Elastic Instabilities of Inflated Rubber Shells

1999 ◽  
Vol 72 (2) ◽  
pp. 263-268 ◽  
Author(s):  
A. N. Gent
Keyword(s):  
Spherical Cavity ◽  
Cylindrical Tube ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
Inflation Pressure ◽  
Elastic Instabilities ◽  
Thin Walled ◽  
Uniform Expansion ◽  
Modest Degree ◽  
Rubber Block

Abstract Using a simple constitutive law for elastic behavior that includes the feature of a maximum allowable strain, equations are derived for inflation pressure as a function of the amount of inflation for three rubber shells: a thin-walled spherical balloon, a small spherical cavity in a large rubber block, and a thin-walled cylindrical tube. The results are compared with those obtained using the neo-Hookean constitutive law. Uniform expansion is generally predicted to become unstable at a modest degree of inflation but the new relations give a second stable inflation state, in accord with experience.

scholarly journals Differential Sea-Ice Drift. II. Comparison of Mesoscale Strain Measurements to Linear Drift Theory Predictions

1974 ◽  
Vol 13 (69) ◽  
pp. 457-471 ◽  
Author(s):  
W. D. Hibler
Keyword(s):  
High Pressures ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
Local Pressure ◽  
Strain Measurements ◽  
Linear Drift ◽  
Special Cases ◽  
Drift Theory ◽  
Sea Ice Drift ◽  
Frequency Behavior

A comparison of mesoscale strain measurements with the atmospheric pressure field and the wind velocity field indicate that the ice divergence rate and vorticity follow the local pressure and wind divergence with significant correlation. For low atmospheric pressures and converging winds the divergence rate was found to be negative with the vorticity being counter-clockwise. The inverse behavior was observed for high pressures and diverging winds. This behavior was shown to agree with predictions based upon the infinite boundary solution of a linearized drift theory in the absence of gradient current effects and using the constitutive law proposed by Glen (1970) for pack ice. The best least-squares values of the constitutive law parametersηandζwere found to be ≈ 1012kg/s. Using typical divergence rates these values yield compressive stresses of the magnitude of 105N/m which are similar to values suggested by the Parmerter and Coon (1972) ridge model. In general, the infinite boundary solution of the linear drift equation indicates that in a low-pressure region that is reasonably localized in space, the ice would be expected to converge for high compactness (winter) and diverge for low compactness (summer).Calculations were also carried out using a more general linear visco-elastic constitutive law that includes memory effects and which includes a generalized Hooke’s law as well as the Glen law as special cases. A best fit of this more general calculation with strain measurements indicates overall a better agreement with viscous behavior than with elastic behavior, with the frequency behavior of the estimated “viscosities” similar to the Glen law behavior at temporal frequencies less than ≈ 0.01 h−1.

A General Solution for the Pressurized Elastoplastic Tube

1992 ◽  
Vol 59 (1) ◽  
pp. 20-26 ◽  
Author(s):  
David Durban ◽  
Michael Kubi
Keyword(s):  
General Solution ◽  
Finite Strain ◽  
Cylindrical Tube ◽  
Yield Function ◽  
Material Behavior ◽  
Deformation Pattern ◽  
Perfectly Plastic ◽  
Plastic Phase ◽  
Thin Walled ◽  
Elastic Perfectly Plastic

The problem of a thick-walled cylindrical tube subjected to internal pressure is investigated within the framework of continuum plasticity. Material behavior is modeled by a finite strain elastoplastic flow theory based on the Tresca yield function. The deformation pattern is restricted by the plane-strain condition but arbitrary hardening and elastic compressibility are accounted for. A general solution is given in terms of quadratures. The analysis also includes treatment of a second plastic phase, characterized by corner relations, that may develop at the inner boundary. It is shown that the interface between the two plastic regions moves initially outwards and then, beyond a certain strain level, it moves back inwards. Some useful and simple results are given for thin-walled tubes of hardening materials and for thick-walled elastic/perfectly plastic tubes.

A New Constitutive Model for the Compressibility of Elastomers at Finite Deformations

2001 ◽  
Vol 74 (4) ◽  
pp. 541-559 ◽  
Author(s):  
Jeffrey E. Bischoff ◽  
Ellen M. Arruda ◽  
Karl Grosh
Keyword(s):  
Uniaxial Tension ◽  
Volume Change ◽  
Constitutive Models ◽  
Hydrostatic Compression ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
Compression Tests ◽  
Volume Response ◽  
Using Data ◽  
Nonlinear Elastic

