Abstract
We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence of a weak solution based on it. Furthermore, we also consider an alternating iteration method and show that it is nothing but an alternating minimizing method of the total energy. The convergence to a monolithic formulation and the alternating iteration method are numerically studied with the finite element method.
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Acknowledgments
The authors are grateful to Prof. Frédéric Hecht for his useful comments on numerical computation with FreeFem++. This work is supported by JSPS KAKENHI Grant Number JP16H03946 and JP17H02857.
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Kimura, M., Suzuki, A. (2020). Deformation Problem for Glued Elastic Bodies and an Alternative Iteration Method. In: Itou, H., Hirano, S., Kimura, M., Kovtunenko, V.A., Khludnev, A.M. (eds) Mathematical Analysis of Continuum Mechanics and Industrial Applications III. CoMFoS 2018. Mathematics for Industry, vol 34. Springer, Singapore. https://doi.org/10.1007/978-981-15-6062-0_6
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DOI: https://doi.org/10.1007/978-981-15-6062-0_6
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