The Creep of Thick Tubes Under Internal Pressure

1957 ◽  
Vol 24 (3) ◽  
pp. 464-466
Author(s):  
C. D. Weir
Keyword(s):  
Internal Pressure ◽  
Strain Rate ◽  
Shear Strain ◽  
Rate Equation ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Stress Deviator ◽  
Constant Density ◽  
Creep Stress ◽  
Shear Strain Energy

Abstract Using the usually accepted assumption that the strain rate of a material undergoing creep is given by the product of the stress deviator and a function of the shear-strain energy, and assuming constant density, equations are derived for the creep stresses in a thick-walled tube under internal pressure for a generalized form of the shear strain-energy function. It is shown that these reduce to previously published equations on the substitution of a power law stress-strain rate equation. The nonisothermal case is considered also and creep-stress equations are obtained in a similarly generalized form.

Minimum-weight beams with shear strain energy

2011 ◽  
Vol 16 (1) ◽  
pp. 145-154 ◽  
Author(s):  
Byoung Koo Lee ◽  
Sang Jin Oh ◽  
Tae Eun Lee ◽  
Jung Su Park
Keyword(s):  
Shear Strain ◽  
Strain Energy ◽  
Minimum Weight ◽  
Shear Strain Energy

An Energy Approach to the Mechanics of Discontinuous Chip Formation

1964 ◽  
Vol 86 (2) ◽  
pp. 157-162 ◽  
Author(s):  
W. K. Luk ◽  
R. C. Brewer
Keyword(s):  
Shear Stress ◽  
Shear Strain ◽  
Normal Stress ◽  
Chip Formation ◽  
Strain Energy ◽  
Energy Condition ◽  
Stress And Strain ◽  
Rupture Plane ◽  
Shear Stress And Strain ◽  
Shear Strain Energy

After briefly reviewing previous work in this field, the authors propose that rupture of the chip work contact (to give a discontinuous chip) is governed by a limiting shear strain energy condition. Assuming that shear stress and strain at rupture are dependent on the compressive normal stress, a criterion for the direction of the rupture plane is deduced. Using some results given by Field and Merchant, the authors then compare their calculated direction of rupture with that experimentally observed. Some indication that the agreement is not entirely fortuitous is afforded by checking the calculated shear strain energy at fracture with that calculated from force and chip measurements.

On Energy Strength Theories for Geomaterials

2013 ◽  
Vol 353-356 ◽  
pp. 901-904
Author(s):  
Shou Yi Xue
Keyword(s):  
Energy Density ◽  
Shear Strain ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Volumetric Strain ◽  
Dissipated Energy ◽  
Energy Theory ◽  
Shear Strain Energy ◽  
Shear Energy ◽  
Strain Energy Density Theory

The composition of the energy in the process of material deformation and failure and the relationship between energy and strength were summarized; the features, essences and main problems of the energy release rate theory, the three-shear energy theory and the net shear strain energy density theory were illustrated. It is pointed out that the roles of distortion strain energy, volumetric strain energy and dissipated energy are not identical, especially distortion strain energy and volumetric strain energy must be separately processed. The three-shear energy theory and the net shear strain energy density theory can properly deal with the problems, and also well reflect the intermediate principal stress effect. The above research results can provide references for further discussions.

Finite Axisymmetric Deformations of Initially Cylindrical Reinforced Membranes

1972 ◽  
Vol 45 (6) ◽  
pp. 1677-1683 ◽  
Author(s):  
A. D. Kydoniefs
Keyword(s):  
Stress Field ◽  
Internal Pressure ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Incompressible Material ◽  
Parameter System ◽  
Axial Section ◽  
Variable Pitch ◽  
Two Parameter

Abstract We consider the axisymmetrie deformations of an initially cylindrical membrane composed of an elastic, homogeneous, isotropic and incompressible material reinforced with a two-parameter system of perfectly flexible and inextensible helicoidal cords of variable pitch. The undeformed configuration is determined so that the deformed membrane has a given axial section under specified internal pressure. The corresponding stress field and cord tensions are obtained. The solution given is exact and valid for the general form of the strain—energy function.

