A NURBS-based inverse analysis of swelling induced morphing of thin stimuli-responsive polymer gels

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Gels are a mixture of cross-linked polymers and solvents, and have been widely studied in recent years for a diverse range of biomedical applications. Because gels can undergo large, reversible shape changes due to swelling, their complex physical response must be modeled by coupling large reversible deformation and mass transport. An ongoing challenge in this field is the ability to capture swelling or residual swelling-induced of such stimuli-responsive gels from initially flat two-dimensional (2D) to three-dimensional (3D) curved shapes. Specifically, because such shape changes typically involve large deformations, shape changes, and the exploitation of elastic instabilities, it remains an open question as to what external stimulus should be prescribed to generate a specific target shape. Therefore, we propose a novel formulation that tackles, using both nonlinear kinematics and material models, the coupling between elasticity and solvent transport using Kirchhoff–Love shell theory discretized using isogeometric analysis (IGA). Second, we propose an inverse methodology that chemomechanically couples large deformation and mass transport to identify the external stimuli prescribed to generate a specific target shape. Our numerical examples demonstrate the capability of identifying the required external stimuli, with the implication that the reconstructed target shapes are accurate, including cases where the shape changes due to swelling involve elastic instabilities or softening. Overall, our study can be used to effectively predict and control the large morphological changes of an important class of stimuli-responsive materials.