scholarly journals Analysis of the Nonlinear Elastic Response of Rubber Membrane with Embedded Circular Rigid Inclusion

2015 ◽  
Vol 45 (3) ◽  
pp. 23-36 ◽  
Author(s):  
Sang Jianbing ◽  
Xing Sufang ◽  
Wang Ling ◽  
Wang Jingyuan ◽  
Zhou Jing
Keyword(s):  
Rigid Inclusion ◽  
Strain Energy Function ◽  
Elastic Response ◽  
Elastic Behaviour ◽  
Elasticity Analysis ◽  
Rubber Membrane ◽  
Circular Rigid Inclusion ◽  
Incompressible Materials ◽  
Nonlinear Elastic ◽  
Constitutive Parameters

AbstractRubber membranes exhibit a particular nonlinear elastic behaviour known as hyper elasticity. Analysis has been proposed by utilizing the modified strain energy function from Gao’s constitutive model, in order to reveal the mechanical property of rubber membrane containing circular rigid inclusion. Rubber membrane is taken into incompressible materials under axisymmetric stretch, based on finite deformations theory. Stress distribution of different constitutive parameters has been analyzed by deducing the basic governing equation. The effects on membrane deformation by different parameters and the failure reasons of rubber membrane have been discussed, which provides reasonable reference for the design of rubber membrane.

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.

Finite plane strain

1953 ◽  
Vol 246 (910) ◽  
pp. 181-213 ◽  
Keyword(s):  
Plane Strain ◽  
Strain Energy Function ◽  
General System ◽  
Infinite Body ◽  
Approximation Process ◽  
Elastic Deformations ◽  
Circular Rigid Inclusion ◽  
Incompressible Materials ◽  
Shear Problem ◽  
Finite Elastic Deformations

A general theory of plane strain, valid for large elastic deformations of isotropic materials, is developed using a general system of co-ordinates. No restriction is imposed upon the form of the strain-energy function in the formulation of the basic theory, apart from that arising naturally from the assumption of plane strain. In applications, attention is confined to incompressible materials, and the general method of approach is illustrated by the examination of a number of problems which are capable of exact solution. These include the flexure of a cuboid, and of an initially curved cuboid, and a generalization of the shear problem. A method of successive approximation is then evolved, suitable for application to problems for which exact solutions are not readily obtainable. Attention is again confined to incompressible materials, and the approximation process is terminated when the second-order terms have been obtained. In considering problems in plane strain, complex variable techniques are employed and the stress and displacement functions are expressed in terms of complex potential functions. In dealing with finite elastic deformations, a complex co-ordinate system may be chosen which is related either to points in the deformed body or to points in the undeformed body, and in the present paper both methods are developed. The theory is applied to obtain solutions for an infinite body which contains either a circular hole or a circular rigid inclusion, and which is under a uniform tension at infinity.

Effect of Constitutive Parameters on Formation of a Spherical Void in a Compressible Nonlinear Elastic Material

1994 ◽  
Vol 61 (2) ◽  
pp. 395-401 ◽  
Author(s):  
Shiro Biwa ◽  
Eiji Matsumoto ◽  
Toshinobu Shibata
Keyword(s):  
Strain Energy ◽  
Finite Elasticity ◽  
Void Formation ◽  
Strain Energy Function ◽  
Elastic Materials ◽  
Spherical Void ◽  
Nonlinear Elastic Material ◽  
Nonlinear Elastic ◽  
Constitutive Parameters ◽  
Bifurcation Behavior

Void formation in materials under isotropic tension is considered within the theory of finite elasticity. This phenomenon is described as the bifurcation of the solution containing a spherical cavity from the state of homogeneous deformation of a solid hyperelastic sphere. The equation giving the bifurcation point is derived, and the critical stretch and stress are numerically calculated for a special class of compressible nonlinear elastic materials for which the strain energy function was proposed by Hill. The effects of constitutive parameters on the post-bifurcation behavior as well as on the critical stretch and stress are discussed.

