Efficient coupling methods for the dynamic modelling of heterogeneous systems

Thesis

The ability to predict the behaviour of systems, subject to time-dependent loads, is crucial for a wide variety of engineering applications. Employed from the nano to the macro-scale, the Finite Element Method (FEM) has proven to be a versatile computational approach for dynamic modelling. However, current implementations of the method struggle to balance the competing demands of computational efficiency versus accurate and stable simulations. Coupling methods appear to be a solution to this problem. This research focuses on the formulation and application of novel coupling methods with explicit FEM. It enhances the current state-of-the-art methods, particularly for those applied to heterogeneous systems. This thesis investigates concurrent coupling methods; leveraging multi-time step integration temporally, and non-matching mesh algorithms spatially. Enabling the use of different time steps across subdomains, whilst circumventing their requirement to spatially conform, produces a framework to handle heterogeneous discretisations effectively.

The proposed method utilises a partitioning of a computational domain, to solve the dynamic equilibrium in each subdomain independently. Kinematic and kinetic continuity of these subdomain interfaces are enforced, to ensure a precise solution without the generation of numerical artifacts. This optimisation not only expedites the simulation runtime, but also enables more flexible geometric modelling. The algorithms are benchmarked against traditional monolithic methods, including special limit cases, with highly heterogeneous configurations. The tolerance to which conservative laws are obeyed are quantified, with particular attention given to the behaviour at the coupled interfaces.

The results show a combined coupling of multi-time stepping and non-matching meshes produce a computational speedup of over 12X uncoupled methods. To assess the speedup and stability in complex heterogeneous systems, the stress wave propagation in metamaterials and the dynamic loading of a compact-tension specimen are demonstrated. These depict the ability of the framework to resolve deformation in real world systems. The proposed algorithms implicate the inefficient implementations of current solvers, by providing the tools for resolving short term phenomena.

Authors: Chan, KF

• DOI: 10.5287/ora-8j2k4ep5b
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: multi-time step integration; non-matching meshes; Finite Element Method
• Subjects: Solid dynamics; Computational mechanics