Abstract Although traditional constitutive models for rubbery elastic materials are incompressible, many materials that demonstrate nonlinear elastic behavior are somewhat compressible. Clearly important in hydrostatic deformations, compressibility can also significantly affect the response of elastomers in applications for which several boundaries are rigidly fixed, such as bushings, or triaxial states of stress are realized. Compressibility is also important for convergence of finite element simulations in which a rubbery elastic constitutive law is in use. Volume changes that reflect compressibility have been observed historically in both uniaxial tension and hydrostatic compression tests; however, there appear to be no data obtained from both types of tests on the same material by which to validate a compressible hyperelastic law. In this paper, we propose a new compressible hyperelastic constitutive law for elastomers and other rubbery materials in which entropy and internal energy changes contribute to the volume change. Using data from the literature, we show that this law is capable of reproducing both the pressure—volume response of elastomers in hydrostatic compression, as well as the stress—stretch and volume change—stretch data of elastomers in uniaxial tension.

scholarly journals Experimental Investigation and Numerical Simulation of C-Shape Thin-Walled Steel Profile Joints

Buildings ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 636
Author(s):  
George Taranu ◽  
Ionut-Ovidiu Toma
Keyword(s):  
Negative Impact ◽  
Strain Curve ◽  
Experimental Tests ◽  
Tensile Tests ◽  
Elastic Behavior ◽  
Experimental Program ◽  
Static Structure ◽  
Solid Models ◽  
Low Mass ◽  
Thin Walled

The versatility of steel, its high resistance in relation to its low mass, as well as the easily accessible technology in the context of using recyclable materials and the low negative impact on the environment represent important arguments in using thin-walled steel profiles to make structures for buildings with a low height regime. This paper presents the results of an experimental program that investigated the behavior of three types of joints in a T-shape form made of thin-walled steel profiles to make shear wall panels or truss beam floors. Due to the small dimensions of the C-profiles of 89 × 41 × 12 × 1 mm, and of the technology of their joining, manufacturers prefer the hinged connections of elements with self-drilling screws. The purpose of the research presented in this paper is to assess the maximum capacity of the joints, the elastic and post-elastic behavior until failure, and also the mechanisms failure. The types of joints analyzed are commonly used in the production of structural systems for houses. The experimental program, which consisted of testing 5 specimens for each type of joint in tension (shear on screws), showed different behavior in terms of load-displacement. The experimental, tested models were analyzed by finite element simulations in an ANSYS nonlinear static structure with 3D solid models. The materials were defined by a bilinear true stress–strain curve obtained after some experimental tensile tests of the steel. The results of the experimental tests showed that the main failure mechanism is a yielding of the holes where the screws were mounted and a shearing of the profile walls. Adding an additional screw on each side increases the capacity of the joints, but not until a yield loss is obtained. In conclusion, it is shown that the solution is suitable for a low level of loading in a static manner; however, additional studies are necessary in order to develop and verify other solutions, thus improving the strength of the connection.

On the Dynamics of Fractional Visco-Elastic Beams

2012 ◽  
Author(s):  
Salvatore Di Lorenzo ◽  
Francesco P. Pinnola ◽  
Antonina Pirrotta
Keyword(s):  
Elastic Beam ◽  
Constitutive Law ◽  
Dynamic Loads ◽  
Elastic Behavior ◽  
Advanced Manufacturing ◽  
Suitable Model ◽  
Bernoulli Beam ◽  
Static Behavior ◽  
Creep Tests ◽  
Euler Bernoulli Beam

With increasing advanced manufacturing process, visco-elastic materials are very attractive for mitigation of vibrations, provided that you may have advanced studies for capturing the realistic behavior of such materials. Experimental verification of the visco-elastic behavior is limited to some well-known low order models as the Maxwell or Kelvin models. However, both models are not sufficient to model the visco-elastic behavior of real materials, since only the Maxwell type can capture the relaxation tests and the Kelvin the creep tests, respectively. Very recently, it has been stressed that the most suitable model for capturing the visco-elastic behavior is the spring-pot, characterized by a fractional constitutive law. Based on this assumption, the quasi-static behavior has been investigated very recently, however for noise control there is a need of exploiting the dynamic behavior of such a fractional visco-elastic beam. The present paper introduces the dynamic response of fractional visco-elastic Euler-Bernoulli beam under dynamic loads.

scholarly journals Nickel-titanium pseudo-elastic behavior under equi-biaxial dynamic loading conditions

2018 ◽  
Vol 183 ◽  
pp. 02054
Author(s):  
Pierre Quillery ◽  
Bastien Durand ◽  
Olivier Hubert ◽  
Han Zhao
Keyword(s):  
Thermal Emission ◽  
Solid Phase ◽  
Dynamic Compression ◽  
Nickel Titanium ◽  
Impact Testing ◽  
Constitutive Law ◽  
Scale Model ◽  
Elastic Behavior ◽  
Temperature Phase ◽  
Stress Strain