Further Study on the Net Shear Strain Energy Density Theory

2013 ◽  
Vol 423-426 ◽  
pp. 1644-1647
Author(s):  
Shou Yi Xue
Keyword(s):  
Energy Density ◽  
Shear Strain ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Volumetric Strain ◽  
Material Strength ◽  
Strength Theory ◽  
Shear Strain Energy ◽  
Strain Energy Density Theory

The net shear strain energy density strength theory was systematically explained. Firstly, the composition of elastic strain energy and the roles of their own were analyzed, and it is pointed out that the distortion strain energy is the energy driving failure and the volumetric strain energy can help improve the material strength. Therefore, ultimate energy driving material damage should be the shear strain energy after deducting the friction effect, namely the net shear strain energy, which indicates rationality of the assumption adopted by the net shear strain energy strength theory. Secondly, the empirical laws of geomaterial strength were summarized and explained by using the net shear strain energy theory, which verifies the new theory is appropriate.

scholarly journals Joined dissimilar orthotropic elastic cylindrical membranes under internal pressure and longitudinal tension

1993 ◽  
Vol 34 (3) ◽  
pp. 296-317 ◽  
Author(s):  
V. G. Hart ◽  
Jingyu Shi
Keyword(s):  
Internal Pressure ◽  
Energy Function ◽  
Strain Energy ◽  
Numerical Solutions ◽  
Circumferential Stress ◽  
Strain Energy Function ◽  
The Body ◽  
Surgical Implants ◽  
Elastic Membranes ◽  
Preliminary Study

AbstractFollowing work in an earlier paper, the theory of finite deformation of elastic membranes is applied to the problem of two initially-circular semi-infinite cylindrical membranes of the same radius but of different material, joined longitudinally at a cross-section. The body is inflated by constant interior pressure and is also extended longitudinally. The exact solution found for an arbitrary material is now specialised to the orthotropic case, and the results are interpreted for forms of the strain-energy function introduced by Vaishnav and by How and Clarke in connection with the study of arteries. Also considered in this context is the similar problem where two semi-infinite cylindrical membranes of the same material are separated by a cuff of different material. Numerical solutions are obtained for various pressures and longitudinal extensions. It is shown that discontinuities in the circumferential stress at the joint can be reduced by suitable choice of certain coefficients in the expression defining the strain-energy function. The results obtained here thus solve the problem of static internal pressure loading in extended dissimilar thin orthotropic tubes, and may also be useful in the preliminary study of surgical implants in arteries.

Multiphase Constitutive Model of " Matrix-Strengthen Particle of Saturated Soil "

2010 ◽  
Vol 168-170 ◽  
pp. 1098-1101
Author(s):  
Wen Xu Ma ◽  
Ying Guang Fang ◽  
Zhe Li
Keyword(s):  
Particle Size ◽  
Constitutive Model ◽  
Shear Strain ◽  
Strain Gradient ◽  
Strain Energy ◽  
Continuum Models ◽  
Internal Length ◽  
Micro Scale ◽  
The Matrix ◽  
Shear Strain Energy

In this article soil is treated as non-uniform material including two parts : the matrix particles and the reinforcement particles. Through soil shear strain energy and micro-crack assumptions, we establish a multiphase constitutive model connecting macro and micro scale based on classical continuum models, which includes the strain gradient, internal length scales and particle size. This model have been verified reasonable by artificial soil experiment.

Nonlinear Thermohyperviscoelastic Constitutive Model for Soft Materials with Strain Rate and Temperature Dependency

2020 ◽  
Vol 12 (06) ◽  
pp. 2050059
Author(s):  
Zahra Matin Ghahfarokhi ◽  
Mehdi Salmani-Tehrani ◽  
Mahdi Moghimi Zand
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Soft Materials ◽  
Material Behavior ◽  
Temperature Dependent ◽  
Dependent Behavior ◽  
Temperature Dependent Behavior

Soft materials, such as polymeric materials and biological tissues, often exhibit strain rate and temperature-dependent behavior when subjected to external loads. To characterize the thermomechanical behavior of isotropic soft material, a thermohyperviscoelastic constitutive model has been developed through an additive decomposition of strain energy function into elastic and viscous parts. A three-term generalized Rivlin strain energy function is utilized to formulate the hyperelastic part of the model, while a new viscous potential function is proposed to describe the effect of strain rate and temperature on material behavior. Toward this end, a new procedure has been proposed to determine the viscous mechanical properties as a function of strain-rate and temperature. Comparing with the previously published experimental data for linear low-density polyethylene reveals that the proposed model can sufficiently capture the nonlinearity, rate- and temperature-dependent behavior of the soft materials.

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