Guangwang Su, Mustapha Bouallala, Van Thien Nguyen, Boling Chen, Mathematical and numerical simulation using a deep neural network for a frictionless contact problem with unilateral constraints in viscoelasticity
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DOI: 10.23952/jnva.10.2026.5.04
Volume 10, Issue 5, 1 October 2026, Pages 927-940
Abstract. In this paper, we address a frictionless contact problem involving a viscoelastic body and an obstacle. The process is assumed to be quasi-static. The contact is modeled with normal compliance and unilateral stress, incorporating the Signorini contact condition. We derive a variational formulation of the model and demonstrate the existence and uniqueness of a weak solution using the theory of variational inequalities and fixed point arguments. By converting the initial contact problem into a minimization framework, we utilize a deep neural network to approximate the solution and address the minimization challenge. Finally, we provide numerical results that showcase the method’s efficiency and precision.
How to Cite this Article:
G. Su, M. Bouallala, V.T. Nguyen, B. Chen, Mathematical and numerical simulation using a deep neural network for a frictionless contact problem with unilateral constraints in viscoelasticity, J. Nonlinear Var. Anal. 10 (2026), 927-940.