On the behaviour of spherical inclusions in a cylinder under tension loads

In the present paper the behaviour of a hyperelastic body is studied, considering the presence of one, two and more spherical inclusions, under the effect of an external tension load. The inclusions are modeled as nonlinear elastic bodies that undergo small strains. For the material constitutive relation, a relatively new type of model is used, wherein the strains (linearized strain) are assumed to be nonlinear functions of the stresses. In particular, it is used a function such that the strains are always small, independently of the magnitude of the external loads. In order to simplify the problem, the hyperelastic medium and the inclusions are modelled as axial-symmetric bodies. The finite element method is used to obtain results for these boundary value problems. The objective of using these new models for elastic bodies in the case of the inclusions is to study the behaviour of such bodies in the case of concentration of stresses, which happens near the interface with the surrounding matrix. From the results presented in this paper, it is possible to observe that despite the relatively large magnitude for the stresses, the strains for the inclusions remain small, which would be closer to the actual behaviour of real inclusions made of brittle materials, which cannot show large strains.

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A new type of constitutive equation for nonlinear elastic bodies. Fitting with experimental data for rubber-like materials

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2021.0330 ◽

2021 ◽

Vol 477 (2252) ◽

pp. 20210330

Author(s):

Roger Bustamante ◽

Kumbakonam R. Rajagopal

Keyword(s):

Experimental Data ◽

Constitutive Equation ◽

Constitutive Relation ◽

Cauchy Stress ◽

Gibbs Potential ◽

Hencky Strain ◽

Biaxial Stretching ◽

Elastic Bodies ◽

New Type ◽

Nonlinear Elastic

In this article, we develop a new implicit constitutive relation, which is based on a thermodynamic foundation that relates the Hencky strain to the Cauchy stress, by assuming a structure for the Gibbs potential based on the Cauchy stress. We study the tension/compression of a cylinder, biaxial stretching of a thin plate and simple shear within the context of our constitutive relation. We then compare the predictions of the constitutive relation that we develop and that of Ogden’s constitutive relation with the experiments of Treloar concerning tension/compression of a cylinder, and we show that the predictions of our constitutive relation provide a better description than Ogden’s model, with fewer material moduli.

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Strain-dependent twist–stretch elasticity in chiral filaments

Journal of The Royal Society Interface ◽

10.1098/rsif.2007.1145 ◽

2007 ◽

Vol 5 (20) ◽

pp. 303-310 ◽

Cited By ~ 19

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.

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CIRCULAR CONTACT OF NONLINEAR ELASTIC BODIES SUBJECTED TO IMPORTANT STRAINS

ANNALS OF THE ORADEA UNIVERSITY Fascicle of Management and Technological Engineering ◽

10.15660/auofmte.2012-1.2694 ◽

2012 ◽

Vol XXI (XI), 2012/1 (1) ◽

Author(s):

Românu Ionuţ Cristian ◽

Muscă Ilie

Keyword(s):

Elastic Bodies ◽

Nonlinear Elastic ◽

Circular Contact

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Energy Minimization for Isotropic Nonlinear Elastic Bodies

Multiscale Modeling in Continuum Mechanics and Structured Deformations ◽

10.1007/978-3-7091-2770-4_1 ◽

2004 ◽

pp. 1-51 ◽

Cited By ~ 5

Author(s):

M. Šilhavý

Keyword(s):

Energy Minimization ◽

Elastic Bodies ◽

Nonlinear Elastic

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The State of Stress and Strain Adjacent to Notches in a New Class of Nonlinear Elastic Bodies

Journal of Elasticity ◽

10.1007/s10659-019-09724-0 ◽

2019 ◽

Vol 135 (1-2) ◽

pp. 375-397 ◽

Cited By ~ 1

Author(s):

Vojtěch Kulvait ◽

Josef Málek ◽

K. R. Rajagopal

Keyword(s):

The State ◽

Stress And Strain ◽

New Class ◽

Elastic Bodies ◽

State Of Stress ◽

Nonlinear Elastic

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Nonlinear Spiking Neural P Systems

International Journal of Neural Systems ◽

10.1142/s0129065720500082 ◽

2020 ◽

Vol 30 (10) ◽

pp. 2050008 ◽

Cited By ~ 7

Author(s):

Hong Peng ◽

Zeqiong Lv ◽

Bo Li ◽

Xiaohui Luo ◽

Jun Wang ◽

...

Keyword(s):

The State ◽

P Systems ◽

Number Generator ◽

Computational Power ◽

Nonlinear Functions ◽

Computing Systems ◽

Spiking Neural P Systems ◽

System A ◽

New Variant ◽

New Type

This paper proposes a new variant of spiking neural P systems (in short, SNP systems), nonlinear spiking neural P systems (in short, NSNP systems). In NSNP systems, the state of each neuron is denoted by a real number, and a real configuration vector is used to characterize the state of the whole system. A new type of spiking rules, nonlinear spiking rules, is introduced to handle the neuron’s firing, where the consumed and generated amounts of spikes are often expressed by the nonlinear functions of the state of the neuron. NSNP systems are a class of distributed parallel and nondeterministic computing systems. The computational power of NSNP systems is discussed. Specifically, it is proved that NSNP systems as number-generating/accepting devices are Turing-universal. Moreover, we establish two small universal NSNP systems for function computing and number generator, containing 117 neurons and 164 neurons, respectively.

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