Multiscale modelling of heterogenous materials: combining accuracy and computational efficienc

The increasing demand for overall accuracy of numerical modelling and the desire for high spatial and temporal resolution on localised phenomena are the driving forces of the development of increasingly more refined numerical models. However, the high computational cost associated to the refined models can hinder their ability to simulate the behaviour of large components. Multiscale models aim to combine the high accuracy of small scale (micro and/or meso) modelling with the computational efficiency required for simulations at the macroscale that are of relevance for industrial applications.



Multiscale approaches can be broadly divided into hierarchical and concurrent.

The first set of approaches relies on, often statistically based, description of the material behaviour at lower scales to inform the macroscopic response of relatively large domains, whilst the second performs concurrent simulations at multiple scales using ad-hoc algorithms to exchange relevant information between separate domains.



Both hierarchical and concurrent multiscale approaches face additional complexities in the simulation of highly dynamic conditions, as the interaction of stress/pressure waves with “artificial boundaries” can lead to numerical artifacts (e.g. spurious wave reflections, high-frequency filters). Whilst the hierarchical approach requires additional simulations at lower scales to account for the dynamic nature of the loading, novel algorithms must be implemented within the concurrent multiscale approach to limit the occurrence of spurious waves in the domain.



At Impact and Shock Mechanics Laboratory (University of Oxford) we are developing both approaches in order to analyse a wide range of scenarios involving high-rate deformation and failure of different classes of materials. This requires the implementation of automated pre- and post- processing of lower scale models enabling microscale informed simulations of large components subjected to complex, highly dynamic, stress states, with the possibility to combine hierarchical and concurrent algorithms to increase the accuracy and the computational efficiency of the simulations. In this talk I will be presenting the overall framework being developed and some relevant examples of multiscale modelling of high-rate phenomena.