Summary
A system of boundary integral equations is derived for Biot's full equations of dynamic poroelasticity in the Laplace transformed domain starting from first principles. These equations give the displacement vector in both the solid and fluid phases in terms of surface tractions and displacements, as well as in terms of any non-zero initial conditions and body forces. The fundamental solutions for instantaneous point body forces acting in each of the two phases are found in closed form by exploiting the use of four scalar potentials that reduce the problem to two decoupled second-order systems in the Laplace transformed domain. Finally, a parallel is drawn between dynamic poroelasticity and dynamic thermoelasticity by discovering analogies between the variables and material constants of each case.
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Manolis, G.D., Beskos, D.E. Integral formulation and fundamental solutions of dynamic poroelasticity and thermoelasticity. Acta Mechanica 76, 89–104 (1989). https://doi.org/10.1007/BF01175798
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DOI: https://doi.org/10.1007/BF01175798