Time-dependent response of structures

Since the advent of computational mechanics, the development of cutting-edge computational frameworks for the emerging fast dynamics problems has been a major field of interest for industry. Applications which require this technology include crash and hyper-velocity impact analysis, dynamic fracture and explosion/implosion modelling, all of which are applicable to the manufacturing, defence, automotive and aerospace industries. These very complex problems are characterised by highly nonlinear behaviour due to the conjunction of large deformations (i.e. geometric nonlinearities) and, possibly, nonlinear constitutive relationships (i.e. material nonlinearities). Unfortunately, existing (displacement-based) low order Finite Element Method (FEM) codes still present a number of persistent shortcomings, namely (1) numerical artefacts due to shear and/or volumetric locking, (2) hour-glassing and pressure checker-boarding, (3) inaccuracy in capturing shock wave propagation, (4) the difficulty of addressing nearly incompressible materials and (5) reduced order of convergence for strains (or stresses) in comparison with displacements.

To overcome the shortcomings, a new computational paradigm is recently established on the basis of a set of physical conservation laws. These laws can be re-formulated as a system of first order conservation laws, with a similar structure to the mathematical equations used in Computational Fluid Dynamics (CFD). Taking advantage of this representation, a wide range of well-established spatial discretisation techniques in CFD can now be suitably adapted and exploited in the field of solid mechanics, including: cell- and vertex-centred Finite Volume Method, stabilised FEM, variational multi-scale approach and very recently proposed mesh-free Smooth Particle Hydrodynamics method. Finally, and to maximise the impact of this work, the new framework is implemented from scratch in the modern CFD code “OpenFOAM”. The OpenFOAM tool-kit is released and currently available here.

On-going collaboration projects (with Swansea University and University of Greenwich) include:

  • Thermo-elasticity and thermo-plasticity
  • Shock hydrodynamics
  • Contact mechanics
  • Dynamic fracture
  • Free surface fluid flows
  • Arbitrary Lagrangian Eulerian formulation for fast solid dynamics
  •  Unified formulation for fluid structure interaction problems

Current and past funders: