Three Dimensional Finite Element Implementation For A Dynamic Solid Fluid Mixture At Finite Strain

Download or read book Three-dimensional Finite Element Implementation for a Dynamic Solid-fluid Mixture at Finite Strain written by Davoud Ebrahimi and published by . This book was released on 2007 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the mixture theory formulation of a fluid saturated porous solid subjected to dynamic large strain deformation, a 3D finite element implementation is presented. Under standard mixture theory assumptions, describing motion of the fluid phase relative to the solid phase and following solid phase motion, field equations in the u-p form are derived by applying balance of mass and balance of momentum of the continuum mixture. Solid and fluid volume fractions are used as evolving state parameters through the finite deformation analysis. A compressible neo-Hookean hyperelastic constitutive model with a Kelvin solid viscous enhancement for the solid phase is assumed, along with a generalized form of Darcy's law for the fluid phase. In turn, the governing nonlinear coupled partial differential equations are spatially discretized using a Bubnov-Galerkin method. An unconditionally stable finite differencing procedure is used for the time domain numerical integration. For efficient numerical solution of the 3D nonlinear time dependent coupled formulation which includes both geometric and material nonlinearities, a full consistent tangent matrix of the system of equations has been derived. A mixed hexahedral finite element, quadratic in solid displacement and linear in fluid pore pressure, and the associated consistent tangent matrix are implemented in a C++ finite element code, Tahoe. The implementation is verified with available 1D and 2D benchmark problems. New numerical solutions for 3D large strain dynamic behavior of saturated porous media will be presented. The computational efficiency of the implemented formulation in achieving quadratic convergence is illustrated by means of several numerical examples.