An identification method to calibrate higher-order parameters in local second-gradient models

Abstract

A numerical method is presented for identifying the material parameters that appear in second-gradient models. For local second-gradient models, additional material parameters must be defined in numerical models. The objective of the present study is to develop a simple numerical identification procedure for these additional coefficients. The method combines modelling of laboratory tests with analytical implements. Numerical studies are then used to validate the method for a shale and to investigate the effects of both the internal length and the additional coefficients on the numerical responses. The procedure provides the first coherent results achieved at the laboratory scale.© 2015 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved. r é s u m é Une méthode numérique permettant d'identifier les paramètres matériaux spécifiques aux modèles second gradient est présentée. Pour les modèles second gradient locaux, des paramètres matériaux supplémentaires sont définis dans les modèles numériques. L'objectif est de développer une procédure d'identification numérique simple pour ces coefficients supplémentaires. La méthode combine la modélisation d'essais de laboratoire et des développements analytiques. Des études numériques permettent de valider la méthode sur une argile et d'investiguer les effets de la longueur interne et des coefficients supplémentaires sur la réponse numérique. La procédure fournit les premiers résultats cohérents à l'échelle du laboratoire.

Compaction Banding in High‐Porosity Carbonate Rocks: 2. A Gradient‐Dependent Plasticity Model

“…Thus, some assumptions must be set in order to restrict the general micromorphic model to the considered gradient model. Raude et al (2015) have presented the formulation of a “second gradient dilation model,” where the only additional degree of freedom is the first gradient of the volumetric strain ∇ ϵ v (see also Forest & Sievert, 2006). Here, a similar approach is presented but for a “third gradient dilation model.” To do so, only the volumetric quantities of the higher‐order stresses and of the kinematic variables are considered: and and …”

“…Nonetheless, few works have been dedicated to the calibration of higher‐order continua based on local measurements (e.g., for Cosserat continuum: Esin et al, 2017; Wang et al, 2016). A back analysis of the thickness of deformation bands as observed in element tests can give access to the material length of the underlying constitutive model (e.g., Raude et al, 2015). However, this procedure poorly constrains the calibrated higher‐order parameters since other model parameters influence the deformation band thickness and the slope of the softening branch of the stress‐strain curve.…”