Tight bounds for three-dimensional nonlinear incompressible elastic composites

León-Mecías, Ángela; Pérez-Fernández, Leslie D.; Bravo‐Castillero, Julián; Sabina, Federico J.

doi:10.1016/j.ijengsci.2008.04.007

Cited by 1 publication

(2 citation statements)

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“…In the incompressible realization of the J 2 deformation theory of plasticity, is the equivalent stress, p 0 ! 1, and 1 3pl is the initial shear modulus and p n is a reference nonlinear compliance in the Ramberg-Osgood model with hardening exponent equal to 3 [6,9,26].…”

Section: A Class Of Porous Nonlinear Materialsmentioning

confidence: 99%

“…In the context of nonlinear inclusions in a linear matrix, we have found that, when the microstructure is accounted for in detail, the Ponte Castañeda lower bound is capable of providing excellent estimates for the effective energy density for different geometrical configurations and physical frameworks [5][6][7][8][9] that improve remarkably over previous uses [10,11]. The accuracy of such an estimate is guaranteed by the availability of a nontrivial upper bound by Talbot [10,11] which, together with the lower bound, provides very narrow ranges of effective behavior [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

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Negligible microstructure in a class of porous nonlinear materials via variational bounds

Pérez-Fernández

León-Mecías

Bravo‐Castillero

2017

Math Methods in App Sciences

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Communicated by I. SevostianovThis work is devoted to the estimation of the effective energy density of porous nonlinear materials by means of variational bounds. Because of the unavailability of an improved upper bound, attention is turned to the improved bound obtained by considering constant nonzero polarization fields in the formal lower bound, which follows from the generalization to nonlinear behavior of the Hashin-Shtrikman variational principles. A particular class of nonlinearity is considered which is relevant in different physical situations. Also, 11 different microstructures are considered. Several computational experiments performed show that the elementary upper bound and the improved lower bound are indistinguishable, suggesting that nonlinearity dominates over the microstructural effects. In other words, at least for the nonlinearity considered here, the influence of microstructure on the effective behavior is negligible. So, in this case, there is no need to search for an improved upper bound, as the elementary one provides a simple but accurate estimate of the effective energy density.

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Section: A Class Of Porous Nonlinear Materialsmentioning

confidence: 99%