Discrete to scale-dependent continua for complex materials: A generalized voigt approach using the virtual power equivalence

The mechanical behaviour of complex materials, characterized at finer scales by the presence of heterogeneities of significant size and texture, strongly depends on their microstructural features. By lacking in material internal scale parameters, the classical continuum does not always seem appropriate for describing the macroscopic behaviour of such materials, taking into account the size, the orientation and the disposition of the heterogeneities. This often calls for the need of non-classical continuum descriptions, which can be obtained through multiscale approaches aimed at deducing properties and relations by bridging information at different levels of material descriptions. Current researches in solid state physics as well as in mechanics of materials show that energy-equivalent continua obtained by defining direct links with lattice systems, as widely investigated by the corpuscular-continuous approaches of nineteenth century, are still among the most promising approaches in material science. The aim is here to point out the suitability of adopting discrete to scale-dependent continuous models, based on a generalization of the so-called Cauchy-Born (Voigt) rule used in crystal elasticity and in classical molecular theory of elasticity, in order to identify continua with additional degrees of freedom (micromorphic, multifield, etc.) which are essentially non-local models with internal length and dispersive properties. It is shown that, within the general framework of the principle of virtual powers, the correspondence map relating the finite number of degrees of freedom of discrete models to the continuum kinematical fields provides a guidance on the choice of the most appropriate continuum approximation for heterogeneous media. Some applications of the mentioned approach to ceramic matrix composites and masonry-like materials are discussed

The “question of the technique”: from the designing idea to the realized form

This work aims at focusing the inner relationship between the formal intuition of the design process and the structural/technological boundaries behind the creation of any architectural constructed form. Through the analysis of some noteworthy architectural examples, we highlight the reasons for which their designers achieved a virtuous equilibrium between shape, design and constructive awareness. In a contemporary era in which the major architectural production seems more interested to show off and amaze the spectators with huge scales and charming contaminations from the entertainment industry, a call for the need of the Vitruvian lesson appears essentials: the more we push our creativity as designers, the more we need to keep it firmly stick to the principles of firmitas, utilitas and venusta

Scale effects in orthotropic composite assemblies as micropolar continua: A comparison between weak-and strong-form finite element solutions

The aim of the present work was to investigate the mechanical behavior of orthotropic composites, such as masonry assemblies, subjected to localized loads described as micropolar materials. Micropolar models are known to be effective in modeling the actual behavior of microstructured solids in the presence of localized loads or geometrical discontinuities. This is due to the introduction of an additional degree of freedom (the micro-rotation) in the kinematic model, if compared to the classical continuum and the related strain and stress measures. In particular, it was shown in the literature that brick/block masonry can be satisfactorily modeled as a micropolar continuum, and here it is assumed as a reference orthotropic composite material. The in-plane elastic response of panels made of orthotropic arrangements of bricks of different sizes is analyzed herein. Numerical simulations are provided by comparing weak and strong finite element formulations. The scale effect is investigated, as well as the significant role played by the relative rotation, which is a peculiar strain measure of micropolar continua related to the non-symmetry of strain and work-conjugated stress. In particular, the anisotropic effects accounting for the micropolar moduli, related to the variation of microstructure internal sizes, are highlighted

Editorial

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Multi-scale and multi-physics modelling for complex materials

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A Study on the Effect of Doping Metallic Nanoparticles on Fracture Properties of Polylactic Acid Nanofibres via Molecular Dynamics Simulation

All-atom molecular dynamics simulations are conducted to elucidate the fracture mechanism of polylactic acid nanofibres doped with metallic nanoparticles. Extensional deformation is applied on polymer nanofibres decorated with spherical silver nanoparticles on the surface layer. In the ob-tained stress–strain curve, the elastic, yield, strain softening and fracture regions are recognized, where mechanical parameters are evaluated by tracking the stress, strain energy and geometrical evolutions. The energy release rate during crack propagation, which is a crucial factor in fracture mechanics, is calculated. The results show that the presence of doping nanoparticles improves the fracture properties of the polymer nanofibre consistently with experimental observation. The na-noparticles bind together polymer chains on the surface layer, which hinders crack initiation and propagation. The effect of the distribution of nanoparticles is studied through different doping decorations. Additionally, a discussion on the variation of internal energy components during uniaxial tensile loading is provided to unravel the deformation mechanism of nanoparticle-doped nanofibres

