Castigliano’s Second Theorem for Deformation Determination of a Cracked Body

Abstract

In this paper, a continuum theory capable of describing the deformation of a cracked body based on Castigliano’s second theorem is presented. The additional deformation due to the crack presence is described by the concept of stress intensity factor (SIF) of linear elastic fracture mechanics. Both the crack opening distance and the body deformation can be easily computed for any arbitrary loading on any boundary. As a demonstration, the proposed theory is applied to cases of edge-cracked infinite plane and edge-cracked beam, and the results show high accuracy when compared to those predicted by the numerical finite-element method.