UC Berkeley

In this study an analytical and numerical modeling of the interaction between the process of diffusion and the mechanics of a solid are developed. It is then implemented on a fiber composite material, and several cases are simulated and analyzed. Starting with the a free energy as a function of the deformation and concentration, &Psi(F,C), a constitutive model is derived for the strain energy function &Psi_m(F), the coupled term of the free energy, &Psi_md(F,C), and the diffusion part of the free energy, &Psi_d(C). With these terms we define the stress, the coupling terms, and the diffusion flux respectively. These are then used in the balance of mass, the balance of linear momentum and the continuity equation. The equations are discretized using a finite difference scheme for the time variable, and a nonlinear finite element method for the spacial variables. The coupling is implemented using a staggering methodology. The staggering scheme allows for easy implementation and provides a convenient framework. Several phenomena are modeled, for example, strain-dependent diffusivity, concentration based saturation, diffuso-elasticity and nonuniform diffusion induced swelling. The simulations involve various parametric studies including using different elastic strain energy functions, such as Kirchhoff Saint Venant. Moreover, the simulations are conducted for both isotropic and orthotropic materials where we explore such effects as free swelling, and combined mechanical loading and diffusion boundary conditions.