Response of a thin coating of a porous elastic material whose generalised Young’s modulus depends on the density

Mathematics and Mechanics of Solids, vol. 30, pp. 1233–1248

Abstract

Mechanics of a thin elastic coating is analysed using nonlinear constitutive relations based on the concept of a density-dependent Young’s modulus. In contrast to previous considerations on the subject, the proposed framework does not assume weak nonlinearity. Two-term asymptotic expansions are derived for four setups of boundary conditions along the upper face of the coating; in doing so, the lower face is supposed to be clamped. Explicit approximate formulae obtained in the paper have the potential to be implemented in diverse industrial applications related to thin porous coatings.

Authors 4

1. Barış Erbaş corresponding

   Eskisehir Technical University

   Affiliation as printed

   Department of Mathematics, Eskişehir Technical University, Eskişehir, Turkey

2. Mikhail Itskov Aachen Department of Continuum Mechanics

   RWTH Aachen University · Keele University

   Affiliation as printed

   Department of Continuum Mechanics, RWTH Aachen University, Aachen, Germany; School of Computer Science and Mathematics, Keele University, Keele, UK

   School of Computer Science and Mathematics, Keele University, Keele, UK

3. Julius Kaplunov Aachen Department of Continuum Mechanics

   RWTH Aachen University · Keele University

   Affiliation as printed

   School of Computer Science and Mathematics, Keele University, Keele, UK; Department of Continuum Mechanics, RWTH Aachen University, Aachen, Germany

   School of Computer Science and Mathematics, Keele University, Keele, UK

4. Kumbakonam Ramamani Rajagopal

   Texas A&M University

   Affiliation as printed

   Department of Mechanical Engineering, Texas A&M University, College Station, TX, USA

   Department of Mechanical Engineering, Texas A&M University, College Station, TX, USA