Completion

Abstract

This work represents the completion of the many developments in recent years on failure theory for homogeneous and isotropic materials. Presented here is the resulting failure formalism in final and technically complete form. Significant further results are also given for the verification of the failure formalism. The scope of this paper goes from the history of misguided failure theory investigations right up to the present final tested forms ready for applications. For every predicted failure level in terms of the stresses, there is an accompanying ductility level. This ranges from brittle failure up to fully ductile failure. The entire theory is calibrated by only two specified parameters (failure properties). Nothing else is needed. The seemingly interminable, actually centuries long search for the missing theory of failure has finally been brought to a resolute and successful conclusion.