Classification of linear viscoelastic solids based on a failure criterion |
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Authors: | Amitabh Narain Daniel D Joseph |
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Institution: | (1) Department of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, 49931 Houghton, MI, USA;(2) Department of Aerospace Engineering and Mechanics, University of Minnesota, 55455 Minneapolis, MN, USA |
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Abstract: | An isotropic, incompressible linear viscoelastic solid subjected to a step shear displacement fails if the relaxation function G(s) is such that 0<G(0)< and – <G (0) 0. In this case, the discontinuity in displacement propagates into the interior of the body. The discontinuity will not propagate however if G(0)= or G (0)=– . In the former case there is a diffusion-like smoothening of discontinuous data characteristic of parabolic equations. The case G(0)= may be achieved by composing the kernel as a sum of a smooth kernel and a delta function at the origin times a viscosity coefficient. If the viscosity is small, the smoothing will take place in a propagating layer which scales with the small viscosity. The case of G (0)=– is interesting in the sense that the solution is C
smooth but the boundary of the support of the solution propagates at a constant wave spped. If 0<G(0)< and – <G (0)<0, then the material accomodates stress waves under step traction leading to an elastic steady state. |
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