A numerical framework for continuum damage - discontinuum transition

Abstract

A framework is derived for the proper and consistent description of a discontinuity (a crack) as the result of a damaging process in a continuous medium. The damaging process in the continuous medium is described using a gradient-enhanced damage theory, so that well-posedness of the boundary-value problem is maintained until the damage process is completed and a discontinuity arises. At that moment the partition-of-unity property of finite element shape functions is exploited to partition the displacement field into two continuous fields, separated via a Heaviside function. It is demonstrated that the additional boundary conditions that arise in a gradient-enhanced damage theory, can be accounted for in a natural and transparent manner.