Stress concentration in incompressible multicomponent materials

Stress concentration in nonlinear viscoelastic composites

“…In the hereditary theory of viscoelasticity, the mechanical properties of the medium are given by elastic constants, creep kernels, and relaxation kernel [5,6,10]. The problem of identifying the creep and relaxation kernels, establishing the connection between kernels and determining the parameters of kernel is one of the main problems of the theory of viscoelasticity [6,8,9]. In the case of a uniaxial stressed state, the heredity kernels and the parameters of the nuclei are determined directly from the results of approximating the direct measurements of deformations or stresses in the process of creep or relaxation by functions that define the kernel.…”

“…Function ( ) G t is relaxation function of nonlinear viscoelasticity or Lame third order constants tensor in pure elastic case. Using the technique described in the previous works [5,8] the solution can be written as the convolution type integral over B t  domain…”

“…Subsequently the reference configuration of the inclusion material may spontaneously jump at 0 t  and thereafter is smoothly changing in such a way that the new reference configuration is obtained by giving the old reference configuration a not known strain ( ) e t . We solve this problem by using an extension of method [5,8] to nonlinear viscoelastic deformation. By taking the Carson transforms we can reduce (6), (7), (12) to the corresponding elastic problem.…”

“…Equations (1) is quasi-linear because ( ) e t  is nonlinear in the deformation tensor ( ) t C , but the convolution operator is linear. While the general theory is precisely that given in [8], the component form of the tensor equations is here given in terms of the components of the compliance tensor. This choice is dictated by the fact that we are mainly interested in the creep behavior of composites [6,10].…”

Thermal-stress concentration near inclusions in viscoelastic random composites

“…It is usually assumed that the inclusions are imbedded in a linear defect-free continuum. As a result, three topics are important, namely macroscopic interacting cracks and multi-component inclusions [6], distributed microscopic damage [7,8] and third the nonlinear properties of the constituents [5,9,10]. The early analytical work regarding damage of composites used linear elastic fracture mechanics, making it less successful in applications than those applied to metals.…”