Limit analysis of structures made of nonlocal materials

A plastic limit analysis procedure is proposed for structural elements made of an elastic-plastic associative nonlocal material in the hypothesis of a nonlocal behavior restricted only to the elastic phase. The pertinent elastic-plastic nonlocal constitutive model is the one first proposed by Eringen [1] in strain space plasticity for Von Mises materials with associated flow rule and in which the (averaged) nonlocal quantity is indeed only the elastic strain. Such model of nonlocal plasticity was later used in [2] to tackle shakedown problems of cracked bodies and is hereafter assumed. Moreover, the nonlocal elasticity here considered refers to an even more recent formulation, namely to a strain-difference-based integral model utilized by the present authors to generate a nonlocal version of the finite element method (NL-FEM) [3]. The idea here promoted is to apply the NL-FEM within a numerical procedure for limit analysis, already employed by the authors in different contexts [4]. Such limit analysis is, in facts, carried on numerically by the simultaneous use of the linear matching method (LMM) and the elastic compensation method (ECM) both based on sequences of elastic analyses able to mimic the behavior of the structure at an impending plastic collapse state. The NL-FEM can then be used in a straightforward manner performing sequences of nonlocal FE elastic analyses. The goal is challenging but the key idea is simple and is motivated by the will to apply limit analysis in the context of those structures made by advanced materials characterized by a mechanical behavior in which size effects or phenomena arising at a micro- and/or a nano-scale affect the macroscopic mechanical behavior. A context in which a nonlocal continuum approach is, among others, an available and effective tool. A simple numerical application is presented and critically discussed highlighting advantages, novelties, drawbacks as well as possible future fields of application of the proposed formulation. References [1] A.C. Eringen. On nonlocal plasticity. Int. Journal of Engineering Science 19, 1461-1474, 1981. [2] C. Polizzotto, G. Borino and P. Fuschi. Shakedown of cracked bodies with nonlocal elasticity. Proceeding of ECCOMAS2000. Barcelona 11-14 September 2000. [3] P. Fuschi, A.A. Pisano and D. De Domenico. Plane stress problems in nonlocal elasticity: finite element solutions with a strain-difference-based formulation, Journal of Mathematical Analysis and Applications 431, 714-736, 2015. [4] A.A. Pisano, P. Fuschi, D. De Domenico. Limit analysis on RC-structures by a multi-yield-criteria numerical approach, In: Direct Methods for Limit and Shakedown Analysis of Structures: advanced computational algorithms and material modeling 199-219. Springer Int. Publishing Switzerland. 2015. Powered by