Computation of the homogenized nonlinear elastic response of 2D and 3D auxetic structures based on micropolar continuum models

2017 ◽  
Vol 170 ◽  
pp. 271-290 ◽  
Author(s):  
K. El Nady ◽  
F. Dos Reis ◽  
J.F. Ganghoffer
Keyword(s):  
Elastic Response ◽  
Continuum Models ◽  
Micropolar Continuum ◽  
Auxetic Structures ◽  
Nonlinear Elastic ◽  
2D And 3D

scholarly journals A priori analysis of a higher-order nonlinear elasticity model for an atomistic chain with periodic boundary condition

2020 ◽  
Author(s):  
Yangshuai Wang ◽  
Lei Zhang ◽  
Hao Wang
Keyword(s):  
Nonlinear Elasticity ◽  
A Priori ◽  
Higher Order ◽  
Elastic Response ◽  
Continuum Models ◽  
Order Accuracy ◽  
Born Model ◽  
Convergence Results ◽  
Key Issues ◽  
Nonlinear Elastic

Abstract Nonlinear elastic models are widely used to describe the elastic response of crystalline solids, for example, the well-known Cauchy–Born model. While the Cauchy–Born model only depends on the strain, effects of higher-order strain gradients are significant and higher-order continuum models are preferred in various applications such as defect dynamics and modeling of carbon nanotubes. In this paper we rigorously derive a higher-order nonlinear elasticity model for crystals from its atomistic description in one dimension. We show that, compared to the second-order accuracy of the Cauchy–Born model, the higher-order continuum model in this paper is of fourth-order accuracy with respect to the interatomic spacing in the thermal dynamic limit. In addition we discuss the key issues for the derivation of higher-order continuum models in more general cases. The theoretical convergence results are demonstrated by numerical experiments.

scholarly journals Black rubber and the non-linear elastic response of scale invariant solids

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Matteo Baggioli ◽  
Víctor Cáncer Castillo ◽  
Oriol Pujolàs
Keyword(s):  
Strain Curve ◽  
Effective Field ◽  
Elastic Response ◽  
Elastic Behaviour ◽  
Scale Invariant ◽  
Stress Strain ◽  
Nonlinear Stress ◽  
Hyper Elastic ◽  
Simple Class ◽  
Nonlinear Elastic

Abstract We discuss the nonlinear elastic response in scale invariant solids. Following previous work, we split the analysis into two basic options: according to whether scale invariance (SI) is a manifest or a spontaneously broken symmetry. In the latter case, one can employ effective field theory methods, whereas in the former we use holographic methods. We focus on a simple class of holographic models that exhibit elastic behaviour, and obtain their nonlinear stress-strain curves as well as an estimate of the elasticity bounds — the maximum possible deformation in the elastic (reversible) regime. The bounds differ substantially in the manifest or spontaneously broken SI cases, even when the same stress- strain curve is assumed in both cases. Additionally, the hyper-elastic subset of models (that allow for large deformations) is found to have stress-strain curves akin to natural rubber. The holographic instances in this category, which we dub black rubber, display richer stress- strain curves — with two different power-law regimes at different magnitudes of the strain.

Fast and slow nonlinear elastic response of disparate rocks and the influence of moisture

2016 ◽  
Vol 140 (4) ◽  
pp. 3326-3326 ◽  
Author(s):  
Jacques Riviere ◽  
Parisa Shokouhi ◽  
Robert A. Guyer ◽  
Paul A. Johnson
Keyword(s):  
Elastic Response ◽  
Nonlinear Elastic

scholarly journals On the Geometrically Nonlinear Elastic Response of Class θ = 1 Tensegrity Prisms

2018 ◽  
Vol 5 ◽  
Author(s):  
Ida Mascolo ◽  
Ada Amendola ◽  
Giulio Zuccaro ◽  
Luciano Feo ◽  
Fernando Fraternali
Keyword(s):  
Elastic Response ◽  
Geometrically Nonlinear ◽  
Nonlinear Elastic

Constitutive equations for the nonlinear elastic response of rubbers

2006 ◽  
Vol 185 (1-2) ◽  
pp. 31-65 ◽  
Author(s):  
A. D. Drozdov ◽  
J. deClaville Christiansen
Keyword(s):  
Constitutive Equations ◽  
Elastic Response ◽  
Nonlinear Elastic
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