Main Topics :

• General concepts for second and higher gradient media
• Phenomenology of existing and designed composites and metamaterials
• Homogenization techniques and related numerical and mathematical problems
• Beams and plates constituted by metamaterials
• Strain and stress localization phenomena
• Dynamic behavior of metamaterials and composites
• Acoustic properties of metamaterials and composites
• Generalized continua in Biomechanics and mechanics of growing tissues
• Damage and fracture in generalized continua

Scope and Description

New trends about the theoretical models will be discussed and the debate on the issues raised by the design of composites and metamaterials will be encouraged. Indeed many emerging problems  are to be confronted in this highly promising and novel research field. The colloquium will address primarily the following:

1. to identify the effective micro-macro identification procedure allowing for the characterization of suitable macro-models for complex microstructured metamaterials and composites
2. to determine the methods for finding those microstructures which are able to produce a given class of macroscopic behavior
3. to find the most interesting technological and engineering applications for the designed metamaterials and composites
4. to guide towards the formulation of new mathematical problems and numerical methods auxiliary to the conceived applications

While being particularly suitable to model natural materials, nowadays classical continuum models have a limited scope of predictivity where metamaterials and composites are concerned. Therefore, in order to describe some new and interesting (maybe not yet observed) phenomena,  generalized continua need to be introduced.

Keeping in mind the application of macroscopic models to the development of newly and especially designed technological artefacts, many open problems need to be confronted. The most important of these involves the identification of macroscopic constitutive parameters in terms of microscopic properties of considered systems: the homogenization procedures proposed up to now present serious theoretical drawbacks and need to be refined. The impact of the underlying microstructure on macro-crack formation and propagation is investigated in porous metals for ductile fracture but also in quasi-brittle materials. There is still no consensus for the determination of higher order elastic or nonlinear properties from the detailed geometry of the unit cell of composites. Techniques are competing in this endeavor and their efficiency may be decisive to convincingly address instability and fracture problems of heterogeneous materials.

Important applications of the models using generalized continua are to be found in the design of metamaterials to be used in biomechanics, mechanics of growing tissues, phase transition, damage and fracture theories, strain and stress concentration phenomena, granular mechanics and geo-mechanics. A special and particularly important application field is that represented by the design of acoustic metamaterials, artificially fabricated in order to control, direct, and manipulate every form of sound may it be in the form of sonic, ultrasonic or infrasonic waves propagating in solids, liquids or gases.

A large modeling effort is being demanded by the discovery of ever more interesting phenomena: only recently it was demonstrated how to synthesize a composite medium exhibiting negative effective bulk modulus, negative effective mass density, or both properties. Of course the principle of conservation of energy implies that in these materials the ‘exotic’ behavior is limited to a given class of states, in which a suitably and previously stored (in some hidden degrees of freedom) quantity of energy, can be ‘given back’. Also recently, new meta-materials were conceived which despite showing the overall aspect and behavior of solids, in some regimes behave mechanically like a fluid.

Other current applications deal with the development of micromechanical techniques to derive the effective properties of generalized continua as a function of the local properties and geometry of composite materials. These new methods are oriented not only towards elastic behavior but also towards plasticity and damage because the generalized continua can provide a better description of the instability phenomena including buckling, shear banding and damage or crack propagation in heterogeneous materials. Gradient models were often used in the past based on a purely phenomenological treatment of regularization procedure. A new generation of micro-structurally informed generalized continua is emerging especially in the context of plasticity such as crystal plasticity and damage such as in quasi-brittle or ductile materials. In this context, phase field models coming from the physics community can be interpreted in the framework of generalized continua and both approaches can benefit from each other for a more efficient description of fracture phenomena.