A nonlocal operator method for finite deformation higher-order gradient elasticity

We present a general finite deformation higher-order gradient elasticity theory. The governing equations of the solid along with boundary conditions various orders are derived from variational principle using integration by parts on surface. objectivity energy functional is achieved carefully selecting invariants under rigid-body transformation. third-order theory includes more than 10.000 material parameters. However, certain simplifications, parameters can be greatly reduced; down to 3. With this simplified formulation, we develop nonlocal operator method and apply it several numerical examples. analysis shows that high exhibits stiffer response compared ’conventional’ hyperelastic solid. tests also demonstrate capability in solving physical problems.