3rd TAGRA

Contact mechanics examines the interaction of bodies using the theory of elasticity and finds applications across various engineering disciplines involving solid structures. Structural damage often results from fractures in regions with high stress concentrations, making it crucial to accurately determine contact stress distributions during the design phase. With advancements in materials science, production methods have emerged that enable tailoring material properties based on location within the material. These materials, known as Functionally Graded Materials (FGMs), are heterogeneous composites where properties vary continuously according to a specific function. This study investigates the continuous contact problem involving a two-layer system resting on an elastic half-plane, subjected to a rigid flat block load. The upper layer, with a thickness of ℎ1, is an FGM whose density and shear modulus vary exponentially. The lower layer, with a thickness of ℎ2, is homogeneous with constant material properties. All surfaces in the system are assumed to be frictionless. A rectangular rigid block applies an external load 𝑃 on the functionally graded layer. The problem is solved analytically by using elasticity theory and integral transform technics. The study considers various parameters, including density ratios (γ/ℎ1 = 1.38629, γ/h1=0.0001, γ/h=−1.38629), block width-to-height ratios (𝑎/ℎ1 =0.25, 𝑎/ℎ1 =0.5, 𝑎/ℎ1=1, 𝑎/ℎ1=2), and stiffness parameters (βh1=-1.38629, βh1=0.0001, βh1=1.38629). The contact stresses at the interfaces are determined, along with the initial separation load and the critical separation distances (λ𝑐𝑟, xcr) between the FGM and homogeneous layers. Results are presented in the form of figures, graphs, and tables.