Mathematical modeling and numerical analysis of elastic body with thin inclusion

This article studies elastic multi-component structure consisting of matrix body with thin inclusion. Mathematical model dwells on membrane shell theory for thin inclusion, while classical elasticity theory is used for matrix medium under the assumption of perfect bonding on the media interface. We prove the existence and uniqueness of the weak problem solution. In order to implement finite element scheme, a coupled model is developed. Simulations are performed for the plane coupled problem. Eventually we compare the solutions obtained with the classical approach results and estimate a posteriori errors for different meshes to assess the model. Bridging theory with practice, the model's applicability to engineering problems is demonstrated finally.