A Mixed Symmetric BEM For Multi-domain,Multi-material And Crack Interface Problems InElastostatics

We discuss a variational approach that leads to a symmetric boundary element formulation suitable for multi-material and crack interface problems in heterogeneous domains arranged as assemblies of homogeneous subdomains. The variational principle is based on a Lagrangian functional comprising the system’s potential energy augmented by the side imposition of the classical integral representation of the interior solution within each homogeneous subdomain. Any applied boundary tractions and all interface traction continuity conditions are automatically satisfied by the variational principle. Following a single condensation of the subdomain boundary tractions and the Lagrange multipliers, the boundary and interface displacements are left as the only unknowns. Upon discretization, there results a block-sparse system, with each block representing a single homogeneous subdomain (or part thereof). We validate the variational approach via numerical experiments entailing cracks at single and bi-material interfaces.