Finite element method evaluation of thermomechanical responses of fluid-saturated porous media under finite deformation.

摘要

The coupled thermomechanical responses of fully fluid-saturated porous continua are examined with particular emphasis on nonlinear phenomena resulting from finite deformation and nonlinear constitutive properties. A set of field equations governing the three-dimensional transient response of fluid-saturated porous continua are derived from a continuum thermodynamics mixture theory based on mass balance, momentum balance, and energy balance laws as well as the Clausius-Duhem inequality.; Numerical procedures for the two-dimensional response, employing updated Lagrangian formulations for the solid skeleton deformation and the weak formulations for fluid thermal transport equations, are implemented in a fully-implicit form. Temperature dependent mechanical properties along with finite deformation of the homogeneous thermo-viscoplastic solid matrix are assumed. A two-dimensional finite element model with a four node quadrilateral element is developed. An iterative scheme based on the full Newton-Raphson method is used for simultaneously solving the nonlinear equations. Perzyna's viscoplastic model is adopted in an incremental form for describing the viscoplastic behavior of geological materials. A material constitutive relationship between the Jaumann stress rate and the rate of deformation tensor is adopted to obtain the current stresses.; Several simple examples are investigated for model validation, constitutive model sensitivity evaluation and finite deformation response of the solid skeleton under thermomechanical loading. The responses obtained from the developed solution algorithm are compared with the results reported by other investigators. Good agreement for the benchmark cases is obtained. Subsequently, more complex finite deformation problems with applications to nuclear waste isolation are investigated. To simulate the heat source resulting from the radioactive nuclear waste, time-dependent temperature boundary conditions are used. The presented field applications illustrate the feasibility of the developed finite element model simulation in predicting the long term temperature, pore pressure, displacement and stress responses of the fluid-saturated porous media subjected to thermomechanical loading. The presented formulations and numerical procedures are also applicable to problems related to the structural response evaluations associated with various porous materials, including ceramics, composites and polymers.