Modelling of hydrated soft tissues using hybrid-Trefftz finite elements

My PhD Thesis is complete. This article provides the abstract and the link to download the PDF file of the Thesis. It is the so called provisory version (documento provisório), since the jury might have some suggestions for improvements before the actual defence.


The hybrid-Trefftz formulation of the finite element method is applied to the transient, physically and geometrically linear analysis of incompressible saturated porous media. Two finite element models are developed, namely the stress model and the displacement model.

The stress (displacement) model develops from the direct approximation of the stress and pressure fields (displacements in each phase of the mixture) in the domain of the element and of the solid and fluid displacements (forces and pressure) on its boundary. The domain approximation bases are extracted from the formal solution of the system of differential equations that govern the behaviour of incompressible saturated porous media.

The finite element equations are derived directly from the local conditions on equilibrium, compatibility, elasticity and incompressibility. The structure of the resulting algebraic solving systems is symmetric, except for the velocity induced terms, sparse, naturally p-adaptive and well-suited to parallel processing. The associated variational statements are recovered and sufficient conditions for the existence and uniqueness of the finite element solutions are stated.

A comprehensive set of validation tests is presented. The benchmark tests used in the literature are solved in the frequency domain to assess the convergence characteristics of the alternative stress and displacement elements. They are implemented also in the time domain to assess the quality of the estimates they produce for the stress, pressure, displacement and velocity fields at every instant of the analysis.

Keywords: Trefftz elements, Incompressible saturated porous media, Spectral analysis, Time domain analysis.

Download: [PDF, 9.5 MB] (final version now)

Reference: Toma, M. (2007). Modelling of hydrated soft tissues using hybrid-Trefftz finite elements. Lisbon, Portugal [PhD thesis]: Technical University of Lisbon, Instituto Superior Técnico, 228 p.



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