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

Abstract

The description of the mechanical behaviour of brick/block masonry through equivalent continua is presented here as a paradigmatic example of the problem of gross modelling of discontinuous and heterogeneous materials as continua with microstructure. The approaches reported in the literature differ for the way identification of the continuum is carried out or the nature of the continuum itself. In this paper, continuous models equivalent to rigid particle systems with free or constrained rotations are derived within the general framework of the principle of virtual work. In particular, an integral equivalence procedure is used to derive micropolar, second gradient and classical models. The non-classical models have in the field equations non-standard kinematic and static descriptors accounting for the presence of the material internal structure. The differences in the material responses of the various continua are identified referring to their internal work formulas. For the reference material, it is shown that, unlike the Cauchy continuum, both micropolar and second gradient models are effective in the presence of load and geometrical singularities, which involve significant scale effects on the material response. On the other hand, the second gradient model, as well as the classical model, disregards the role of relative rotation between the local rigid rotation (macrorotation) and the microrotation, which is related to the presence of non-symmetric strains. This circumstance, significant in strongly anisotropic systems, allow us to point out the advantages of the micropolar modelling especially for orthotropic masonry assemblies made of elements of any size. These statements are discussed by means of selected numerical examples of masonry panels differing in size, shape and arrangement, under shear loading conditions. © 2013 Springer-Verlag Wien

Particulate random composites homogenized as micropolar materials

“…This implies that the micropolar effects cannot be neglected in the presence of non-symmetric strain and shear effects. Like in the extensively investigated case of anisotropic periodic materials [18,24], further confirmations of the suitability of micropolar model are expected with the investigation of media with particles of different shapes and also with the investigation of non-linear constitutive behaviors.…”

Continuous and discrete models for masonry like material: A critical comparative study

“…For micropolar continuum see for example Masiani et al (1995), Masiani and Trovalusci (1996), Boutin (1996), Sulem and Mühlhaus (1997), Smyshlyaev and Cherednichenko (2000), Forest et al (2001), Casolo (2009), Salerno and De Felice (2009), Addessi et al (2010), De Bellis and Addessi (2011) and Pau and Trovalusci (2012). For higher order continuum see for example Stefanou et al (2010), Bacigalupo and Gambarotta (2012) and Trovalusci and Pau (2014).…”

“…In this section the works of Salerno and De Felice (2009), Pau and Trovalusci (2012) and Trovalusci and Pau (2014) are chosen as benchmark. In these papers the problem of Cauchy and micropolar equivalent continua is dealt with.…”

A multiphysics and multiscale approach for modeling microcracked thermo-elastic materials

“…In [54], it is shown that the virtual power format can be so generalized as to deduce the balance laws of three-dimensional thermomechanics. On the other side, in [70,77] it has been shown that the Principle of Virtual Powers (PVP) can be expedient to perform coarse-graining procedures in the framework of the homogenization techniques. These corpuscular-continuous approaches are based on the assumption that a selected microscopic level structure of matter can be described as discontinuous, and that the transition from the coarse scale is governed by an a priori map between the large set of degrees of freedom od discrete systems and the deformation fields of the continuum.…”

“…A model within the framework of generalized continuum mechanics, as the one we propose, may be computationally efficient, provided that a proper physical meaning of the additional fields is proposed and a constitutive identification for the internal and the external actions is performed [74,64,69,4,27,51,5,2,77]. In the present model, on the purely mechanical side, in addition to the standard displacement field, we consider a kinematical microstructural field, representing the mean jump of the displacement field due to the presence of microcracks; on the thermal side, we not only consider the thermal displacement, a nonstandard thermal state variable firstly considered by Helmholtz, but we also introduce an additional microstructural kinetic variable, whose time derivative represents the mean jump of the temperature field due to the presence of microcracks, and that we can call microtemperature.…”