scholarly journals Theoretical description of large deformations in criss-cross composites (with application to Tensylon®)

2020 ◽  
Vol 23 (2) ◽  
pp. 269-281
Author(s):  
Pavel S. Mostovykh
Keyword(s):  
Theoretical Model ◽  
Anisotropic Material ◽  
Large Deformations ◽  
Theoretical Description ◽  
Elastic Behaviour ◽  
Large Strains ◽  
Experi Mental Data ◽  
Deforma Tion

A theoretical model of an anisotropic material, Tensylon®, under large strains is proposed. This model is capable to describe the material’s response in in-plane tension at different angles to the fibrils. At 0° and at 90°, i.e., along the fibrils in either “criss” or “cross” plies, it quantitatively predicts the experimentally observed elastic behaviour until failure. At 45° to the fibrils, it quantitatively describes the experi- mental data in the elastic and plastic domains. The description remains accurate up to strains of 35%, that corresponds to 30÷40% of deforma- tion gradient components. The infinitesimal strains model would give at least 25% of error under such circumstances.

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.

Dynamic Response of Dielectric Elastomers

2004 ◽  
Author(s):  
Eric M. Mockensturm ◽  
Nakhiah Goulbourne
Keyword(s):  
Large Deformations ◽  
Electrical Energy ◽  
Material Behavior ◽  
Dielectric Elastomers ◽  
Large Strains ◽  
Inertial Effects ◽  
Stable Equilibria ◽  
Electrostatic Pressure ◽  
Linear Material ◽  
Multiple Stable Equilibria

Dielectric elastomers have received a great deal of attention recently for effectively transforming electrical energy to mechanical work. Their large strains and conformability make them enticing materials for many new types of actuators. Unfortunately, their non-linear material behavior and large deformations make actual devices difficult to model. However, the reason for this difficulty can also be used to design actuators that utilize these material and geometric non-linearities to obtain multiple stable equilibria. In this work, we investigate one of the simplest possible configurations, a spherical membrane, using a model that incorporates both mechanical and electrostatic pressure as well as inertial effects that become important when transitioning from one equilibrium to another.

The Axisymmetric Deformation of Linearly and Nonlinearly Elastic Spinning Tubes Under End Thrusts and Torques

1998 ◽  
Vol 65 (1) ◽  
pp. 99-106
Author(s):  
T. J. McDevitt ◽  
J. G. Simmonds
Keyword(s):  
Anisotropic Material ◽  
Large Strain ◽  
Axisymmetric Deformation ◽  
Large Strains ◽  
Shells Of Revolution ◽  
Large Rotation ◽  
Elastic Tubes ◽  
Axisymmetric Bending ◽  
Combined Parameters ◽  
Nonlinearly Elastic

We consider the steady-state deformations of elastic tubes spinning steadily and attached in various ways to rigid end plates to which end thrusts and torques are applied. We assume that the tubes are made of homogeneous linearly or nonlinearly anisotropic material and use Simmonds” (1996) simplified dynamic displacement-rotation equations for shells of revolution undergoing large-strain large-rotation axisymmetric bending and torsion. To exploit analytical methods, we confine attention to the nonlinear theory of membranes undergoing small or large strains and the theory of strongly anisotropic tubes suffering small strains. Of particular interest are the boundary layers that appear at each end of the tube, their membrane and bending components, and the penetration of these layers into the tube which, for certain anisotropic materials, may be considerably different from isotropic materials. Remarkably, we find that the behavior of a tube made of a linearly elastic, anisotropic material (having nine elastic parameters) can be described, to a first approximation, by just two combined parameters. The results of the present paper lay the necessary groundwork for a subsequent analysis of the whirling of spinning elastic tubes under end thrusts and torques.

THE RESEARCH FOR AN IDENTIFICATION OF CRACK – LIKE CORROSION – MECHANICAL DEFECT BY ACOUSTIC IN-LINE INSPECTION TOOLS

2020 ◽  
pp. 56-63
Author(s):  
A. D. Zhukov ◽  
M. V. Grigoriev ◽  
V. N. Danilov
Keyword(s):  
Theoretical Model ◽  
Acoustic Waves ◽  
Corrosion Damage ◽  
Signal Amplitude ◽  
Theoretical Description ◽  
Oil Pipeline ◽  
Pipeline Inspection ◽  
Acoustic Equation ◽  
Simplifying Assumptions ◽  
Mechanical Defect

Problem of an identification of cracks in dents or corrosion damage, which is considered as a crack – like corrosion – mechanical defect type, is considered for acoustic in – line inspection tools during an in – line inspection of oil pipelines. For this purpose, a theoretical model has been provided and considered as a vertical notch with a convex base. For modeling an interaction of acoustic waves with the defect model there has been used a corresponded formula of an acoustic equation at a ray – acoustic approximation. Considering used simplifying assumptions there have obtained certain boundary conditions for acoustic equation of the crack – like corrosion mechanical defect. Based on this theoretical model here an experimental research were provided at specially manufactured test specimen which contained vertical notches with base of different curvature. At the specimen there are has been obtained a difference of echo signals amplitude from convex and flat surface based notches. Obtained results showed a sufficient agreement with provided by theoretical modeling and approve an adequacy of the proposed model for a theoretical description of considered interaction shear waves with the defect imitation. According to obtained trend of an echo – signal amplitude variation a method for identification of cracks in dents or corrosion damage during an oil pipeline inspection by inline inspection tools has been provided.

