A Quasi-Static Nonlinear Model of Shape Memory Polymer Composite Beams for Space Applications

Abstract

Shape Memory Polymer Composites (SMPC) structures, due to their ability to be packed into compact volumes and then later on transformed back to their original shapes, are an ideal solution for deployment problems of large light-weight space structures. Although much research on constitutive laws and qualitative analysis of mechanics of SMPC structures has been carried out, little has been reported in the literate about the development of dynamic equations for SMPC structures. This paper documents a macroscopic model for shape fixation and shape recovery processes of an SMPC cantilever beam, with special attention given to quasi-static states describing the shape fixation process. In the development, a nonlinear geometric model is combined with a temperature-dependent constitutive law. Based on this beam model, numerical results are obtained through use of finite difference approximation and Newton's method in iterative solution. Additionally, the dynamic equations of the SMPC cantilever beam are devised.

A numerical approach for modeling response of shape memory polymer composite corrugated structure

“…Ohki et al [7] considered a chopped fiber composite configuration, where experimental results predicted a higher actuation force under constrained response. Similar studies for continuous fiber reinforced composite [8] and nanotube composite [9,10] predicted higher actuation force leading to a quick recovery. Improvement in mechanical stiffness and strength was observed with higher actuation force where SMP was reinforced with carbon fiber [11,12].…”

“…The variation in shear modulus and the Poisson's ratio are shown in figures 10(c) and (d). The variation in these quantities is a direct consequence of the constitutive equations presented in the previous section, equations (7) and (8). These characteristic results predict that the shape memory response along fiber direction will be quite low compared to the direction transverse to the fiber direction.…”

Effect of reinforcing layer on shape fixity and time-dependent deployment in shape-memory polymer textile composites

“…Moreover, Bergman et al introduced a rule of mixtures and lamination theory in the Yang model [33], and constructed a general model in terms of fiber arrangement and stacking sequence [34]. While the Bergman model has high flexibility for application to structures, it cannot simulate the time-dependent deployment of SMPC, due to a lack of knowledge about the physical properties that affect time-dependent behavior.…”

A finite element model of shape memory polymer composite beams for space applications

“…The intent is to eventually develop modeling and design tools for deployable structures in space applications. The current investigation is an extension of the previous work performed by Yang [1] and Bergman [2][3][4][5], who studied the dynamics of a one-dimensional (transverse motion) shape memory polymer (SMP) cantilever beam using linear and nonlinear geometry, respectively. The current paper addresses the analysis of the SMP beam using the finite element method by considering nonlinear geometry, a composite material, and the full temperature dependent material model.…”