Poro_Thermoelastic Duality and FE-based strategies for the analysis of biological tissues

Many analytical and numerical approaches have been proposed in order to solve poroelastic problems describing the behavior of biological tissues. The main difficulty associated to numerical strategies concerns the solution of the coupled poroelastic equations for determining the solid response in terms of deformation and filtration. The proposal of this work is to find a strategy to numerically solve poroelastic problems employing the Finite Element Method (FEM). In particular, the strategy presented is based on the well known similarity between thermoelasticity and poroelasticity theories. This analogy allows to solve transient poroelastic problems as corresponding thermoelastic ones, interpreting the temperature as a pressure and thermal gradients as velocities. With this aim, the relationship between thermoelasticity and poroelasticity is formulated in terms of dimensionless parameters to ensure numerical stability, because the elasticity moduli, filtration coefficients and porosity have essentially different orders of magnitude. Thus, the dimensionless equations obtained are implemented in numerical FEM-based computations. Such transferring to equivalent thermoelastic problems enables to apply the FEM package ANSYS® 11, which provides opportunities to solve coupled thermoelastic problems in transient non linear settings. Two numerical examples are finally presented. The first one is concerning a very important problem of drug delivery in solid tumors. The second example is, instead, related to the investigation of the role played by trigonal-like microstructure in osteons in bone adaptive, growth and remodeling processes.