Second-gradient continua: From Lagrangian to Eulerian and back
Francesco dell’Isola, Simon R. Eugster, Roberto Fedele, Pierre Seppecher
Abstract
In this paper, we represent second-gradient internal work functionals in Lagrangian (referential) and Eulerian (spatial) descriptions, and we deduce the corresponding expressions for the Piola transformations of stress and double-stress tensors and of external forces and double-forces. We also derive, in both the Eulerian and Lagrangian description, the expression of surface and edge contact interactions (which include forces and double-forces) for second-gradient continua in terms of the normal and the curvature of contact boundary surfaces and edge shapes.
Topics & Concepts
Eulerian pathCurvatureClassical mechanicsMathematicsLagrangianEnhanced Data Rates for GSM EvolutionBoundary (topology)Mathematical analysisStress (linguistics)Work (physics)GeometryExpression (computer science)PhysicsMechanicsComputer scienceLinguisticsTelecommunicationsPhilosophyProgramming languageThermodynamicsNonlocal and gradient elasticity in micro/nano structuresElasticity and Material ModelingContact Mechanics and Variational Inequalities