Patrizia Trovalusci

Abstract:

The mechanical behaviour of complex materials, characterized by complex non-linear behavior and complex internal sub-structure (micro), strongly depends on their microstructural features. In particular, in the modelling of these materials, such as particle composites that are polycrystals with interfaces or with thin or thick interfaces, as well as rock or masonry-like materials, the discrete and heterogeneous nature of the matter must be taken into account. This is because interfaces and/or material internal phases dominate the gross behaviour. This is definitely ascertained. What is not completely recognized instead is the possibility of preserving the memory of the microstructure, and of the presence of material length scales, without resorting to the discrete modelling which can often be cumbersome in terms of non-local continuum descriptions. In the possibility of accounting for non-symmetries in strains and stresses, the classical Cauchy continuum (Grade1) does not always seem appropriate for describing the macroscopic behaviour while taking into account the size, the orientation and the disposition of the micro-heterogeneities. This occurs in the case of materials made of particles of prominent size and/or strong anisotropy anisotropic media which lack in-material internal scale parameters. This calls for the need of non-classical continuum descriptions [1, 2], that can be obtained through multiscale approaches, aimed at deducing properties and relations by bridging information at proper underlying sub-levels via energy equivalence criteria. In the framework of such a multiscale modelling, the non-local character of the description is then crucial for avoiding physical inadequacies and theoretical computational problems. In particular, there are problems in which a characteristic internal (material) length, l, is comparable to the macroscopic (structural) length, L [3]. Among non-local theories, it is useful to distinguish between 'explicit' or 'strong' and 'implicit' or 'weak' non-locality [4]. Implicit non-locality concerns generalize continua with extra degrees of freedom, such as micromorphic continua [1] or continua with configurational forces [2].
This talk wants firstly to focus on the origins of multiscale modelling, related to the corpuscular(molecular)-continuous models developed in the 19th century and to give explanations 'per causas' of elasticity (Cauchy, Voigt, Poincare). This is in order to find conceptual guidelines for deriving discrete-to scale-dependent continua that are essentially non-local models with internal length and dispersive properties [4, 5]. Then, a discrete-to-scale dependent continuous formulation, developed for particle composite materials, based on a generalized version of Voigt's molecular/continuum approach is proposed [6]. Finally, with the aid of some numerical simulations concerning ceramic matrix composites (CMC), and microcracked media and masonry assemblies, the focus will be on the advantages of micropolar modelling with respect to other generalized continuum formulations [7-9].

[1] Eringen, A.C. (1999), Microcontinuum Field Theories, Springer-Verlag, New York
[2] Gurtin, M. E. (2000), Configurational Forces as Basis Concept of Continuum Physics, Springer-Verlag, Berlin.
[3] Trovalusci P., Ed. (2016), Materials with Internal Structure. Multiscale and Multifield Modeling and Simulation, P. Trovalusci (Ed.), Springer Tracts in Mechanical Engineering, Vol.18:109-131, Springer.
[4] Trovalusci, P. (2014), Molecular approaches for multifield continua: origins and current developments. CISM (Int. Centre for Mechanical Sciences) Series, 556: 211-278, Springer.
[5] Trovalusci, P., Capecchi, D., Ruta, G. (2009), Genesis of the multiscale approach for materials with microstructure, Archive of Applied Mechanics, 79(11): 981-997.
[6] Trovalusci, P., Varano, V., Rega, G. (2010), A generalized continuum formulation for composite materials and wave propagation in a microcracked bar, Journal of Applied Mechanics, 77(6):061002/1-11.
[7] Trovalusci, P., Pau, A. (2014), Derivation of microstructured continua from lattice systems via principle of virtual
works. The case of masonry-like materials as micropolar, second gradient and classical continua. Acta Mechanica,
225(1):157-177
[8] Fantuzzi, N., Trovalusci P., Dharasura S. (2019), Mechanical behaviour of anisotropic composite materials as micropolar continua, Frontiers, 59 (6):1-11 (https://doi.org/10.3389/fmats.2019.00059).
[9] Settimi, V., Trovalusci, P., Rega, G. (2019), Dynamical properties of a composite microcracked bar based on a generalized continuum formulation, Continuum Mechanics and Thermodynamics, 1-18. (DOI: 10.1007/s00161-019-00761-7)