Lattice models applied to cyclic behavior description of quasi-brittle materials: Advantages of implicit integration.

Abstract : Comprehension and quantification of quasi-brittle materials behavior requires complex experiments when focusing on cyclic or multi-axial loadings. As an alternative, virtual testing, which can be computed using lattice discrete elements models (LDEM), is particularly interesting. LDEM already provide a physical description of the quasi-brittle materials behavior, but further attention has to be paid to numerical integration. LDEM are explicitly integrated, such integration has been proven in the literature to be accurate when cracking is involved, by means of efficient schemes such as the ``Saw-tooth'' algorithm. In order to extend the range of application of LDEM to more complex loading paths, such as compressive or cyclic loadings, involving contact and friction mechanisms, qualitativeness as well as quantitativeness of explicit integration has to be assessed anew. We hereby propose an implicit quasi-static integration scheme for LDEM based on specific non-linearities encountered in quasi-brittle materials, namely contact and fracture, to circumvent expected stability and accuracy issues. Efficiency of both schemes is investigated by means of simulations of a uniaxial cyclic test and a compression test.
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Maxime Vassaux, Benjamin Richard, Frédéric Ragueneau, Alain Millard, Arnaud Delaplace. Lattice models applied to cyclic behavior description of quasi-brittle materials: Advantages of implicit integration.. International Journal for Numerical and Analytical Methods in Geomechanics, Wiley, 2014, pp.43. ⟨10.1002/nag.2343⟩. ⟨hal-01177051⟩

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