Stress-strain state in the matrix of stochastically reinforced composites

Thermal-stress concentration near inclusions in viscoelastic random composites

“…It is shown, in the framework of the effective-field hypothesis [6] that, from a solution of the classical linear elastic problem with zero stress-free strains for the composite, the relations for the effective nonlinear, stored energy and average viscoelastic strains inside the components can be found. For a single inclusion the micro-mechanical approach is based on the Green-function technique [5], as well as on the interfacial Hill operators [17,26]. As a generalization of the results [10], we consider here a certain representative meso-domain B with a characteristic function f B (x, α) containing a set X I of inclusions v I with characteristic functions f I (x, α), (I = 1, 2, 3, .…”

“…According to the proposed calculation scheme we find the solution of this equation after integrating with probability density functions of the type (17). Herewith, the nonlinear part on the right-hand side of (33) is expressed through macro-deformations e 0 (1) of the representative volume of composite that are already known in the first approximation…”

“…Therefore, developing algorithms for designing new multi-constituent composites with advanced properties requires an in-depth study of the stress in microstructural elements and the calculation of the overall thermo-elastic parameters within the scope of nonlinear continuum theory. The results given in [1,3,17] involve effective thermo-elastic modules of nonlinear compressible and incompressible random composites containing two components: a matrix and a set of inclusions. The problem addressed in [10] concerns the microstructure stress determination in nonlinear incompressible multi-constituent composites.…”

“…Following the technique of [17], we have the following expressions for the tensor coefficients of the stress concentration in the elements of multi-component viscoelastic material…”

Mixed Volume and Boundary Integral Equation Method with Elliptical Inclusions and a Circular/Elliptical Void

“…A number of analytical techniques are available for solving stress analysis of inclusion problems when the geometry of the inclusions is simple (i.e., cylindrical, spherical, or ellipsoidal) and when they are well separated [2][3][4]. However, these approaches cannot be applied to more general problems where the inclusions are of arbitrary shape and their concentration is high.…”