Hybrid-Trefftz stress and displacement elements for transient analysis of incompressible saturated porous media

The stress and displacement models of the hybrid-Trefftz finite element formulation are developed for the analysis of incompressible saturated porous media. They are used to model the frequency and time domain response of soft tissue specimens under two-dimensional and axisymmetric testing conditions. The alternative stress and displacement models are complementary in terms of the supporting approximation criteria. The stress (displacement) model is derived from the direct approximation of the stress and pressure fields (the displacements in the solid and fluid phases) in the domain of the element. Two sets of numerical tests are performed; namely the tests implemented in frequency domain and those in time domain, for both two-dimensional and axisymmetric problems. The tests on the frequency domain are designed to assess the basic aspects of the performance of the element. The tests on the time domain are obtained using a non-periodic spectral decomposition time integration procedure.