The transformation between the Lagrangian and Eulerian descriptions of the equilibrium equations for second-grade elastic materials is reconsidered in the setting of a convected-coordinate formulation of the relevant kinematics. The third-order contortion tensor, equivalent to the strain gradient and representing the change of the Levi-Civita connection induced by deformation, is adopted as the basic descriptor of the refined kinematics associated with the second-gradient theory.
LAGRANGIAN AND EULERIAN FORMULATIONS OF SECOND-GRADE ELASTICITY VIA CONVECTED COORDINATES
R. Fedele;
2025-01-01
Abstract
The transformation between the Lagrangian and Eulerian descriptions of the equilibrium equations for second-grade elastic materials is reconsidered in the setting of a convected-coordinate formulation of the relevant kinematics. The third-order contortion tensor, equivalent to the strain gradient and representing the change of the Levi-Civita connection induced by deformation, is adopted as the basic descriptor of the refined kinematics associated with the second-gradient theory.File in questo prodotto:
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