On the Ellipticity of the Equations of Nonlinear Elastostatics for a Special Material.
CALIFORNIA INST OF TECH PASADENA DIV OF ENGINEERING AND APPLIED SCIENCE
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This paper deals with the ellipticity of the equations of finite elastostatics for a compressible material that corresponds to a special choice of the strain-energy density and has received repeated attention in the literature. The possible failure of ellipticity of the appropriate system of displacement equations of equilibrium at solutions involving large deformations was suggested by certain difficulties encountered in an attempt to determine the deformations and stresses arising in such a material near the tip of a crack. It is shown here that ellipticity prevails only if the principal stretches are suitably restricted and breaks down, in particular, at a local state of uni-axial tension or compression of sufficiently severe intensity.
- Numerical Mathematics
- Solid State Physics