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In most of standard Finite Element (FE) codes it is not easy to calculatedispersion relations from periodic materials. Here we propose a new strategy tocalculate such dispersion relations with available FE codes using user elementsubroutines. Typically, the Bloch boundary conditions are applied to the globalassembled matrices of the structure through a transformation matrix orrow-and-column operations. Such a process is difficult to implement in standardFE codes since the user does not have access to the global matrices. In thiswork, we apply those Bloch boundary conditions directly at the elemental level.The proposed strategy can be easily implemented in any FE code. This strategycan be used either in real or complex algebra solvers. It is general enough topermit any spatial dimension and physical phenomena involving periodicstructures. A detailed process of calculation and assembly of the elementalmatrices is shown. We verify our method with available analytical solutions andexternal numerical results, using different material models and unit cellgeometries

A general-purpose element-based approach to compute dispersion relations in periodic materials with existing finite element codes