First order conservation law framework for large strain explicit contact dynamics

Runcie, Callum John (2023) First order conservation law framework for large strain explicit contact dynamics. PhD thesis, University of Glasgow.

Abstract

This thesis presents a novel vertex-centred finite volume algorithm for explicit large strain solid contact dynamic problems where potential contact loci are known a priori. This methodology exploits the use of a system of first order conservation equations written in terms of the linear momentum and a triplet of geometric deformation measures, consisting of the deformation gradient tensor, its co-factor and its determinant, in combination with their associated Rankine-Hugoniot jump conditions. These jump conditions are used to derive several dynamic contact models ensuring the preservation of hyperbolic characteristic structure across solution discontinuities at the contact interface, which is a significant advantage over standard quasi-static contact models where the influence of inertial effects at the contact interface is completely neglected. By taking advantage of this conservative formalism, both kinematic (velocity) and kinetic (traction) contact-impact conditions are explicitly enforced at the fluxes through the use of the appropriate jump conditions. Specifically, the kinetic contact condition was enforced, in the traditional manner, through the linear momentum equation, while the kinematic contact condition was easily enforced through the geometric conservation equations without requiring a computationally demanding iterative scheme. Additionally, a Total Variation Diminishing shock capturing technique can be suitably incorporated in order to improve dramatically the performance of the algorithm at the vicinity of shocks, importantly no ad-hoc regularisation procedure is required to accurately capture shock phenomena. Moreover, to guarantee stability from the spatial discretisation standpoint, global entropy production is demonstrated through the satisfaction of semi-discrete version of the classical Coleman-Noll procedure expressed in terms of the time rate of the Hamiltonian energy of the system. Finally, a series of numerical examples is presented in order to assess the performance and applicability of the proposed algorithm suitably implemented across MATLAB and a purpose built OpenFOAM solver.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Supported by funding from the University of Glasgow, College of Science and Engineering.
• Subjects: T Technology > TJ Mechanical engineering and machinery
• Colleges/Schools: College of Science and Engineering > School of Engineering
• Supervisor's Name: Lee, Dr. Chun Hean and Grassl, Dr. Peter
• Date of Award: 2023
• Depositing User: Theses Team
• Unique ID: glathesis:2023-83555
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 26 Apr 2023 12:01
• Last Modified: 26 Apr 2023 14:20
• Thesis DOI: 10.5525/gla.thesis.83555
• URI: https://theses.gla.ac.uk/id/eprint/83555

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