On the stress singularities generated by anisotropic eigenstrains and the hydrostatic stress due to annular inhomogeneities |
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| Institution: | 1. School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;2. The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;3. Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK;1. Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, United States;2. Department of Mathematics, Texas A&M University, College Station, TX 77843, United States;1. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong;2. Sorbonne Universités, Université Pierre-et-Marie-Curie, Laboratoire Jacques-Louis-Lions, 75005 Paris, France |
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| Abstract: | The problems of singularity formation and hydrostatic stress created by an inhomogeneity with eigenstrain in an incompressible isotropic hyperelastic material are considered. For both a spherical ball and a cylindrical bar with a radially symmetric distribution of finite possibly anisotropic eigenstrains, we show that the anisotropy of these eigenstrains at the center (the center of the sphere or the axis of the cylinder) controls the stress singularity. If they are equal at the center no stress singularity develops but if they are not equal then stress always develops a logarithmic singularity. In both cases, the energy density and strains are everywhere finite. As a related problem, we consider annular inclusions for which the eigenstrains vanish in a core around the center. We show that even for an anisotropic distribution of eigenstrains, the stress inside the core is always hydrostatic. We show how these general results are connected to recent claims on similar problems in the limit of small eigenstrains. |
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| Keywords: | Geometric elasticity Inclusions Anisotropic eigenstrain Residual stresses Stress singularity |
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