Finite cover method for linear and non-linear analyses of heterogeneous solids

We introduce the finite cover method (FCM) as a generalization of the finite element method (FEM) and extend it to analyse the linear and non-linear mechanical behaviour of heterogeneous solids and structures. The name 'FCM' is actually an alias for the manifold method (MM) and the basic idea of the method has already been established for linear analyses of structures with homogeneous materials. After reviewing the concept of physical and mathematical covers for approximating functions in the FCM, we present the formulation for the static equilibrium state of a structure with arbitrary physical boundaries including material interfaces. The problem essentially involves the discontinuities in strains, and possibly has the discontinuities in displacement caused by interfacial debonding or rupture of material interfaces. We simulate such non-linear mechanical behaviour after presenting simple numerical examples that demonstrate the equivalence between the approximation capabilities of the FCM and those of the FEM.