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 higher-order gradient solid along with boundary conditions of various orders are derived from a variational principle using integration by parts on the surface. The objectivity of the energy functional is achieved by carefully selecting the invariants under rigid-body transformation. The third-order gradient solid theory includes more than 10.000 material parameters. However, under certain simplifications, the material parameters can be greatly reduced; down to 3. With this simplified formulation, we develop a nonlocal operator method and apply it to several numerical examples. The numerical analysis shows that the high gradient solid theory exhibits a stiffer response compared to a 'conventional' hyperelastic solid. The numerical tests also demonstrate the capability of the nonlocal operator method in solving higher-order physical problems. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

A general finite deformation higher-order gradient elasticity theory is proposed in the paper, reducing the material parameters significantly under certain simplifications. A nonlocal operator method is developed and applied to numerical examples, demonstrating the stiffness response of the high gradient solid theory and the capability of the nonlocal operator method in solving higher-order physical problems.