A four-component mixture theory applied to cartilaginous tissues : numerical modelling and experiments

Input Regularization for Integer Optimal Control in BV with Applications to Control of Poroelastic and Poroviscoelastic Systems

“…Let Ω ⊂ ℝ 3 be the open, bounded domain occupied by the fluid-solid mixture, with Lipschitz boundary 𝜕Ω. Motivated by applications in biomechanics (like tissue perfusion [3,15,24,36,38,47]), we work under the assumptions of full saturation, negligible inertia, small deformations and incompressible mixture components (in the sense that the solid and fluid phases can't undergo volume changes at the microscale). Due to the complex composition of biological tissue, which exhibit both elastic and viscoelastic behaviors, we consider both poroelastic and poroviscoelastic systems, where the effective stress tensor is of Kelvin-Voigt type.…”

A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics

“…Numerical simulation of Darcy's flow in a porous medium coupled with quasi-static mechanical deformation is based on the coupled poromechanics theory [1,2]. The focus of this work is the iterative solution of the linear algebraic system arising from the discretization of the governing system of partial differential equations (PDEs) by the well-established three-field (displacement/velocity/pressure) formulation, e.g., [3][4][5][6][7][8]. In particular, we consider the block linear system Ax = F obtained by combining a mixed finite element discretization in space with implicit integration in time using the θ-method [9]:…”