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a b s t r a c tThe main goal of the present paper is to present a mathematical framework for modelling multi-phase non-saturated soil consolidation with pollutant transport based on stress state configurations with special emphasis in its versatility. Non-linear saturation and permeability dependence on suction for both water and pollutant transport is regarded. Furthermore, through the introduction of a suction saturation surface instead of simple suction saturation curves, the implementation of the saturation-suction coupling effect is considerably simplified. The achieved differential equation system is discretized within a Galerkin approach along with the finite element method implementation. A widespread set of practical situations is encompassed by simply setting certain coefficients of the discrete system of equation according to concrete problem conditions. When the model is coped with certain selected fringe conditions, the approach adaptability feature came up showing a robust performance.

SUMMARYThe aim of this paper is to implement and to apply a mathematical model to analyse solid mechanics problems involving non-linear hypoelastic isotropic or orthotropic materials using the finite element method. An updated Lagrangian description with a corotated Kirchhoff stress tensor was taken on. This description leads to a non-symmetric stiffness matrix. An alternative, using a symmetric constitutive matrix is addressed and some of its main mathematical and numerical characteristics are highlighted. Numerical examples for simple systems were solved and good results were obtained using a symmetric constitutive matrix, although average relative errors increase with the influence of shear stress effects. Important saving in processing time and computer memory may be obtained if a symmetric constitutive matrix is used.

The main goal of the present paper is to present a mathematical framework for modelling tumour growth based on stress state decomposition technique (SSDT). This is a straightforward extension of the model for multi-phase nonsaturated soil consolidation with pollutant transport presented by the authors and may be regarded as an alternative to classical frameworks based on TCAT theory. In this preliminary work, the Representative Volume Element (RVE) for tumour is proposed along with its comparison with the corresponding one for soils modelling developed formerly by the authors. Equations standing for tumour phase are flawlessly brought into correspondence with those of gaseous phase in the soil problem showing that a similar task may be carried out for the remainders phases taking part in both RVEs. Furthermore, stresses induced by nonlinear saturation and permeability dependence on suction for soil interstitial fluids transport finds its counterpart on the contact between the cancer cell membrane and interstitial fluids rendering a higher primary variables coupling degree than what was attained in TCAT theory. From these preliminaries assessments, it may be put forward that likewise the stress state decomposition procedure stands for an alternative for modelling multi-phase nonsaturated soil consolidation with pollutant transport; it does for modelling cancer as well.