The Goodman contact element in geotechnical engineering based on the virtual element method

This paper introduces the Goodman contact element based on the virtual element method framework. Since the virtual element method can calculate polygonal elements with any number of nodes, the limitation of mesh matching of the contact part required by the Goodman contact element is overcome by adding nodes to the contact element. Combine the virtual element method with the Goodman contact element to enable the Goodman contact element to solve practical problems in geotechnical engineering. In this paper, first, we derive the elastoplastic virtual element equations, and then, the Goodman contact stiffness matrix based on the virtual element method is calculated. Finally, several numerical examples are shown. In numerical models, the sensitivity of the virtual element method to mesh distortion is studied. We also investigate the shape sensitivity of the algorithm and the convergence of the Voronoi element through several frictionless contact examples. And then, the contact examples under friction state and elastic-plastic constitutive law are carried out. Finally, the contact force between soil and wall under the non-matching mesh in the gravity retaining wall commonly used in geotechnical engineering is presented.

Automated summary

This paper introduces the Goodman contact element based on the virtual element method framework. By adding nodes to the contact element, the limitation of mesh matching is overcome, and practical problems in geotechnical engineering can be solved. The virtual element method is applied to derive the elastoplastic equations and calculate the Goodman contact stiffness matrix. Numerical examples are provided to study mesh distortion sensitivity, shape sensitivity, convergence, and frictional and elastic-plastic contact cases. The contact force between soil and wall in a gravity retaining wall with non-matching mesh is also presented.