TY - JOUR

T1 - A NURBS-based inverse analysis of swelling induced morphing of thin stimuli-responsive polymer gels

AU - Vu-Bac, N.

AU - Rabczuk, T.

AU - Park, H. S.

AU - Fu, X.

AU - Zhuang, X.

N1 - Funding Information: The authors gratefully acknowledge the support of the ERC Starting Grant (802205) from European Union and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453). Professor Krister Svanberg from Royal Institute of Technology is acknowledged gratefully for providing the MMA code used in this study.

PY - 2022/7/1

Y1 - 2022/7/1

N2 - 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.

AB - 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.

KW - Instability shape changes

KW - Inverse analysis

KW - Isogeometric analysis

KW - Kirchhoff–Love shells

KW - Stimuli-responsive polymer gels

UR - http://www.scopus.com/inward/record.url?scp=85131137428&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2022.115049

DO - 10.1016/j.cma.2022.115049

M3 - Article

AN - SCOPUS:85131137428

VL - 397

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 115049

ER -