Microstructural effects on the response of a multi-layered elastic substrate

• Published in: International journal of solids and structures 2022-04, Vol.241, p.111394, Article 111394
• Main Authors: Wongviboonsin, Wipavee, Le, Toan Minh, Lawongkerd, Jintara, Gourgiotis, Panos A., Rungamornrat, Jaroon
• Format: Article
• Language: English
• Subjects: Boundary conditions; Couple stress theory; Functionally graded materials; Functionally gradient materials; Integral transforms; Linear algebra; Microstructural effects; Microstructure; Multi-layered media; Multilayers; Quadratures; Scale effect; Stiffness; Substrates; Surface coating
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2021.111394

•Size-dependent elastic response of surface loaded multilayered media is investigated.•Effects of material microstructures are modeled by couple stress elasticity.•Analytical solution scheme via integral transform and stiffness method is adopted.•Substrate coated by FGMs is simulated via discretization and multilayer scheme.•Microstructures can either boost or lower stresses transferred to substrate surface. The size dependent response of a multi-layered elastic substrate under surface loading is investigated in the present work. The effect of material microstructure is modeled using the generalized continuum theory of couple stress elasticity. In the formulation, the displacement field is chosen as a primary unknown and the generalized Navier’s equation is established for a generic material layer. The Fourier integral transform method is directly applied to derive the general solution of the elastic field for the generic layer, and such solution is subsequently utilized to form the layer stiffness equation in the transform space. Boundary conditions together with the field continuity across the material interfaces are enforced, via the standard assembly procedure, to obtain a system of linear algebraic equations governing all unknowns of the multi-layered system. An efficient quadrature is adopted to carry out all involved integrals arising from the integral transform inversion. Detailed results are reported that confirm the validity of our results through the comparison with well-known solutions and demonstrate the capability of the proposed model to simulate various scenarios of layered media including those made of functionally graded materials. The important role of the material length scale effect on the predicted response is also elucidated.