![]() ![]() This chapter covers the computational homogenization of periodic architectured materials in elasticity and plasticity, as well as the homogenization and representativity of random architectured materials.Įlektrische Maschinen und Motoren sind in unserem heutigen Leben allgegenwärtig und Bestandteil vieler Gebrauchsgüter sowie zentrales Betriebsmittel für die Produktion in Industrie und Gewerbe. Furthermore, computational homogenization is the basis for computational topology optimization which will give rise to the next generation of architectured materials. Homogenized behavior of architectured materials can thus be used in large structural computations, hence enabling the dissemination of architectured materials in the industry. As a matter of fact, one engineering challenge is to predict the effective properties of such materials computational homogenization using finite element analysis is a powerful tool to do so. The present chapter aims at providing such models, in the case of mechanical properties. Indicators of geometrical and mechanical percolation, especially relevant for connected microstructures, are proposed and estimated using 3D image analysis.Īrchitectured materials involve geometrically engineered distributions of microstructural phases at a scale comparable to the scale of the component, thus calling for new models in order to determine the effective properties of materials. This is due to a different percolation behaviour of the hard phase in the materials, which is investigated in the last section of the article. In particular, material A is twice as stiff as material B. Numerical predictions of the effective properties using simulations on a large number of subdomains extracted from the samples with periodic boundary conditions are in satisfactory agreement with available experimental results. The samples of material A are found to be representative, whereas at least twice as large sample volumes would be necessary to predict the properties of material B with a precision of 5%. A numerical and statistical computational homogenization methodology first proposed for random models of microstructures in is extended here to the case of real microstructures in order to estimate the size of representative volume elements (RVE) for both materials. Direct simulations on the entire samples show that KUBC and SUBC provide strongly different apparent properties, which rises the question of the representativity of the samples. For that purpose, finite element simulations based on explicit meshing of the microstructures are performed on six samples of the materials, with different boundary conditions: kinematic uniform (KUBC), stress uniform (SUBC) and periodic boundary conditions. It does not store any personal data.Three-dimensional confocal images of two materials A and B from food industry made of two constituents with highly contrasted properties, having the same volume fraction but different morphologies, are used to estimate their effective elastic and thermal properties. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. The cookie is used to store the user consent for the cookies in the category "Performance". This cookie is set by GDPR Cookie Consent plugin. The cookies is used to store the user consent for the cookies in the category "Necessary". ![]() The cookie is used to store the user consent for the cookies in the category "Other. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". The cookie is used to store the user consent for the cookies in the category "Analytics". These cookies ensure basic functionalities and security features of the website, anonymously. Necessary cookies are absolutely essential for the website to function properly. ![]()
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