Theory Manual Version 3.4
$\newcommand{\lyxlock}{}$
Section 3.4: Weak Formulation for Multiphasic Materials Up Section 3.4: Weak Formulation for Multiphasic Materials Subsection 3.4.2: Linearization along

3.4.1 Linearization along

The linearization of the first term in along yields where is the spatial elasticity tensor of the mixture, and is the spatial elasticity tensor of the solid matrix, The linearization of the second term is where with representing the spatial tangents, with respect to the strain, of the effective permeability and solute diffusivity, respectively. These fourth-order tensors exhibit minor symmetries but not major symmetry, as described recently [7]. Since is given by substituting (2.6.2-3) into (3.3-8), the evaluation of is rather involved and it can be shown that where and The next term in linearizes to where we used a backward difference scheme to approximate the time derivative, and represents the time increment relative to the previous time point. The next term is given by where where Using a backward difference scheme for the time derivative, the last term is
Section 3.4: Weak Formulation for Multiphasic Materials Up Section 3.4: Weak Formulation for Multiphasic Materials Subsection 3.4.2: Linearization along