Nicola Bombace1, Ettore Barbieri2, Nik Petrinic3
1 Department of Engineering Science, University of Oxford, OX13PJ; email@example.com
2 School of Engineering and Material Science, Queen Mary University of London, E1 firstname.lastname@example.org
3 Department of Engineering Science, University of Oxford, OX13PJ,email@example.com
Both elastic and inelastic deformation, depend strongly upon the behaviour of the constitutive components at multiple scales. Since the limits of the currently available computational power hinder the “brute force” simulation of the whole component using the smallest relevant scale, a “smarter” approach is required for the accurate simulation of domains sensibly larger than the desired special resolution.
The main distinction of the several “multi-scale” approaches developed in the past decades is in hierarchical and concurrent methods.
Hierarchical methods homogenise the information gathered at the lower scales in the macro model, imposing the Hill-Mandel principle. Therefore, they require the introduction of more complex homogenisation schemes to account for the presence of localised
Concurrent methods, instead, combine the different scales in the same model, introducing an high special refinement in the parts of the domain that are expected to exhibit high deformation/stress gradients.
The work described introduces a new three-dimensional multi-scale adaptive method for explicit formulation, which allows a more computationally efficient simulation of dynamic problems. The introduction of the different spatial and temporal scales only when and where needed, remove the limitation of knowing a-priori the hot-spots, hence simulating de-facto the whole domain at the lowest scale of interest.