The subject of origami design is garnering increased attention from the science, mathematics, and engineering communities. However, relatively little research exists on understanding the behavioral aspects of the material system undergoing the folding operations. This work considers the design and analysis of a novel concept for a self-folding structure. It consists of an active, self-morphing laminate that includes thermally actuated shape memory alloy (SMA) layers and a compliant passive layer. Multiple layers allow folds in both the positive and negative directions relative to the laminate normal. The layers are configured to allow continuously variable folding operations based only on which regions are heated. For the purposes of demonstration, an example problem is considered whereby a thin structure is designed that can be stored in a flat sheet configuration and then morph using sets of folds toward two distinct shapes. We examine the effects of fold width, layer thicknesses, and activation power history on the geometric configurations that can be obtained. The design efforts are supported by a comprehensive and accurate three-dimensional constitutive model for SMAs implemented into a finite element analysis (FEA) framework. Shell elements and laminate theory are used to increase the computational efficiency of the analysis. Discussion of the complex effects of active folding in an SMA laminate sheet with in-plane homogeneity, including transient effects, are discussed.

The subject of origami design has recently garnered increasing attention from the science, mathematics, and engineering communities. Mathematically rigorous frameworks have been developed that allow the identification of folding patterns needed to obtain a final three-dimensional goal shape. However, relatively little research exists on the problem of understanding the behavioral aspects of the material system undergoing the folding operations. This work considers the design and analysis of a novel concept for a self-folding material system. The system consists of an active, self-morphing laminate structure that includes thermally actuated shape memory alloy (SMA) layers and a compliant passive layer. Multiple layers allow folds in both directions (e.g., cross-folds). The layers are configured to allow continuously variable folding operations based only on which regions are heated. For the purposes of demonstration, an example problem is considered whereby an autonomous planetary landing craft is designed that can be stored in a flat sheet configuration, morph using a set of folds into a stable shape for safe descent through a gaseous atmosphere, and then, once landed, morph again toward a cylindrical shape for the purpose of rolling locomotion. We examine the effects of fold width, layer thicknesses, and activation parameters on the geometric configurations that can be obtained. The design efforts are supported by realistic morphing structural analysis tools. These include a comprehensive and accurate three-dimensional constitutive model for SMAs implemented into a finite element analysis (FEA) framework (the Abaqus Unified FEA suite) using a robust and efficient numerical integration scheme. Shell elements and laminate theory are used to increase the computational efficiency of the analysis. Model pre-processing, submission, and post-processing scripting methods are used to automate the design assessment tasks.

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