A Novel Arbitrary Lagrangian Eulerian Framework for Large Strain Solid Dynamics

In the realm of Computer-Aided Engineering applied to fast solid dynamics, the intricate mechanical behaviours exhibited by materials when subjected to strong dynamic forces, high speed impacts and complex interactions are modelled efficiently and with high fidelity.Employed in diverse fields such as aerospace, automotive, defence and more, the principal interest is to simulate and comprehend the responses of solids, providing insights into stress propagation and deformation patterns. However, the pursuit of such ambitious goals faces inherent limitations: the accurate representation of material behaviours is an ongoing challenge, and the intricate interplay between simulation accuracy and computational efficiency demands thoughtful insights. More specifically, the chosen kinematics paradigm and the discretisation of the continuum often restrict numerical frameworks in the array of problems they can simulate. Simulations in fast solid dynamics may feature locking, numerical instabilities, checker-boarding, or other difficulties related to the nonlinear nature of the equations of state. In the objective to address the aforementioned shortcomings, this thesis will build on the set of equations introduced in [1, 2] by developing a new mixed formulation based on first-order hyperbolic equations and written with the Arbitrary Lagrangian-Eulerian viewpoint. That approach, used here to describe solid bodies and studied by [3–6], aims at circumventing bottlenecks of Lagrangian and Eulerian methods by distinguishing the behaviour of the mesh from the evolution of the continuum. The ALE formulation introduces a referential (fixed) domain separate from the spatial and material domains and used for motion description. The computational mesh partially follows the material points to reduce element distortion. A key aspect of this work is to adapt the mesh via solving dedicated conservation laws incorporated in a general mixed formulation, removing the need of an ad hoc procedure. The ALE methodology shows promise in addressing challenges in large strain solid dynamics, including hyper-velocity dynamic impact/contact and crack propagation. An acoustic Riemann solver based on upwinding stabilisation, as well as a linear gradient reconstruction, will be used to counteract instabilities brought by the Vertex-Centred Finite Volume Method employed in the framework, and to enhance the overall accuracy. The nonlinear hardening laws will be solved using a Newton-Raphson algorithm. The new framework introduced in this work will be implemented from scratch on the open-source platform OpenFOAM, a tool of choice in industrial and academic environments. The time integration will be tackled by the multi-stage Total Variation Diminishing Runge-Kutta method. Eventually, the robustness and accuracy of the novel computational framework will be examined through a series of challenging numerical examples involving complex body deformations, as well as plastic and thermal considerations.