Equation of State, Nonlinear Elastic Response, and Anharmonic Properties of Diamond-Cubic Silicon and Germanium: First-Principles Investigation

2015 ◽  
Vol 70 (6) ◽  
pp. 403-412 ◽  
Author(s):  
Chenju Wang ◽  
Jianbing Gu ◽  
Xiaoyu Kuang ◽  
Shikai Xiang
Keyword(s):  
Elastic Constants ◽  
Theoretical Calculations ◽  
Theoretical Data ◽  
Elastic Response ◽  
Experimental Result ◽  
Elastic Behaviour ◽  
Third Order Elastic Constants ◽  
Silicon And Germanium ◽  
Nonlinear Elastic ◽  
Good Agreement

AbstractNonlinear elastic properties of diamond-cubic silicon and germanium have not been investigated sufficiently to date. Knowledge of these properties not only can help us to understand nonlinear mechanical effects but also can assist us to have an insight into the related anharmonic properties, so we investigate the nonlinear elastic behaviour of single silicon and germanium by calculating their second- and third-order elastic constants. All the results of the elastic constants show good agreement with the available experimental data and other theoretical calculations. Such a phenomenon indicates that the present values of the elastic constants are accurate and can be used to further study the related anharmonic properties. Subsequently, the anharmonic properties such as the pressure derivatives of the second-order elastic constants, Grüneisen constants of long-wavelength acoustic modes, and ultrasonic nonlinear parameters are explored. All the anharmonic properties of silicon calculated in the present work also show good agreement with the existing experimental results; this consistency not only reveals that the calculation method of the anharmonic properties is feasible but also illuminates that the anharmonic properties obtained in the present work are reliable. For the anharmonic properties of germanium, since there are no experimental result and other theoretical data till now, we hope that the anharmonic properties of germanium first offered in this work would serve as a reference for future studies.

scholarly journals Strain-dependent twist–stretch elasticity in chiral filaments

2007 ◽  
Vol 5 (20) ◽  
pp. 303-310 ◽  
Author(s):  
M Upmanyu ◽  
H.L Wang ◽  
H.Y Liang ◽  
R Mahajan
Keyword(s):  
Degrees Of Freedom ◽  
Single Walled Carbon Nanotubes ◽  
Design Principles ◽  
Elastic Behaviour ◽  
Large Strains ◽  
Theoretical Frameworks ◽  
Nonlinear Elastic ◽  
Walled Carbon Nanotubes ◽  
Strain Dependent ◽  
Microscopic Origin

Coupling between axial and torsional degrees of freedom often modifies the conformation and expression of natural and synthetic filamentous aggregates. Recent studies on chiral single-walled carbon nanotubes and B-DNA reveal a reversal in the sign of the twist–stretch coupling at large strains. The similarity in the response in these two distinct supramolecular assemblies and at high strains suggests a fundamental, chirality-dependent nonlinear elastic behaviour. Here we seek the link between the microscopic origin of the nonlinearities and the effective twist–stretch coupling using energy-based theoretical frameworks and model simulations. Our analysis reveals a sensitive interplay between the deformation energetics and the sign of the coupling, highlighting robust design principles that determine both the sign and extent of these couplings. These design principles have already been exploited by nature to dynamically engineer such couplings, and have broad implications in mechanically coupled actuation, propulsion and transport in biology and technology.

The Influence of the Shape and Rigidity of an Elastic Inclusion on the Transverse Flexure of Thin Plates

1943 ◽  
Vol 10 (2) ◽  
pp. A69-A75
Author(s):  
Martin Goland
Keyword(s):  
Stress Distribution ◽  
Future Study ◽  
Rigid Inclusion ◽  
Elastic Inclusion ◽  
Thin Plates ◽  
Elastic Plates ◽  
Perforated Plates ◽  
Circular Rigid Inclusion ◽  
Special Cases ◽  
Elastic Inclusions

Abstract The purpose of this paper is to investigate the influence of several types of inclusions on the stress distribution in elastic plates under transverse flexure. An “inclusion” is defined as a close-fitting plate of some second material cemented into a hole cut in the interior of the elastic plate. Depending upon the properties of the material of which it is composed, the inclusion is described as rigid or elastic. In particular, the solutions presented will deal with the effects of circular inclusions of differing degrees of elasticity and rigid inclusions of varying elliptical form. Since the rigid inclusion and the hole are limiting types of elastic inclusions, and the circular shape is a special form of the ellipse, plates with either a circular hole or a circular rigid inclusion are important special cases of this discussion. It is hoped that the present analysis of several types of inclusions will aid in a future study of perforated plates stiffened by means of reinforcing rings fitted into the holes.

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