Optimization of Shape and Material Properties: Advanced Mathematical Methods and 3D Printing
May 18, 2020 — May 22, 2020
- Rodica Toader (Università di Udine)
- Giovanni Noselli (SISSA, Trieste)
3D printing has opened the possibility to create functional end-use parts of a complexity that could not be achieved with traditional manufacturing technologies. It thus represents a promising step towards ways of optimizing and saving materials, reducing costs and environmental impact.
While additive manufacturing is being continually improved, a major thrust in research is devoted to the optimal design of composite and micro-architected materials with unprecedented properties.
This course will present some advanced mathematical tools for modelling both the elastic and inelastic behaviour of solids, and applications related to the engineering technology of additive manufacturing.
In particular, Gamma-convergence rigorously justifies the use of phase field models to approximate quasistatic crack growth in brittle materials. In order to identify significant parameters or cavities to predict the optimal shape of a printed object, topology optimization will be considered.
The mechanical properties of materials and structures obtained by these methods will be analysed, and a particular attention will be devoted to the study of instability phenomena in periodic composites and to the propagation of elastic waves in micro-architected materials.
Effective fracture properties of heterogeneous solids will be studied in view of applying 3D printing techniques to design materials with improved failure properties. Numerical methods used in this context will be also presented.
The course is addressed to master students, PhD students, postdocs and young researchers. It can be of interest also to engineers and professionals as it provides an insight into the tools at the basis of numerical methods largely used in practice.