Mechanical Behavior of Anisotropic Composite Materials as Micropolar Continua

The macroscopic behavior of materials with anisotropic microstructure described as micropolar continua is investigated in the present work. Micropolar continua are characterized by a higher number of kinematical and dynamical descriptors than classical continua and related stress and strain measures, namely the micro-rotation gradient (curvature) and the relative rotation with their work conjugated counterparts, the micro-couple, and the skew-symmetric part of the stress, respectively. The presence of such enriched strain and stress fields can be detected especially when concentrated forces and/or geometric discontinuities are present. The effectiveness of the micropolar model to represent the mechanical behavior of materials made of particles of prominent size has been widely proved in the literature, in this paper we focus on the capability of this model to grossly capture the behavior of anisotropic solids under concentrated loads for which the relative strain, that is a peculiar strain measure of the micropolar model, can have a salient role. The effect of material anisotropy in the load diffusion has been investigated and highlighted with the aid of numerical parametric analyses, performed for two dimensional bodies with increasing degrees of anisotropy using a finite element approach specifically conceived for micropolar media with quadratic elements implemented within Comsol Multiphysics© framework. The present studied cases show that a significant diffusion and redistribution of the load is due to an increasing in the level of material anisotropy

Material Symmetries in Homogenized Hexagonal-Shaped Composites as Cosserat Continua

In this work, material symmetries in homogenized composites are analyzed. Composite materials are described as materials made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry described by a limited set of parameters. The purpose of this study is to analyze different geometrical configurations of the assemblies corresponding to various material symmetries such as orthotetragonal, auxetic and chiral. The problem is investigated through a homogenization technique which is able to carry out constitutive parameters using a principle of energetic equivalence. The constitutive law of the homogenized continuum has been derived within the framework of Cosserat elasticity, wherein the continuum has additional degrees of freedom with respect to classical elasticity. A panel composed of material with various symmetries, corresponding to some particular hexagonal geometries defined, is analyzed under the effect of localized loads. The results obtained show the difference of the micropolar response for the considered material symmetries, which depends on the non-symmetries of the strain and stress tensor as well as on the additional kinematical and work-conjugated statical descriptors. This work underlines the importance of resorting to the Cosserat theory when analyzing anisotropic materials

New insights on homogenization for hexagonal-shaped composites as Cosserat continua

In this work, particle composite materials with different kind of microstructures are analyzed. Such materials are described as made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry is described by a limited set of parameters. Three different textures are analyzed and static analyses are performed for a comparison among the solutions of discrete, micropolar (Cosserat) and classical models. In particular, the displacements of the discrete model are compared to the displacement fields of equivalent micropolar and classical continua realized through a homogenization technique, starting from the representative elementary volume detected with a numeric approach. The performed analyses show the effectiveness of adopting the micropolar continuum theory for describing such materials

Computational approach for form-finding optimal design

In this paper, an optimization strategy for a canopy, based on computational modelling approaches is presented. The design approach is applied to a realistic roof structure of an ecological island (waste collection centre) and has been completely redesigned with the aid of a Genetic Algorithm and a Dynamic Relaxation Algorithm. The preliminary design of the roof structure can be formulated as a shape optimization problem, involving functional needs and constraints at different scales of the structure. The proposed hypothesis solution was studied by using an optimization procedure through algorithms in the software Rhinoceros3D®/Grasshopper®. The main aim of this work is to explore different modelling approaches for form-finding that can be built from the use of numerical simulations based on algorithms. To this aim, the need to meet various requirements (structural, functional, formal) involving a team of architects and engineers can be interpreted as a matter of structural optimizatio