Shape memory alloys (SMA) undergo a solid-solid phase transformation called martensitic transformation, involving a "high temperature" phase (austenite) and a "low temperature" phase (martensite). The stress-strain pseudo-elastic behavior of a nickel-titanium under equi-biaxial dynamic compression is measured thanks to a new home-made impact testing set-up using split Hopkinson bars. The use of thermal and optical cameras allows strain and heating sources fields to be identified. The stress field is estimated by the combination of the strain gauges information placed on bars, and a finite element analysis of the specimen. Experimental average stress-strain behavior and thermal emission are finally compared to the results of a finite difference axisymmetric model where the constitutive law is given by a fully coupled stochastic multi scale model.

scholarly journals Cumulative Effect of Pressing and Drying on Stress Generation within a Green Ceramic Compact

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
E. Vidal-Sallé ◽  
D. Falgon ◽  
R. Peczalski ◽  
J-C. Boyer
Keyword(s):  
Ceramic Powder ◽  
Cumulative Effect ◽  
Constitutive Law ◽  
Stress Generation ◽  
Convective Drying ◽  
Elastic Behavior ◽  
Drying Process ◽  
Material Density ◽  
External Edge ◽  
Internal Stress Field

The internal stress field induced by uniaxial pressing and subsequent convective drying of a green ceramic powder was simulated by the finite element method. A density dependent elastoplastic constitutive law was used for the mechanical modeling of the compaction. A diffusive water transfer equation and a purely elastic behavior with imposed hydrostrain involving shrinkage were applied for the modeling of the drying process. The key material properties (hydrodiffusivity, hydrocontraction coefficient, Young’s modulus, Poisson’s ratio, and yield surface parameters) had been experimentally measured and introduced as functions of material density and water content. If residual stresses due to the compaction operation were taken into account, the maximum value of the tensile stress at the top external edge of the wheel and at the beginning of the drying process was two times higher than for a stress free green ceramic compact. Beyond the residual stress onset, the compaction operation induced density heterogeneities which had important consequences on the mechanical behavior of the compact.

Small deformations of a nonlinear viscoelastic tube: theory and application to polypropylene

1976 ◽  
Vol 281 (1306) ◽  
pp. 543-566 ◽  
Keyword(s):  
Axial Force ◽  
Tensile Strain ◽  
Strain Tensor ◽  
Cylindrical Tube ◽  
Proportional Loading ◽  
Shear Creep ◽  
Nonlinear Viscoelastic ◽  
Thin Walled Tube ◽  
Thin Walled ◽  
Small Deformations

The response of an isotropic, nonlinear viscoelastic, thin-walled tube to combinations of axial force F , axial couple G and pressure difference p is considered theoretically and experimentally. Theory is based on the membrane theory of thin shells, applied to a thin-walled circular cylindrical tube. The components of two dimensional stress and strain in the wall of the tube are derived, allowing for arbitrarily large deformations; but restriction to small deformations is shown to be necessary if the history of stress is to be controlled at will through F , G and p . For arbitrary choice of F , G and p as functions of time the strain is shown to depend on three stress tensors P , Q , R independent of time, and three scalar functions of time. An expression for the linear strain tensor in terms of P , Q , R is obtained which involves four scalar functions ϕ 0 , ϕ 1 , ϕ 2 , ϕ 3 . These functions depend on the invariants of P , Q , R and on the three scalar functions of time. If any one of P , G , p is always zero then R = 0 and only ϕ 0 , ϕ 1 , ϕ 2 are required. In the case of proportional loading ( Q = R = 0 ) only ϕ 0 and ϕ 1 are required and any one of the three strain components can be calculated from the remaining two. Creep and recovery experiments under simultaneous axial force and couple were conducted on a thin-walled tube of polypropylene at 65.5 °C. Theory was used to calculate the circumferential tensile strain from the measured shear strain and longitudinal tensile strain. For this particular tube ϕ 0 and ϕ 1 were found to be related in a special manner, implying that nonlinearity can be adcquatcly described by allowing the shear creep compliance to change with stress history. By varying separately combinations of the invariants of P , ϕ 1 was found to depend on both hydrostatic and deviatoric components ofthe applied stress.

The Stiffness of a Two-Cell Anisotropic Tube

1981 ◽  
Vol 32 (4) ◽  
pp. 338-353 ◽  
Author(s):  
E.H. Mansfield
Keyword(s):  
Single Cell ◽  
Fibre Composite ◽  
Cylindrical Tube ◽  
Shear Stresses ◽  
Longitudinal Stress ◽  
Bearing Material ◽  
Principal Moments Of Inertia ◽  
Principal Axes ◽  
Tension Axis ◽  
Thin Walled

SummaryAn analysis is made of the general two-cell thin-walled cylindrical tube subjected to longitudinal tension, bending and torsion. The walls of the tube may be of fibre composite with an asymmetric lay-up resulting in a coupling between direct and shear stresses and strains. The two-cell tube differs from the single-cell tube in that the tension axis and the principal axes of bending are not necessarily aligned to the c.g. and the principal moments of inertia of the longitudinal stress bearing material.

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