On the ultimate strength of heterogeneous slender structures based on multi-scale stress decomposition

This paper presents an algorithm based on asymptotic methods for computing the effective ultimate and high cyclic fatigue strength of heterogeneous periodic plates, shells, and textiles. The rigorous analysis and convergence proof of this asymptotic method builds upon a series of our previous papers. The method allows to decompose the local stresses as products of periodic stress-concentrations, given as functions of unit cells or graphs/lattices in them, and the macroscopic strain components. In addition, this paper establishes bounds for the applicability of the method and presents several examples to demonstrate the qualitative advantages of this approach, e.g. for the standard shear and compression tests for plates. The main objective of this paper is to substantially reduce the problem dimension and complexity, thereby enabling more efficient computations.