A multifield model for blocky materials based on multiscale description

Abstract

A multiscale approach to model the mechanical behaviour of blocky materials that exhibit microscale features is proposed. From the description of these materials at microscopic level, as systems of interacting rigid elements, a formula for the stored energy is given in order to derive the macroscopic constitutive equations of a linear elastic equivalent multifield continuum. This continuum results. to be a micropolar continuum suitable to describe the mechanical behaviour of brick/block masonry, as well as jointed rocks or matrix/particle composites, accounting for the size, the orientation and the arrangement of the elements. This multiscale approach proves to be effective also in the non-linear framework. The material non-linear behaviour is represented through internal constraints derived from delimitations imposed to the interactions of the block system. Some numerical examples show the correspondence between discrete and continuum modelling, both in the linear and in the non-linear frame. (c) 2005 Elsevier Ltd. All rights reserved

Genesis of the multiscale approach for materials with microstructure

“…Such formulations become significant in problems in which macroscopic length scales are comparable to material internal length scales and the field equations for the classical continuum become ill-posed. In this regard, various homogenization techniques, also addressed to numerical simulations, have also been developed within the framework of micromorphic materials [19][20][21][22][23][24][25] or other multifield materials [26][27][28][29].…”

Macroscale modelling of microstructure damage evolution by a rigid body and spring model

“…Modelling the mechanical degradation when the effects at the microstructure level entail taking the local rotation of the blocks and the orthotropy of shear strength into account is the focus of this contribution. To do this, the main hypothesis of the proposed constitutive model is that the damage evolution can be described using a limited number of mesoscale mechanisms that are strictly related with the internal microstructure geometry [Malyszko 2005;Trovalusci and Masiani 2005] (ii) (iii) (iv) (v) (i) Figure 4. Heuristic description of the five types of damage mechanism considered at the mesoscale.…”

“…Dealing with regular textures, the micro/macroscale transition can thus be performed toward an enriched generalised continuum, which retains some information on the microstructure and internal length [Masiani et al 1995;Sulem and Mühlhaus 1997;Forest and Sab 1998]. More recently, the relationship between the micro and macroscale for the specific case of masonry-like periodic rigid block assemblies has also been handled by resorting to a multiscale strategy [Trovalusci and Masiani 2005;Brasile et al 2007]. …”

Static analysis of masonry vaults, constitutive model and numerical analysis

“…A comparison among different models of this type can be found in [Genna et al 1998], and an application to the study of vaults is presented in [Theodossopoulos et al 2002]. Many models have been proposed that, by using homogenization techniques, allow one to take into account the masonry texture, their application is in general limited to the study of panels [Luciano and Sacco 1997;Maier et al 1992;Trovalusci and Masiani 2005].…”