The Elastic—Plastic Contact of Rough Surfaces and its Relevance in the Study of Wear

1988 ◽  
Vol 202 (4) ◽  
pp. 269-274 ◽  
Author(s):  
J Halling ◽  
R D Arnell ◽  
K A Nuri
Keyword(s):  
Theoretical Model ◽  
Probability Distribution ◽  
Experimental Evidence ◽  
Rough Surfaces ◽  
Plasticity Index ◽  
Elastic Behaviour ◽  
Asperity Height ◽  
Real Contact ◽  
Nominal Pressure ◽  
Unique Relationship

In a recent paper it was shown that the limit of elastic behaviour of rough surfaces could be defined by a unique relationship between the plasticity index and the nominal pressure. Specific experimental evidence suggested that the best theoretical model was one when the asperity height probability distribution was assumed Gaussian with a truncation of 3 σ. This paper extends this argument by showing that for a given ratio of plastic-elastic area of real contact, similar unique relations exist between the plasticity index and nominal pressure. It is assumed that the maximum non-dimensional elastic deformation is given by the inverse of the square of the plasticity index, and this is supported by experimental results. It is also shown that the model proposed is in error at higher pressures, due to the interaction of the deformations of adjacent asperities.

High-Pressure Elastic Constant of Some Materials of Earth’s Mantle

2016 ◽  
Vol 71 (5) ◽  
pp. 433-437
Author(s):  
Quan Liu
Keyword(s):  
Experimental Data ◽  
High Pressure ◽  
Theoretical Model ◽  
Elastic Behaviour ◽  
Exponential Relationship ◽  
Earth’S Mantle ◽  
Simple Theoretical Model ◽  
Volume Dependence ◽  
Theoretical Investigations ◽  
Good Agreement

AbstractIn the present work, an exponential relationship for the volume dependence of the Anderson–Grüneisen parameter along isotherm and the formulation derived from Tallon’s model have been used to develop a simple theoretical model for the elastic constants as a function of pressure. Applying it to some materials of earth’s mantle at different pressure ranges, the calculated results are in good agreement with the earlier theoretical investigations and available experimental data and thus show that our theory can be applied for predicting the elastic behaviour of earth materials at high pressure.

Theoretical description of molecular permeation via surface diffusion through graphene nanopores

2021 ◽  
Author(s):  
Chengzhen Sun ◽  
Kailin Luo ◽  
Runfeng Zhou ◽  
Bofeng Bai
Keyword(s):  
Theoretical Model ◽  
Diffusion Equation ◽  
Surface Diffusion ◽  
Theoretical Description ◽  
Two Dimensional ◽  
Fick’S Law ◽  
Fick's Law

We establish a theoretical model to describe the surface molecular permeation through two-dimensional graphene nanopores based on the surface diffusion equation and Fick’s law. The model is established by considering...

scholarly journals MODELING THE BEHAVIOR OF THE PHYSICAL AND GEOMETRIC NON-LINEAR FUNCTIONAL HETEROGENEOUS MATERIALS

2021 ◽  
Vol 1 (45) ◽  
pp. 82
Author(s):  
K. Domichev
Keyword(s):  
Geometric Nonlinearity ◽  
Large Deformations ◽  
Heterogeneous Materials ◽  
Spline Functions ◽  
Large Strains ◽  
Strain Rates ◽  
Inhomogeneous Materials ◽  
Physical Relationship ◽  
Small Deformations ◽  
Cauchy Relations

The work is devoted to the problem of modeling the behavior of functionally inhomogeneous materials with the properties of pseudo-elastic-plasticity under complex loads, in particular at large strains (up to 20%), when geometric nonlinearity in Cauchy relations must be taken into account. In previous works of the authors, functionally heterogeneous materials were studied in a geometrically linear formulation, which is true for small deformations (up to 7%). When predicting work with material at large deformations, it is necessary to take into account geometric nonlinearity in Cauchy relations.Studying the behavior of bodies made of functionally heterogeneous materials under unsteady load requires the development of special approaches, methods and algorithms for calculating the stress-strain state. When constructing physical relations, it is assumed that the deformation at the point is represented as the sum of the elastic component, the jump in deformation during the phase transition, plastic deformation and deformation caused by temperature changes.A physical relationship in a nonlinear setting is proposed for modeling the behavior of bodies made of functionally heterogeneous materials. Formulas are obtained that nonlinearly relate strain rates and Formulas are obtained that nonlinearly relate strain rates and displacement rates.Keywords: mathematical modeling, functional heterogeneous materials, geometric nonlinearity, spline functions, pseudo-elastic plasticity, phase transitions

Measurement of Local Strain in Thin Aluminium Interconnects Using Convergent Beam Electron Diffraction (CBED)

1999 ◽  
Vol 594 ◽  
Author(s):  
S. Krämer ◽  
J. Mayer
Keyword(s):  
Electron Diffraction ◽  
Axial Strain ◽  
Local Strain ◽  
Convergent Beam Electron Diffraction ◽  
Elastic Behaviour ◽  
Large Strains ◽  
Beam Electron ◽  
Single Grain ◽  
Convergent Beam ◽  
Line Positions

AbstractEnergy filtered convergent beam electron diffraction (CBED) was used to investigate localized strain in aluminium interconnects. An analysis of the higher order Laue zone (HOLZ) line positions in CBED patterns makes it possible to measure the lattice strain with high accuracy (∼10−4) and high spatial resolution (10 to 100 nm). The strain development in a single grain was measured during thermal cycling between −170°C and + 100°C. The grain showed reversible, elastic behaviour over the whole temperature range building up large strains at low temperatures. By comparing with finite element simulations, a detailed understanding of the tri-axial strain state could be achieved.

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