On nonlinear dilatational strain gradient elasticity

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. The strictly related other generalized models with scalar (one-dimensional) microstructure as poroelasticity. They could be also regarded result a kind “solidification” fluids known Korteweg or Cahn–Hilliard fluids. Using variational approach we derive, for Euler–Lagrange equilibrium conditions both Lagrangian Eulerian descriptions. In particular, show that can support contact forces concentrated edges but surface curves faces piecewise orientable surfaces. characterizing possible externally applicable double curve found examined detail. As linearization small deformations presented. peculiarities model illustrated through axial thick-walled elastic tube propagation waves.