Chun Hean Lee

TL;DR: In this article, a new computational framework for the analysis of large strain fast solid dynamics is introduced, where a first order system of hyperbolic equations is introduced for the simulation of isothermal elastic materials in terms of the linear momentum, the deformation gradient and its Jacobian as unknown variables.

TL;DR: In this paper, a new mixed formulation is presented for the numerical analysis of fast transient dynamics phenomena in large deformations, where the linear momentum, the deformation gradient tensor and the total energy of the system are used as main conservation variables, leading to identical convergence patterns for both displacements and stresses.

TL;DR: This formulation is further enhanced for nearly and truly incompressible deformations with three key novelties, including a new conservation law for the Jacobian of the deformation is added into the system providing extra flexibility to the scheme.

TL;DR: In this paper, a stabilised second order finite element methodology is presented for the numerical simulation of a mixed conservation law formulation in fast solid dynamics, where the unknowns are linear momentum, deformation gradient and total energy, can be cast in the form of a system of first order hyperbolic equations.

TL;DR: A stabilised Petrov–Galerkin framework is presented for both systems of hyperbolic equations, that is, when expressed in terms of either conservation or entropy variables, and an adapted fractional step method is presented to extend the range of applications towards the incompressibility limit.