Multi-scale, multi-physics, and multi-technique computational tools for materials computational modelling

The short course will describe the main aspects of recently developed two - and threedimensional computational frameworks for multi-scale and multi-physics analysis of polycrystalline and composite materials, including the representation of degradation and failure, based on the employment of techniques different from standard FEM. The described models are based on the explicit representation of the considered materials mechanics at the meso-scale, including the initiation, evolution and coalescence of micro-damage and cracking. The strategies to capture the exchange of information between different scales, namely the component level (macroscale) and the material level (mesoscale), will be described, as well as the techniques to include multi-physics representations (e.g. piezoelectric, thermoelastic, chemical diffusion). The potential benefits of employing different techniques for different material phases will be discussed and an example about the coupling of the recent developed Virtual Element Method and the Boundary Element Method will be presented.

The course will describe the main features of the proposed frameworks, their main advantages, current issues and direction of potential further development. Several applications to the computational analysis of damage initiation and micro-cracking of common and piezoelectric polycrystalline aggregates under different loading conditions will be discussed. Examples about modelling damage initiation and evolution in composite unit cells will be presented. The developed tools could find profitable application in the multiscale analysis of polycrystalline and composite components as well as in the design of micro-electromechanical devices (MEMS). Despite the focus on some specific materials and techniques, the framework will highlight the essential features of general multiscale modeling of materials and structures. To engage the students, the course will be structured in three parts.

The first part will briefly introduce the main features of the overall frameworks, to provide a vision of the most recent applications of the employed techniques and motivate their use. The second part will make the students aware of the employed techniques by going into the details of boundary element formulations, traditionally not included in standard engineering courses, and illustrating their strengths for certain classes of problems; additionally, the main features of the virtual element method, a recently emerged generalization of the finite element method, will presented. The third part will reconsider the materials modelling framework and will focus on the inclusion of multi-physics and hybrid techniques for extended modelling capability and enhanced computational efficiency.

Teacher: professor Ivano Benedetti - Università degli studi di Palermo.

Course organised by the Department of Mechanical and Aerospace Engineering - DIMEAS of the Politecnico (Doctorate Research in Ingegneria Meccanica).