Lower bound to the plastic collapse load of structural elements made of nanocomposites

Nano composite materials, for their better performance with respect to traditional composites, are emerging materials, widely employed in structural applications of industrial fields such as aeronautical and automotive. There is a growing literature concerning these materials, however, because of their constitutive complexity, the evaluation of the bearing capacity of structural elements made up with them is mainly pursued experimentally. In fact, the difficulties both in characterizing all the mechanical parameters of the material and in correctly describing its evolution up to collapse or within the post-elastic regime, makes problematic the application of well known numerical procedures, such those based on step by step analyses. In these cases, it may be more effective to follow a limit analysis approach that, even if in approximate way, can directly provide the bearing capacity of the addressed structural elements. On the other hand, it is worth noting that nanomaterials are inherently nonlocal, so a correct description of their constitutive behaviour can be obtained only by means of nonlocal models. The latters, making use of internal material parameters, can take into account, at macro-level, phenomena arising at micro- or nano-level. On the base of the above considerations, the paper proposes a limit analysis numerical procedure, known, in its original formulation, as elastic compensation method, but here rephrased in a nonlocal elastic context to evaluate the lower bound to the collapse load multiplier of structural elements made up of nanocomposites. The procedure, already utilized by the authors in different (local) contexts [1], makes use of sequences of elastic analyses in order to mimic the behaviour of the structure at collapse. In the nonlocal framework, here considered, the elastic analyses are nonlocal and performed by means of a nonlocal finite element code, implemented by the authors in [2]. A nonlocal elastic perfectly plastic constitutive model is assumed with the further hypothesis that the nonlocal behaviour pertains only to the elastic phase. The nonlocal elastic description is given by an enhanced version of the Eringen model, namely the strain-difference-based integral model [3]. The proposed formulation is tested by means of a case study. The obtained results are discussed with the aim to highlight advantages and drawbacks of the entire numerical approach. References [1] 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. [2] 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. [3] C. Polizzotto, P. Fuschi, A.A. Pisano. A strain-difference-based nonlocal elasticity model. Int. J. Solids Struct. (2004);41:2383-2401.