Abstract
In this paper, the superelasticity effects of architected shape memory alloys (SMAs) are focused on by using a multiscale approach. Firstly, a parametric analysis at the cellular level with a series of representative volume elements (RVEs) is carried out to predict the relations between the void fraction, the total stiffness, the hysteresis effect and the mass of the SMAs. The superelasticity effects of the architected SMAs are modeled by the thermomechanical constitutive model proposed by Chemisky et al. 2011. Secondly, the structural responses of the architected SMAs are studied by the multilevel finite element method (FE), which uses the effective constitutive behavior of the RVE to represent the behavior of the macroscopic structure. This approach can truly couple the responses of both the RVE level and structural level by the real-time information interactions between two levels. Through a three point bending test, it is observed that the structure inherits the strong nonlinear responses—both the hysteresis effect and the superelasticity—of the architected SMAs at the cellular level. Furthermore, the influence of the void fraction at the RVE level to the materials’ structural responses can be more specifically and directly described, instead of using an RVE to predict at the microscopic level. Thus, this work could be referred to for optimizing the stiffness, the hysteresis effect and the mass of architected SMA structures and extended for possible advanced applications.
Highlights
Cellular materials are widely used for their high strength-to-weight ratio and high energy absorption performance (Gibson and Ashby [1]; Ashby et al [2])
To specify the microscopic structure more clearly, we introduce RVEkl to denote an representative volume elements (RVEs) corresponding to the integration point l of the macroscopic element k
It is observed that the averaged stiffness and the hysteresis effect of the RVE with a higher void fraction are lower than those of the RVE with a lower void fraction, which is consistent with the response at the macroscopic level
Summary
Cellular materials are widely used for their high strength-to-weight ratio and high energy absorption performance (Gibson and Ashby [1]; Ashby et al [2]). As one of the most popular and effective multiscale methods, the multilevel finite element method (FE2 , see Feyel [33]) to describe the response of high nonlinear structures using generalized continua shows good performance in various applications, such as fiber buckling (Nezamabadi et al [34]), composite shells (Cong et al [35]), rate-dependent response (Tikarrouchine et al [36]) and SMA-based fiber/matrix composites (Kohlhaas and Klinkel [37]; Chatzigeorgiou et al [38]; Xu et al [39]) In this approach, both the structural level and the RVE level are simulated by the finite element method (FEM).
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