Strong Ellipticity Condition Research Articles

Static implications of the strong-ellipticity condition

Static implications of the strong-ellipticity condition

On pure extension

A homogeneous deformation field, called “pure extension” is introduced. Various applications of this field are considered. Pure extension leads to a reasonable static interpretation of the strong-ellipticity condition in linearised elasticity theory. The response of a compressible elastic material to pure extension is related to the speeds of propagation of infinitesimal plane waves. Finally, a generalised Tension-Extension condition is introduced and discussed.

Wave propagation and uniqueness in prestressed elastic solids

A homogeneous isotropic perfectly elastic body is subjected to a large static pure homogeneous deformation with two of the principal extension ratios equal. An infinitesimal deformation is superimposed on the large deformation. The conditions for strong ellipticity of the system of equilibrium equations for the infinitesimal deformation are obtained. These conditions are examined within the context of uniqueness or non-uniqueness of the displacement boundary-value problem for the infinitesimal deformation. It is found that the conditions of strong ellipticity are sufficient but not necessary for uniqueness.