2018
DOI: 10.1016/j.ijsolstr.2018.03.020
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Mori–Tanaka estimates of the effective elastic properties of stress-gradient composites

Abstract: A stress-gradient material model was recently proposed by Forest and Sab [Mech. Res. Comm. 40, 16-25, 2012] as an alternative to the well-known strain-gradient model introduced in the mid 60s. We propose a theoretical framework for the homogenization of stress-gradient materials. We derive suitable boundary conditions ensuring that Hill-Mandel's lemma holds. As a first result, we show that stress-gradient materials exhibit a softening size-effect (to be defined more precisely in this paper), while strain-gradi… Show more

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Cited by 30 publications
(42 citation statements)
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“…Several works have successfully applied the Monte Carlo method to take account of randomness in mechanics. 8388 The main idea of the Monte Carlo method is to reproduce the output responses a certain number of times by randomly choosing values of the input variables in the input space. 84 , 89 That way, fluctuations in each sub-space in the input space can be entirely propagated to the output response through the model mapping.…”
Section: Methodsmentioning
confidence: 99%
“…Several works have successfully applied the Monte Carlo method to take account of randomness in mechanics. 8388 The main idea of the Monte Carlo method is to reproduce the output responses a certain number of times by randomly choosing values of the input variables in the input space. 84 , 89 That way, fluctuations in each sub-space in the input space can be entirely propagated to the output response through the model mapping.…”
Section: Methodsmentioning
confidence: 99%
“…are introduced, see also [33]. Furthermore, (right-) gradient and (right-)divergence operators are denoted as r ð Þ and r Á ð Þ, respectively.…”
Section: Notationmentioning
confidence: 99%
“…Motivated by the theoretical developments of the stress gradient theory presented in [14,31,33], a symmetric positive definite quadratic form for the generalised stress energy density function is assumed…”
Section: Materials Modelmentioning
confidence: 99%
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“…In the first part of the talk, he presented the mathematical formulation of the model and the related physical interpretation. Then, he briefly showed the solution to Eshelby's spherical inhomogeneity problem and derived the Mori-Tanaka estimates of the effective properties of stress-gradient composites with spherical inclusions [40].…”
Section: Formulations Of Generalized Continuum Modelsmentioning
confidence: 99%