Conditions for Strong Ellipticity of Anisotropic Elastic Materials

Conditions for strong ellipticity and M - eigenvalues ∗

Abstract The strong ellipticity condition plays an important role in nonlinear elasticity and in materials. In this paper, we define M-eigenvalues for an elasticity tensor. The strong ellipticity condition holds if and only if the smallest M-eigenvalue of the elasticity tensor is positive. If the strong ellipticity condition holds, then the elasticity tensor is rank-one positive definite. The e...

Remarks on Explicit Strong Ellipticity Conditions for Anisotropic or Pre-stressed Incompressible Solids

We present a set of explicit conditions, involving the components of the elastic stiffness tensor, which are necessary and sufficient to ensure the strong ellipticity of an orthorhombic incompressible medium. The derivation is based on the procedure developed by Zee and Sternberg (Arch. Rat. Mech. Anal. 83 (1983)) and, consequently, is also applicable to the case of the homogeneously pre-stress...

Conditions for the Occurrence of Decoupling Planes in Anisotropic Elastic Materials

Les plans de symŽtrie sont souvent identifiŽs par lÕexistence dÕune polarisation pure perpendiculaire ˆ ces plans. Cependant, ce type de polarisation peut appara”tre sans que le plan soit un plan de symŽtrie. Les plans qui prŽsentent une polarisation pure suivant leurs normales sont appelŽs Ç plans de dŽcouplage È, car le systme de trois Žquations linŽaires couplŽes par les cosinus directeurs ...

A Theoretical Study of Wall Ironing for Anisotropic Workharden Materials

A Theoretical Study of Wall Ironing for Anisotropic Workharden Materials