Acoustoelastic pure-displacement elements based on Biot’s poromechanics theory

From the elastic energy contained in a displacement based porous material the general form of the stiffness and mass matrices are obtained. If both fields can be expanded with equal order polynomials the general form is further simplified and it is shown that the coupling stiffness reduces to the one arising to compute volume changes in an elastic medium. A plane beam and a four node tetrahedron are developed. To avoid spurious rotational modes appearance in the tetrahedron fluid a penalty formulation is used. The effect of the penalty factor in matrix conditioning is analysed. Elements dynamic behaviour is compared.

► Displacement based porous material matrices are developed from the energy.
► Equal expansion for fluid and porous displacements fields simplifies matrices shape.
► Matrices construction becomes a simple to follow recipe.
► 2-D beam and 3-D tetrahedron are developed and spurious modes appearance discussed.
► Effect of fluid rotational penalty factor in porous matrix conditioning is assessed.