Composite materials exhibit an internal structure ('microstructure') at the nano, micro or meso-levels, made of randomly or periodically distributed inclusions embedded into a generally continuous matrix and show complex non-linear behaviour, such as damage, plasticity, fracture, etc. This kind of complex materials, both innovative (fiber composites, nanostructured, bio-materials, porous or textured media) and traditional (concrete, masonry-like materials, etc.) have to meet the demand for high performance in different fields of engineering and technology. To this end, the investigation of the mechanical behaviour of composites, coupled with other concurrent physical phenomena, is mandatory, relying on effective constitutive and structural modelling and advanced numerical methods, especially in validation of real-life case studies.
It is widely recognized that important macroscopic material properties, such as stiffness and strength, are governed by processes occurring at one to several scales below the level of observation. A thorough understanding of how these processes influence the gross behaviour is key to the analysis and the design of existing and/or performance improved composite materials ('multiscale' analysis). A research team expert in the area of multiscale computational methods will drive the main Work Packages (WP) of the project, aiming at developing: (i) constitutive models suitable for taking account at the macroscopic level of the microscopic characteristics; (ii) computational tools as enhanced Finite Element formulations based on mixed-type variational functionals, interactive Multiphysics codes, Virtual Element Method; (iii) advanced tools for structural analysis and optimization of new buildings and for risk mitigation and reliability of Cultural Heritage; (iv) next-generation materials and devices for monitoring and control of vibration, dissipation and damage.
Focus of the research program ACM-MCM is the study of the mechanical behaviour of structures made of composites (ceramic/metal matrix (CMC/MMC), fibre reinforced, nanostructured, porous or textured, up to masonry-like materials) and the design of high performance materials, including reinforced mortar/concrete for consolidating historical masonry with bio-based fibres, which is an important case of application in the Mediterranean area. Main objective is developing of adequate constitutive models and strategies to connect different scales of descriptions for capturing the evolutionary behaviour of structures, using direct micro-modelling at the micro-scale and homogenization and concurrent/multi-domain approaches at the macroscale (multiscale modelling).
MULTISCALE METHODS AND HOMOGENISATION
The development of methodologies and conceptual directions of research for the description of complex materials, made of complex internal structure and complex constitutive behaviour (damage, plasticity, growth, ecc.) in terms of continuous models is a topic of crucial importance in material science and structural engineering. Multiscale models, by adopting various equivalence criteria, allow one to transfer information between gradually increasing descriptive scales (electronic/atomistic-micro-meso-macro) with always less defined level of detail (Ortiz and Philips 1999; Liu et al. 2006). Interest is directed to formulations of non-classical continua equivalent to heterogeneous continuous or discontinuous media at the microscopic scale (Trovalusci, Ostoja-Starzewski 2011; Trovalusci, Schrefler 2012; Trovalusci, 2014).
NON-CLASSICAL/NON-LOCAL CONTINUUM MODELLING
Classical continua (Cauchy) are inadequate for the study, even limited to the elastic range, of problems conditioned by the size of the heterogeneities, as it occurs in the presence of geometric and loading singularities which involve the onset of high stress and strain gradients (Trovalusci and Masiani, 2003, 2005; Trovalusci, Pau 2014). Difficulties arise when the characteristic dimension of the reference material is comparable with the size of the constituents, especially in the presence of softening which causes ill-conditioning of field equations and mesh dependency in numerical solutions (Mühlhaus, Vardoulakis, 1990; de Borst, 1992; Sluys et al., 1993).
A challenging solution, now favored by the development of experimental know how and numerical computational skills, must be deserved to non-local continuum formulations capable to properly preserve memory of the underlying microstructure (inclusions shape, size, orientation, texture) without sacrificing the benefits of the field description. It is useful to distinghuish between non-local models of 'explicit' (a) or 'implicit' (b) type (Kunin, 1982; Eringen, 1965, 1999). (a) Continua with INTERNAL VARIABLES (Coleman, Gurtin 1966), if endowed with internal lengths (Kröner, 1967; Eringen, 1983, 2002) have proved essential in describing plastic strains and/or damage phenomena (Addessi, 2014; Addessi Sacco 2015). (b) MULTIFIELD CONTINUA, i.e. continua with additional degrees of freedom (micromorphic, configurational, etc.; Mindlin 1962; Capriz, 1989; Eringen 1999, Gurtin 2000) with respect to the classical ones, are capable to retain memory of the underlying microstructure (inclusions shape, size, orientation, texture) avoiding physical inadequacies, as thermodynamic incompatibility (Trovalusci, 2015; Favata, Trovalusci, Masiani 2016), and the above mentioned theoretical/numerical drawbacks.
PROGRESS BEYOND THE STATE OF THE ART
The project aims to a significant contribution and a deeper insight to the theory of multifield continua in order to develop more reliable tools for the analysis of coarse scale problems dominated by microstructure, and in particular scale effects. Classical computational homogenization schemes based on the principle of separation of scales are in fact consistent with the standard local continuum mechanics concept, that essentially recalls the principle of local action and homogeneous deformation. When classical simple (Grade 1) models fail, internal length scales and dispersion properties casted within enhanced homogenization procedures are required. The applicability of non-classical continuum theories, however, is strictly connected to the development of constitutive models and numerical procedures, which for several years is undergoing a big propulsive boost especially within the framework of a non-linear computational multiscale approach (Trovalusci, Masiani, 2003, 2005; Forest, 2009; Geers et al., 2007; Addessi and Sacco, 2012; Trovalusci, 2014). Provided by constitutive information and specific strategies for numerical solutions, the multifield theoretical framework appears as one of the main promising challenges in the study of any kind of complex material, even when used for constructions.