Strong ellipticity within the Toupin-Mindlin first strain gradient elasticity theory

We discuss the strong ellipticity (SE) condition within the Toupin-Mindlin first strain gradient elasticity theory. SE condition is closely related to certain material instabilities and describes mathematical properties of corresponding boundary-value problems. For isotropic solids, SE condition transforms into two inequalities in terms of five gradient-elastic moduli.

Automated summary

This paper discusses the application of the strong ellipticity condition in the Toupin-Mindlin first strain gradient elasticity theory, and explains its relationship with material instability and mathematical properties of boundary-value problems.