On the Computation of a Generalised Dynamic J-Integral and its Application to the Durability of Steel Structures

Abstract

A theoretical description and a computational method are presented to calculate the J-integral in the context of the finite element method. In the derivation, we use the theory of configurational forces where the fully three-dimensional case and large deformations for non-linear elastic materials under dynamic loading are taken into account. Analogue to the local balance of momentum, the so-called Eshelby stress holds a configurational force balance, where configurational forces correspond to the volume forces in the physical space. A discretised finite element description is obtained by the weak form of the configurational force balance. Thus, the configurational forces acting on the finite element nodes may be computed as the physical boundary value problem is solved. For the static case and small deformations, the configurational force corresponds to the well known J-integral in fracture mechanics, though not restricted to the crack-mode I state. As a practical example, we show how the J-integral, combined with Paris’ equation, can be used to predict the ultimate life time of a steel structure containing components with cracks.