Advanced segment-to-segment methods for adaptive contact analysis of solid continuum structures

Abstract

The current work is motivated by the ongoing need for efficient and robust methods of contact simulation in large displacement structural analysis problems. Among the various methods for contact discretisation in structural systems featuring solid continuum bodies, segment to segment methods are popular for their relative numerical stability and ability to provide a continuous and complete coupling of the displacement fields over the contacting surfaces. The current work improves on the segment-to-segment contact approach based on the classical Lagrange multiplier method, introducing efficiencies and workarounds in multiple aspects, namely: (1) the contact formulation; (2) the contact detection/enforcement scheme; and (3) the spatial search and the adaptive generation of contact elements. The large displacement contact formulation based on the classical Lagrange multiplier method is derived from first principles in a modular manner, where greater formulation clarity is introduced, and several expressions are streamlined for increased computational efficiency. Novel reduced order variants of the contact formulation are then proposed which further reduce the computational cost without a significant compromise on accuracy. Element-, node- and quadrature-based schemes for detecting and enforcing contact are investigated with workarounds proposed for identified weaknesses. The current work also proposes a spatial search method with increased efficiency at the lower levels of the search hierarchy for irregular meshes of smooth surfaces, based on a bottom-up hierarchical clustering algorithm which results in a relatively uniform distribution of cluster sizes and a neater cluster arrangement at the lower levels of the hierarchy. A novel intermediate procedure between the global and local stages of the contact search is proposed which uses the geometry of the external solid elements to generate tight-fitting bounding volumes at a low cost and further shortlists segment pairs sent to the local stage. Several numerical examples are presented which demonstrate the capabilities of the developed methods.