Second gradient poromechanics

By G. Sciarra, Francesco dell'Isola, O. Coussy. 2007

174 citations recorded by the source corpus.

Second gradient theories have been developed in mechanics for treating different phenomena as capillarity in fluids, plasticity and friction in granular materials or shear band deformations. Here, there is an attempt of formulating a second gradient Biot like model for porous materials. In particular the interest is focused in describing the local dilatant behaviour of a porous material induced by pore opening elastic and capillary interaction phenomena among neighbouring pores and related micro-filtration phenomena by means of a continuum microstructured model. The main idea is to extend the classical macroscopic Biot model by including in the description second gradient effects. This is done by assuming that the surface contribution to the external work rate functional depends on the normal derivative of the velocity or equivalently assuming that the strain work rate functional depends on the porosity and strain gradients. According to classical thermodynamics suitable restrictions for stresses and second gradient internal actions (hyperstresses) are recovered, so as to determine a suitable extended form of the constitutive relation and Darcy's law. Finally a numerical application of the envisaged model to one-dimensional consolidation is developed; the obtained results generalize those by Terzaghi; in particular interesting phenomena occurring close to the consolidation external surface and the impermeable wall can be described, which were not accounted for previously.

Subfields: Biomedical Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0110785ebbff470f0e376ffe72851ae9bfcab975

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In Biomedical Engineering

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof (2015, background): “, [36–38]) whose study is by now within the possibilities of modern computational tools and thus theoretically even more relevant than in the past.”
Reflection and transmission of plane waves at surfaces carrying material properties and embedded in second-gradient materials (2014, background): “[17], [25], [26] for mechanical and electromagnetic interactions or [50], [49], [48], [48], [51] for interactions between fluid flow and a deformable porous matrix).”
Strain gradient and generalized continua obtained by homogenizing frame lattices (2018, background): “(see for instance [81], [69], [3], [4], [55], [75], [85]).”
Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids (2013, unknown): “[134, 135, 136], Quiligotti et al.”
Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps (2013, unknown): “ations for second (and higher) gradient continua can be also obtained by using a simpliﬁed kinematics with respect to the one introduced in this paper and by adopting variational principles (see e.g. [16, 64, 65]). On the otherhand,thefactofobtainingasecondgradientmodelasthelimitcaseofamicromorphico”
A unifying perspective: the relaxed linear micromorphic continuum (2013, unknown): “10) Hitherto, the asymmetric micromorphic model has best been seen and motivated as a higher gradient elasticity model, in which the second derivatives have been replaced by a gradient of a new field [38–40,43,158].”