Failure Mechanics—Part I: The Coordination Between Elasticity Theory and Failure Theory for all Isotropic Materials

Abstract

Failure mechanics is comprised of the failure theory for homogeneous and isotropic materials along with all of its implications and applications. The present failure theory is found to have an intimate connection with elasticity behavior even though plasticity may also transpire. This becomes apparent and useful when the classical theory of elasticity is renormalized to give a simpler and more transparent (but still exact) formalism. The connection or coordination between elasticity and failure then explicitly occurs through the use of the renormalized Poisson's ratio to characterize the ductility of failure. With this unification of failure theory and elasticity theory, failure mechanics can be extended to explain other anomalous aspects of mechanical behavior and prepare it for applications.