With the explosive growth of computational resources and data generation, deep machine learning has been successfully employed in various applications. One important and emerging scientific application of deep learning involves solving differential equations. Here, physics-informed neural networks (PINNs) are developed to solve the differential equations associated with a specific scientific problem. As such, algorithms for solving the differential equations by embedding their initial and boundary conditions in the cost function of the artificial neural networks using algorithmic differentiation must also be developed. In this study, various PINNs are adopted to estimate the stresses in the tablets and the interphase of a single lap joint. The proposed model is represented by two fourth-order non-homogeneous coupled partial differential equations, with the axial stresses in the upper and lower tablets adopted as the dependent variables. The axial stresses are a function of the tablet length, which presents the independent variable. Therefore, the axial stresses in the tablets are estimated by solving the coupled partial differential equations when subjected to the boundary conditions, whereas the remaining stress components are expressed in terms of axial stresses. The results obtained using the developed methodology are validated using the results obtained via MAPLE software.