A multiscale description of particle composites: From lattice microstructures to micropolar continua

Trovalusci, Patrizia; Bellis, Maria Laura De; Masiani, Renato

doi:10.1016/j.compositesb.2017.06.015

Cited by 47 publications

(30 citation statements)

References 49 publications

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“…In bottom-up homogenization approaches one seeks to derive macroscopic, effective materials properties through averaging the micro-heterogeneous material response over a representative volume element (RVE). In the context of the homogenization of a lattice or beam model towards a higher-order continuum on the macro scale this was done for example by Askar and Cakmak (1968); Bažant and Christensen (1972); Dos Reis and Ganghoffer (2012); Kumar and McDowell (2004); Nady et al (2017); Trovalusci et al (2017). We note that these methods may be problematic in structurally disordered materials which exhibit strongly heterogeneous stress and strain patterns with long-range correlations.…”

Section: Discussionmentioning

confidence: 99%

Determining Cosserat constants of 2D cellular solids from beam models

Liebenstein

Zaiser

2018

Mater Theory

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We present results of a two-scale model of disordered cellular materials where we describe the microstructure in an idealized manner using a beam network model and then make a transition to a Cosserat-type continuum model describing the same material on the macroscopic scale. In such scale transitions, normally either bottom-up homogenization approaches or top-down reverse modelling strategies are used in order to match the macro-scale Cosserat continuum to the micro-scale beam network. Here we use a different approach that is based on an energetically consistent continuization scheme that uses data from the beam network model in order to determine continuous stress and strain variables in a set of control volumes defined on the scale of the individual microstructure elements (cells) in such a manner that they form a continuous tessellation of the material domain. Stresses and strains are determined independently in all control volumes, and constitutive parameters are obtained from the ensemble of control volume data using a least-square error criterion. We show that this approach yields material parameters that are for regular honeycomb structures in close agreement with analytical results. For strongly disordered cellular structures, the thus parametrized Cosserat continuum produces results that reproduce the behavior of the micro-scale beam models both in view of the observed strain patterns and in view of the macroscopic response, including its size dependence.

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Section: Discussionmentioning

confidence: 99%

Determining Cosserat constants of 2D cellular solids from beam models

Liebenstein

Zaiser

2018

Mater Theory

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“…The micropolar modeling of lattices does not usually employ mid-surface kinematics (see, e.g. [33][34][35]).…”

Section: Introductionmentioning

confidence: 99%

Two-scale constitutive modeling of a lattice core sandwich beam

Karttunen

Reddy

Romanoff

2019

Composites Part B: Engineering

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Constitutive equations are derived for a 1-D micropolar Timoshenko beam made of a web-core lattice material. First, a web-core unit cell is modeled by discrete classical constituents, i.e., the Euler-Bernoulli beam finite elements (FE). A discrete-to-continuum transformation is applied to the microscale unit cell and its strain energy density is expressed in terms of the macroscale 1-D beam kinematics. Then the constitutive equations for the micropolar web-core beam are derived assuming strain energy equivalence between the microscale unit cell and the macroscale beam. A micropolar beam FE model for static and dynamic problems is developed using a general solution of the beam equilibrium equations. A localization method for the calculation of periodic classical beam responses from micropolar results is given. The 1-D beam model is used in linear bending and vibration problems of 2-D web-core sandwich panels that have flexible joints. Localized 1-D results are shown to be in good agreement with experimental and 2-D FE beam frame results.

