Lagrangian and Eulerian formulations of second-grade elasticity via convected coordinates
Roberto Fedele, David J. Steigmann
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.
Topics & Concepts
Eulerian pathKinematicsLagrangian and Eulerian specification of the flow fieldElasticity (physics)LagrangianEuler–Lagrange equationMathematicsMathematical analysisClassical mechanicsConnection (principal bundle)Transformation (genetics)MechanicsApplied mathematicsFinite strain theoryCoordinate systemInertial frame of referenceGeometryPhysicsVariable (mathematics)Nonlocal and gradient elasticity in micro/nano structuresNumerical methods in engineeringComposite Structure Analysis and Optimization