A NURBS-based inverse analysis of thermal expansion induced morphing of thin shells

Soft, active materials have been widely studied due to their ability to undergo large, complex shape changes in response to both mechanical and non-mechanical external stimuli. However, the vast majority of such studies has focused on investigating the forward problem, i.e. determining the shape changes that result from the applied stimuli. In contrast, very little work has been done to solve the inverse problem, i.e. that of identifying the external loads and stimuli that are needed to generate desired shapes and morphological changes. In this work, we present a new inverse methodology to study residual thermal expansion induced morphological changes in geometric composites made of soft, thin shells. In particular, the method presented in this work aims to determine the prescribed external stimuli needed to reconstruct a specific target shape, with a specific focus and interest in morphological changes from two-dimensional (2D) to three-dimensional (3D) shapes by considering the external stimuli within a thermohyperelastic framework. To do so, we utilize a geometrically exact, rotation-free Kirchhoff–Love shell formulation discretized by NURBS-based shape functions. We show that the proposed method is capable of identifying the stimuli, including cases where thermal expansion induced shape changes involving elastic softening occur in morphing from the initially flat 2D to non-planar 3D shapes. Validation indicates that the reconstructed shapes are in good agreement with the target shape.