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JST-SPH: a total Lagrangian, stabilised meshless methodology for mixed systems of conservation laws in nonlinear solid dynamics

Greto, Giorgio 2018. JST-SPH: a total Lagrangian, stabilised meshless methodology for mixed systems of conservation laws in nonlinear solid dynamics. PhD Thesis, Cardiff University.
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The combination of linear finite elements space discretisation with Newmark family time-integration schemes has been established as the de-facto standard for numerical analysis of fast solid dynamics. However, this set-up suffers from a series of drawbacks: mesh entanglements and elemental distortion may compromise results of high strain simulations; numerical issues, such as locking and spurious pressure oscillations, are likely to manifest; and stresses usually reach a reduced order of accuracy than velocities. Meshless methods are a relatively new family of discretisation techniques that may offer a solution to problems of excessive distortion experienced by linear finite elements. Amongst these new methodologies, smooth particles hydrodynamics (SPH) is the simplest in concept and the most straightforward to numerically implement. Yet, this simplicity is marred by some shortcomings, namely (i) inconsistencies of the SPH approximation at or near the boundaries of the domain; (ii) spurious hourglass-like modes caused by the rank deficiency associated with nodal integration, and (iii) instabilities arising when sustained internal stresses are predominantly tensile. To deal with the aforementioned SPH-related issues, the following remedies are hereby adopted, respectively: (i) corrections to the kernel functions that are fundamental to SPH interpolation, improving consistency at and near boundaries; (ii) a polyconvex mixed-type system based on a new set of unknown variables (p, F, H and J) is used in place of the displacementbased equation of motion; in this manner, stabilisation techniques from computational fluid dynamics become available; (iii) the analysis is set in a total Lagrangian reference framework. Assuming polyconvex variables as the main unknowns of the set of first order conservation laws helps to establish the existence and uniqueness of analytical solutions. This is a key reassurance for a robust numerical implementation of simulations. The resulting system of hyperbolic first order conservation laws presents analogies to the Euler equations in fluid dynamics. This allows the use of a well-proven stabilisation technique in computational fluid dynamics, the Jameson Schmidt Turkel (JST) algorithm. JST is very effective in damping numerical oscillations, and in capturing discontinuities in the solution that would otherwise be impossible to represent. Finally, we note that the JST-SPH scheme so defined is employed in a battery of numerical tests, selected to check its accuracy, robustness, momentum preservation capabilities, and its viability for solving larger scale, industry-related problems.

Item Type: Thesis (PhD)
Date Type: Submission
Status: Unpublished
Schools: Engineering
Uncontrolled Keywords: Computational mechanics; Meshless methods; Conservation laws; Mixed Formulation; SPH; Artificial Dissipation.
Date of First Compliant Deposit: 24 January 2019
Last Modified: 03 Mar 2020 02:22

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