A Multiscale Model for Coupled Heat Conduction and Deformations of Viscoelastic Composites
This study introduces a multiscale model for analyzing nonlinear thermo-viscoelastic responses of particulate composites. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermal and mechanical properties and time-dependent response of the composites. The particle and matrix constituents are made of isotropic homogeneous viscoelastic bodies undergoing small deformation gradients. Perfect bonds are assumed along the sub-cell???s interfaces. The coupling between the thermal and mechanical response is attributed to the dissipation of energy due to the viscoelastic deformation and temperature dependent material parameters in the viscoelastic constitutive model. The micromechanical relations are formulated in terms of incremental average field quantities, i.e., stress, strain, heat flux and temperature gradient, in the sub-cells. The effective mechanical properties and coefficient of thermal expansion are derived by satisfying displacement- and traction continuities at the interfaces during the thermo-viscoelastic deformations. The effective thermal conductivity is formulated by imposing heat flux- and temperature continuities at the subcells??? interfaces. The expression of the effective specific heat at a constant stress is also established. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic materials is developed. The algorithm is then incorporated within each sub-cell of the micromechanical model together with the macroscopic energy equation to determine the effective coupled thermoviscoelastic response of the particulate composite. The numerical formulation is implemented within the ABAQUS, general purpose displacement based FE software, allowing for analyzing coupled heat conduction and deformations of composite structures. Experimental data on the effective thermal properties and time dependent responses of particulate composites available in the literature are used to verify the micromechanical model formulation. The multiscale model capability is also examined by comparing the field variables, i.e., temperature, displacement, stresses and strains, obtained from heterogeneous and homogeneous composite structures, during the transient heat conduction and deformations. Examples of coupled thermoviscoelastic analyses of particulate composites and functionally graded structures are also presented. The present micromechanical modeling approach is found to be computationally efficient and shows good agreement with experiments in predicting the effective thermo-mechanical response of particulate composites and functionally graded materials. Our analyses forecast a better design for creep resistant and less dissipative structures using particulate composites and functionally graded materials.