Multiscale Modelling of Complex Materials
May 21, 2012 — May 25, 2012
- Tomasz Sadowski (Lublin University of Technology, Poland)
- Patrizia Trovalusci ("Sapienza" University of Rome, Italy)
Various types of complex materials, made of very different constituents, are used nowadays in engineering practice. The most important of these are fibrous composites, laminates and heterogeneous multiphase materials with an intricate internal structure including: porosity, reinforcement in the form of short fibres and particles of various properties, shapes and sizes, filled in different media. It is widely recognized that important macroscopic properties like the macroscopic stiffness and strength are governed by multiphysics processes (e.g. damage due to heat transfer or fluid penetration) that occur at one to several scales below the level of observation. A thorough understanding of how these processes influence the reduction of stiffness and strength, is the key both to the analysis of existing, and to the design of improved, complex materials.
The course will bring together experts dealing with materials science, theoretical mechanics, experimental and computational techniques at multiple scales and will provide a sound base and a framework for many applications that are hitherto treated in a phenomenological sense.
The aim of this course is to present a series of lectures by researchers specialized in multiscale and multiphysics modelling and the simulation of complex materials. The basic principles of multiscale modelling strategies will be formulated with reference to modern complex multiphase materials subjected to various types of mechanical and thermal loadings, and to environmental effects. Since the mechanical behaviour plays a central role, the focus will be on problems where mechanics is highly coupled with other concurrent physical phenomena.
The study of how these various length scales and multiphysical processes can be bridged or taken into account simultaneously is particularly relevant for complex materials, because they have a well-defined structure at the nano, micro and meso-levels. For this reason, advances in multiscale modelling and analysis made here, are directly applicable to classes of materials which either have a wider (possibly fractal) range of relevant microstructural scales, such as metals, or have a random microstructures, e.g. cementitious composites.
In order to achieve a comprehensive description of the multiscale phenomena, not directly related to the design of high performance materials, attention will also be focused on the foundations of continuum mechanics currently adopted to model non-classical continua with a substructure, for which internal length scales play a crucial role. This is particularly so for some specific continua, such as second gradient, micropolar, or other multifield media. A special class of continua, characterized by displacement fields discontinuous on singular surfaces and by a cohesive energy defined on the discontinuity set, will be presented as an example of how phenomena occurring at the microscale may strongly influence the macroscopic response. Finally, using variational techniques based on energy minimization, it will be shown how a cohesive model can describe a large class of material responses, including fracture, damage and plasticity.
KEYWORDS: Composite materials, multiscale modelling, computational techniques, ductile fractures.