Boundary Layer Solutions in Elastic Solids
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Circumferential shear deformation in an annular domain is studied for a large class of incompressible isotropic elastic materials. It is demonstrated that large strains are confined in a region adjacent to a boundary, in analogy to the boundary layer phenomenon in fluid mechanics. The size of this region is quantified. An approximate solution technique for the deformation of nonlinear elastic solids, proposed by Rajagopal, is further studied. In this solution, akin to the boundary layer approximation in classical fluid mechanics, the full nonlinear problem is solved in a relatively small region of large strain, while the linearized problem is solved in the remaining region. Error estimates for the approximate solution are obtained.
author list (cited authors)
Chen, Y., & Rajagopal, K. R.