Second-gradient continua are defined as those whose internal virtual work functionals depend on the first and second-gradient of displacement. These can be represented either in Lagrangian (referential) or Eulerian (spatial) description thus defining respectively Piola–Lagrange well Cauchy–Euler stress double-stress. In this paper, we deduce Piola transformation formulae, i.e., relationships be...

the built up layer thickness in secondary deformation zone is one of the important parameters in metal cutting process. the built up layer (bul) is formed in second deformation zone near the tool-chip interface in the back of the chip. this parameter influences the tool life and machined surface quality. this bul should not be confused with the built up edge (bue). the deformation of the bul in...

Abstract We call nonlinear dilatational strain gradient elasticity the theory in which specific class of second continua is considered: those whose deformation energy depends, an objective way, on placement and determinant placement. It interesting particular case complete Toupin–Mindlin elasticity: indeed, it, only effects are due to inhomogeneous dilatation state considered deformable body. T...