On the analytical derivation of consistent density-corrected tangent operators for simulation of compressible porous materials

In this work, we develop a strategy to derive the tangent modulus A that takes into account the corrections imposed by the evolution of the relative density in the analysis of density-dependent materials, compressible materials. Special attention is given to the analytical derivation of consistent density-corrected tangent operators, which means that explicit formulas are derived without any approximations. The whole procedure depends strongly on the choice of the stress–strain measure and on the employed algorithms. Here, we present a Lagrangian finite deformation version. Numerical examples are presented in order to attest the proposed methodology.