Mixed and hybrid stress elements for biphasic media

The hybrid–mixed stress element for transient analysis of compressible and incompressible biphasic media is based on the approximation of the stress and pressure fields in the domain of the element and of the displacements in the solid and fluid phases independently in the domain and on the boundary. The hybrid and hybrid-Trefftz variants are derived constraining the domain approximation to satisfy locally the equilibrium condition and all domain conditions, respectively. As it is typical of stress elements, in these alternative formulations the inter-element and boundary continuity conditions are enforced on the surface forces acting on the solid and fluid phases of the medium. The hybrid-Trefftz stress element is applied to the transient analysis of two-dimensional and axisymmetric biphasic media. The performance of the element is illustrated in terms of sensitivity to distortion and to wavelength, full incompressibility and spectral and transient modelling of both bounded and unbounded domains.