Computational schemes in three-dimensional stability theory (the piecewise-homogeneous model of a medium) for composites with cracks between layers

Abstract

At the present time there exists a large amount of studies devoted to the stability problem of composite materials and structural elements. Most often it is assumed in them that the structural element of the material are rigidly attached, i.e., the continuity conditions of stresses and displacements are satisfied at the boundary between structural elements. In real composite materials the usual concept of ideal contact between structural elements does not always correspond to reality. Different cases of reduced adhesion (interphase contact) between components of the composite are possible due to the manufacturing technology or the operating conditions. This can include cleavage, cracks, non-adhesion, slippage zones, and other imperfections. In this case the assumption of discontinuity of the stress and displacement vectors at the boundary between structural elements is valid. In investigating the stability of a stratified composite with cracks at the separation boundary between media one often uses various approximate theories (such as continuum theories) and applied computational schemes (rods, shells, and others). Their analysis, however, is not the object of the present study. Most accurate results can be obtained within the three-dimensional linearized stability theory of deformable bodies (TLSTDB) [i]. Application of the model of a piecewise-homogeneous medium and of the fundamental relations of TLSTDB makes it possible to eliminate the restrictions imposed on using the applied theories and approximate computational schemes, along with the inaccuracies they involve. Thus, of the presently known approaches to the study of stability of composites with cracks between layers, the most accurate is the model of a piecewise-homogeneous medium along with the fundamental TLSTDB relations. The present study is devoted to analyzing various computational schemes for stability loss of stratified composite materials with cracks at the separation boundary of media within the exact statement mentioned.