September 28, 2015 — October 2, 2015
Daniel Dias-da-Costa (The University of Sydney, Australia and University of Coimbra, Portugal)
Stéphane P.A. Bordas (University of Luxembourg, Luxembourg and Cardiff University, Wales, UK)
Register for this course
A central topic in mechanics consists in building “virtual laboratories” to optimize heterogeneous materials so as to achieve specific targets. This requires building constitutive models on one or more scales, devising and verifying wellsuited numerical schemes to solve the resulting mathematical problems numerically and, most importantly, to design and optimize experimental techniques to ensure the observability of relevant quantities, and validate the models.
Materials are heterogeneous or even discrete at some scale. Those heterogeneities can be accounted for either by averaging properties at smaller scales, or by considering explicitly the micro/meso structures of the materials. However, when failure occurs, it is no longer possible to separate micro from macro effects and more advanced strategies are required, such as error-controlled adaptive model order reduction or adaptive hybrid multi-scale methods.
Discretising the heterogeneities, cracks, dislocations and defects can be cumbersome using standard finite element methods (FEM). Enrichment and implicit boundary strategies can be applied to deal with complex and evolving boundaries/geometries, whereas other approaches aim at completely abolishing the need for finite element meshes. This class of mesh-free methods can be particularly appealing, since fullfield monitoring techniques typically measure data on scattered sets of points that can be directly used for simulation purposes. Sharing some appealing properties with mesh free methods, isogeometric methods were recently introduced with the aim to simplify the design-through analysis concept and were recently used for digital image correlation. Such full-field techniques, used to measure material deformation, have brought up a revolution in mechanical testing of materials.