Theory Manual Version 3.4
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Subsection 3.1.2: Discretization Up Chapter 3: The Nonlinear FE Method Subsection 3.2.1: Linearization

3.2 Weak formulation for biphasic materials

A weak form of the statement conservation of linear momemtum for the quasi-static case is obtained by using Eqs.(2.5.1-2) and (2.5.1-4): where is the domain of interest defined on the solid matrix, is a virtual velocity of the solid and is a virtual pressure of the fluid [77]. is an elemental volume of . Using the divergence theorem, this expression may be rearranged as where is the virtual rate of deformation tensor, is the total traction on the surface , and is the component of the fluid flux normal to , with representing the unit outward normal to . represents an elemental area of . In this type of problem, essential boundary conditions are prescribed for and , and natural boundary conditions are prescribed for and . In the expression of Eq.(3.2-2), represents the virtual work.
Subsection 3.1.2: Discretization Up Chapter 3: The Nonlinear FE Method Subsection 3.2.1: Linearization