Finite cover method with multi‐cover layers for the analysis of evolving discontinuities in heterogeneous media

We extend the finite cover method (FCM), which is known as a generalized finite element method, to crack simulations for quasi‐brittle heterogeneous solids by using only a regular structured mathematical mesh. The proposed version of the FCM is powered by a method of modeling arbitrary numbers of physical cover layers. This ‘multi‐cover layer modeling’ relies crucially on not only the introduction of multiple layers of physical covers, each of which is associated with a single physical domain, but also the identification of the values of level‐set functions for discontinuities, which can be evaluated from their digital image information. Several numerical examples are presented to demonstrate the successful mesh‐based mesh‐free analyses of heterogeneous solids with arbitrarily evolving cracks and interfacial debonding thanks to the introduction of multiple cover layers.