A self-adjoint variational principle for anisotropic viscoelastic Biot’s equations

A variational principle for anisotropic viscoelastic Biot’s equations of motion is presented. It is based upon an extended Hamilton’s principle, also valid for dissipative systems. Using this principle, a functional analogous to the Lagrangian is defined, starting from Biot’s variational formulation based on frame and fluid displacements. Then, a mixed displacement–pressure formulation is presented, which reduces the number of variables of response from six to four. The corresponding functional analogous to the Lagrangian is derived making full use of variational calculus. The derived functionals are self-adjoint and stationary for true motion.