Abstract
This paper reports on recent developments in the field of direct methods, in particular shakedown analysis (SA) from theoretical and numerical points of view. Emphasis is placed on problems connected with the failure of fibre-reinforced periodic composites under variable loads where special attention is paid to the problem of interface debonding between fibre and matrix materials. The approach is based on a local SA in a representative volume element of the composite and the use of averaging techniques to study the influence of each component (matrix, fibre and interface) on the macroscopic response of such composite. For numerical applications, the interior-point difference-of-convex-functions algorithm (IPDCA) is proposed as an efficient method for solving large-scale problems.
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