Evaluation of local fields and effective behavior of viscoelastic heterogeneous materials

Abstract

The dissertation is concerned with the study of the mechanical time-dependent behavior of viscoelastic composite materials and structures. The analysis of such materials should not only take into account their complex structure, but also the time-varying properties of one or more constituents. The first part of the dissertation is concerned with the calculation of local time-varying fields in the viscoelastic fiber-reinforced composites and porous media. A two-dimensional model that represents a section perpendicular to the axes of the fibers is employed. The analysis adopts the correspondence principle based on the Laplace transform, and the problem is treated with the use of a direct boundary integral approach. The unknown boundary parameters are approximated by the truncated Fourier series. The procedures of the analytical (for the case of porous viscoelastic media) and numerical (for the case of fiber-reinforced composites) inversion of the Laplace transform are used to obtain time-varying fields anywhere in the matrix or inside the inclusions. The developed approach possesses several advantages in regard to computational efficiency and accuracy if compared with conventional methods based on the use of collocation and discretization techniques. The second part of the dissertation is concerned with the evaluation of the effective transverse properties of the viscoelastic fiber-reinforced composites. The developed approach relies on the knowledge of local stress fields and adopts the equivalent inhomogeneity technique modified for the case of viscoelastic composite's matrix. The solution is obtained in the Laplace domain, and the Laplace inversion is required to arrive at the time-varying effective properties. The developed approach directly takes into account the interactions between the inhomogeneities. The final part of the dissertation is dealing with the problem of thermal stress evolution in viscoelastic composite structures. These stresses are due to mismatch between the coefficients of thermal expansion of the composite's constituents. The proposed approach employs the Volterra correspondence principle and relies on the ability to obtain the analytical solution for the corresponding elastic problem. The approach adopts the discrete (matrix) representation of Volterra type operators. Particular attention is devoted to the analysis of thermal stress evolution in viscoelastic asphalt binders at low temperatures.