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“…In order to overcome these drawbacks, multiscale techniques, based on homogenization approaches, are a very valuable tool to gather both a synthetic and thorough description of the complex material behaviour. The investigation of the overall static and dynamic behaviour of periodic elastic composite materials has been performed resorting either to asymptotic approaches (Bakhvalov and Panasenko, 1984;Gambin and Kröner, 1989;Allaire, 1992;Boutin, 1996;Fish and Chen, 2001;Andrianov et al, 2008;Tran et al, 2012;Bacigalupo, 2014), or to variational-asymptotic approaches (Smyshlyaev and Cherednichenko, 2000;Peerlings and Fleck, 2004;Bacigalupo andGambarotta, 2012, 2014), or also to identification techniques, among which computational approaches (Forest and Sab, 1998;Kouznetsova et al, 2004;Kaczmarczyk et al, 2008;Bacigalupo and Gambarotta, 2010;De Bellis and Addessi, 2011;Li et al, 2011;Addessi et al, 2013;Lesičar et al, 2014;Trovalusci et al, 2015;Addessi et al, 2016;Biswas and Poh, 2017;Reccia et al, 2018;Trovalusci et al, 2017) and analytical approaches (Bigoni and Drugan, 2007;Mühlich et al, 2012;Bacca et al, 2013a,b;Bacigalupo and Gambarotta, 2013;Bacigalupo et al, 2017;Hütter, 2017). Generalized homogenization approaches have been proposed to date to handle multi-field problems, ranging from thermo-elastic, thermo-diffusive, to piezoelectric and thermo-piezoelectric problems (Gałka et al, 1996;Pettermann and Suresh, 2000;…”

Section: Introductionmentioning

confidence: 99%

Characterization of hybrid piezoelectric nanogenerators through asymptotic homogenization

Bellis

Bacigalupo

Zavarise

2019

Computer Methods in Applied Mechanics and Engineering

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In the framework of energy scavenging for applications in flexible/strechable electronics, hybrid piezoelectric nanogenerators, made up with Zinc oxyde nanorods, embedded in a polymeric matrix, and growth on a flexible polymeric support, are investigated. The ZnO nanorods are arranged in clusters, forming nearly regular distributions, so that periodic topologies can be realistically assumed. Focus is on a dynamic multi-field asymptotic homogenization approach, proposed to grasp the overall constitutive behaviour of such complex microstrutcures. A set of applications, both in static and dynamic regime, is proposed to explore different design paradigms, related to nanogenerators based on three working principles. Both extension and bending nanogenerators are, indeed, analysed, considering either extension along the nanorods axis, or orthogonally to it. The study of the wave propagation is, also, exploited to comprehend the main features of such piezoelectric devices in the dynamic regime. 2017;Liu et al., 2018;Askari et al., 2019). Relevant examples concern either the use of piezoelectric zinc oxide (ZnO) nanowire arrays grown on conductive rigid supports (Yi et al., 2005;Wang and Song, 2006), or the adoption of lead zirconate titanate (PZT), polyvinylidene fluoride (PVDF) and barium titanate (BT). An important improvement in the design of ZnO nanorods-based piezoelectric generators has been achieved by adopting flexible substrates made of electro-active polymeric materials. The main advantage is, indeed, the possibility of exploiting relevant flexural mechanisms, besides the standard direct compression of the device. In Fan et al. (2016) different typologies of flexible nanogenerators are presented and critically commented. Also patterned growth of ZnO nanowires can be exploited to enhance the performances of flexible nanogenerators, as discussed in Yang et al. (2017). Further benefits can be obtained by resorting to so-called hybrid nanogenerators, made up by embedding the ZnO nanorods within a polymeric matrix. More specifically, Stassi et al. (2015) propose highly oriented ZnO nanotubes in a porous polycarbonate (PC) matrix. The result is an efficient nanogenerator based on such a highly flexible ZnOPC composite. Moreover, in Choi et al. ( 2017) a hybrid piezoelectric structure made of ZnO nanowires and a matrix of PVDF polymer is investigated in order to obtain a power enhancement. The authors, indeed, find that the ZnO nanowires are able to deliver internal strain to the PVDF, which increase the electrical power output of the hybrid nanogenerator. Based on the aforementioned considerations, with the aim of energy harvesting from green and sustainable energy resources, our focus is on hybrid flexible nanogenerators, made up with clusters of ZnO nanorods embedded into a polymeric matrix and growth on a flexible support. The choice of ZnO nanorods, is motivated by their relatively simple forming processes using low temperature. In particular, by exploiting innovative growth techniques, it is possible to synthesi...

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A multiscale description of particle composites: From lattice microstructures to micropolar continua

Cited by 47 publications

References 49 publications

Determining Cosserat constants of 2D cellular solids from beam models

Determining Cosserat constants of 2D cellular solids from beam models

Two-scale constitutive modeling of a lattice core sandwich beam

Characterization of hybrid piezoelectric nanogenerators through asymptotic homogenization

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