FE·Meshless multiscale modeling of heterogeneous periodic materials

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The computational mutiscale modeling of periodic heterogeneous materials, characterized bythe assembly of units and joints, represents a compromise between the inaccuracy resulting fromthe macro modeling approach and the computational effort of the meso modeling.Assuming that the heterogeneities are orders of magnitude smaller than the structuredimensions, according to the multiscale approach, the macroscopic stresses and strains around acertain point can be found by averaging the stresses and the strains in a small representative part ofthe microstructure or a representative volume element (RVE) attributed to that point. A first-ordertwo-scale scheme has been used to model heterogeneous polymers [1] or masonry panels [2]. Themacroscopic strain is evaluated at each integration point and then is transferred to the RVE at themesoscale as essential boundary conditions (macro-meso scale transition). As a result of themesoscopic equilibrium problem, the RVE stress field is available and, by averaging it, themacroscopic stress is obtained (meso-macro scale transition). Thus, a new homogeneous materialis created without using complex closed form constitutive relation for the representation of itsbehavior. As the model is based on the use of two scales, two different numerical approaches areemployed: the finite element method at the macroscopic level and the meshless approach [3] at themesoscopic one. The meshless method involves the construction of an approximated function ofthe displacements field, based on the values obtained in correspondence to several nodes,arbitrarily chosen in the domain and with specific domains of influence. The moving least squareapproximation is adopted for the construction of this function. In the present work the RVE iscomposed by the aggregate and the surrounding adhesive joints, which are simulated by zerothicknessinterface models. The non linear behavior of the heterogeneous material results from theinelastic deformation mechanisms occurring at the interfaces, while the units behaves elastically.The interface laws are formulated in the framework of elastoplasticity in order to simulate thesoftening response which occurs along the decohesion process in presence of shear and tensiletractions. The elastoplastic model is developed in a thermodynamically context and for plane stressapplications. Numerical examples show the main features of the multiscale model and the noveltiesintroduced.
Lingua originaleEnglish
Numero di pagine1
Stato di pubblicazionePublished - 2013


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