A stabilised total lagrangian corrected smooth particle hydrodynamics technique in large strain explicit fast solid dynamics

Abstract

An explicit Total Lagrangian mixed momentum/strains formulation [1-5], in the form of a system of first order conservation laws, has been recently proposed to overcome the shortcomings posed by the traditional second order displacement-based formulation, namely: (1) bending and volumetric locking difficulties; (2) hydrostatic pressure fluctuations; and (3) reduced order of convergence for derived variables. Following the work of Bonet and Kulasegaram [6, 7], the main objective of this paper is the adaptation of Corrected Smooth Particle Hydrodynamics (CSPH) in the context of Total Lagrangian mixed formulation. Appropriate nodally conservative Jameson-Schmidt-Turkel (JST) stabilisation is introduced by taking advantage of the conservation laws. This mixed linear momentum-deformation gradient technique performs extremely well in nearly incompressible bending dominated scenarios [1, 2] without the appearance of spurious pressure oscillations. Additionally, as both linear momentum and deformation gradient are used as primary variables of the system, equal order of approximation should be achieved in both fields. A series of numerical examples are carried out to assess the applicability and robustness of the proposed algorithm.