Finite deformation of flexible composites

1990 ◽  
Vol 429 (1877) ◽  
pp. 569-586 ◽  
Keyword(s):  
Finite Deformation ◽  
Constitutive Relations ◽  
Elastic Behaviour ◽  
Flexible Composites ◽  
Lagrangian Strain ◽  
Strain Components ◽  
Nonlinear Elastic ◽  
Fourth Order Polynomial ◽  
Theory And Experiments ◽  
Good Agreement

This paper examines the nonlinear elastic behaviour of flexible composites under finite deformation. The constitutive relations have been derived based on a strain-energy density which, in a fourth-order polynomial form, is assumed to be a function of the lagrangian strain components referring to the initial principal material coordinates. The constitutive equations thus obtained are verified by the following experiments: (1) off-axis tension and simple shear for unidirectional composites, and (2) uniaxial tension for flexible composites with wavy fibres. Good agreement has been found between the theory and experiments.

Circular Contact of Incompressible, Nonlinear-Elastic Bodies

2009 ◽  
Author(s):  
Emanuel Diaconescu ◽  
Marilena Glovnea ◽  
Filip Ciutac
Keyword(s):  
Nonlinear Elasticity ◽  
Simple Approach ◽  
Experimental Results ◽  
Contact Modeling ◽  
Elastic Bodies ◽  
Nonlinear Elastic ◽  
Theory And Experiments ◽  
Circular Contact ◽  
Good Agreement

Contact modeling of rubber bodies is based either on viscoelasticity, nonlinear elasticity or adhesion. This paper advances a simple approach to the analysis of the contacts involving incompressible, nonlinear elastic bodies and reports experimental results on rubber to justify this approach. A good agreement is found between theory and experiments.

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 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.

Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth

2002 ◽  
Vol 470 ◽  
pp. 319-357 ◽  
Author(s):  
ODD M. FALTINSEN ◽  
ALEXANDER N. TIMOKHA
Keyword(s):  
Finite Depth ◽  
Modal System ◽  
Full Account ◽  
Inviscid Flows ◽  
State Response ◽  
Linear Damping ◽  
Convergence Problems ◽  
Run Up ◽  
Fourth Order Polynomial ◽  
Good Agreement

The modal system describing nonlinear sloshing with inviscid flows in a rectangular rigid tank is revised to match both shallow fluid and secondary (internal) resonance asymptotics. The main goal is to examine nonlinear resonant waves for intermediate depth/breadth ratio 0.1 [lsim ] h/l [lsim ] 0.24 forced by surge/pitch excitation with frequency in the vicinity of the lowest natural frequency. The revised modal equations take full account of nonlinearities up to fourth-order polynomial terms in generalized coordinates and h/l and may be treated as a modal Boussinesq-type theory. The system is truncated with a high number of modes and shows good agreement with experimental data by Rognebakke (1998) for transient motions, where previous finite depth modal theories failed. However, difficulties may occur when experiments show significant energy dissipation associated with run-up at the walls and wave breaking. After reviewing published results on damping rates for lower and higher modes, the linear damping terms due to the linear laminar boundary layer near the tank's surface and viscosity in the fluid bulk are incorporated. This improves the simulation of transient motions. The steady-state response agrees well with experiments by Chester & Bones (1968) for shallow water, and Abramson et al. (1974), Olsen & Johnsen (1975) for intermediate fluid depths. When h/l [lsim ] 0.05, convergence problems associated with increasing the dimension of the modal system are reported.

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.

Morphing Continuum Theory: Incorporating the Physics of Microstructures to Capture the Transition to Turbulence Within a Boundary Layer

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Louis B. Wonnell ◽  
James Chen
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Ad Hoc ◽  
Constitutive Relations ◽  
Turbulence Models ◽  
Continuum Theory ◽  
Transition To Turbulence ◽  
Flow Turbulence ◽  
Good Agreement ◽  
Inherent Advantage

A boundary layer with Re = 106 is simulated numerically on a flat plate using morphing continuum theory. This theory introduces new terms related to microproperties of the fluid. These terms are added to a finite-volume fluid solver with appropriate boundary conditions. The success of capturing the initial disturbances leading to turbulence is shown to be a byproduct of the physical and mathematical rigor underlying the balance laws and constitutive relations introduced by morphing continuum theory (MCT). Dimensionless equations are introduced to produce the parameters driving the formation of disturbances leading to turbulence. Numerical results for the flat plate are compared with the experimental results determined by the European Research Community on Flow, Turbulence, and Combustion (ERCOFTAC) database. Experimental data show good agreement inside the boundary layer and in the bulk flow. Success in predicting conditions necessary for turbulent and transitional (T2) flows without ad hoc closure models demonstrates the theory's inherent advantage over traditional turbulence models.

Elastica of Cantilever Beam under Two Follower Forces

1997 ◽  
Vol 1 (2) ◽  
pp. 159-165 ◽  
Author(s):  
Wibisono Hartono
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cantilever Beam ◽  
Elastic Analysis ◽  
The Finite Element Method ◽  
Nonlinear Elastic Analysis ◽  
Displacement Theory ◽  
Follower Forces ◽  
Nonlinear Elastic ◽  
Good Agreement

This paper presents a nonlinear elastic analysis of cantilever beam subjected to two follower forces. Those two proportional forces are always perpendicular to the beam axis. The solution of differential equations based on the large displacement theory, known as elastica is obtained with the help of principle of elastic similarity. For comparison purpose, numerical results using the finite element method are also presented and the results show good agreement.

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