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.

Large-Strain Axisymmetric Deformation of Cylindrical Shells

1987 ◽  
Vol 54 (2) ◽  
pp. 287-291 ◽  
Author(s):  
G. W. Brodland ◽  
H. Cohen
Keyword(s):  
Nonlinear Equations ◽  
Energy Minimization ◽  
Parametric Analysis ◽  
Large Strain ◽  
Cylindrical Shells ◽  
Radial Force ◽  
Axisymmetric Deformation ◽  
The Other ◽  
Large Strains ◽  
Minimization Technique

Nonlinear equations are derived for the axisymmetric deformation of thin, cylindrical shells made of Mooney-Rivlin materials and subject to arbitrarily large strains and rotations. These equations are then implemented numerically using an energy minimization technique. Finally, an extensive parametric analysis is done of cylindrical shells which are clamped at one end and loaded with either a radial force or an edge moment uniformly distributed along the circumference of the other end.

Large Elastic Deformation of Shear Deformable Shells of Revolution: Theory and Analysis

1987 ◽  
Vol 54 (3) ◽  
pp. 578-584 ◽  
Author(s):  
L. A. Taber
Keyword(s):  
Shear Deformation ◽  
Axisymmetric Deformation ◽  
Large Strains ◽  
Normal Strain ◽  
Shells Of Revolution ◽  
Incompressible Hyperelastic Material ◽  
Large Elastic Deformation ◽  
Spherical Caps ◽  
Transition Points ◽  
Thick Shells

Large axisymmetric deformation of pressurized shells of revolution is studied. The governing equations include the effects of transverse normal strain and transverse shear deformation for shells composed of an incompressible, hyperelastic material. Asymptotic solutions to the equations are developed which are valid for moderately large strains. Application to Mooney-Rivlin clamped spherical caps reveals that, for large enough bending and stretching, the consequences of shear deformation include: (1) bending moments can decrease at the edge after the load passes a critical point; (2) even thick shells can behave as membranes; (3) transition points can occur in the shell which divide regions of shell-like behavior from regions of membrane-like behavior.

A Simplified Displacement-Rotation Form for the Equations of Motion of Nonlinearly Elastic Shells of Revolution Undergoing Combined Bending and Torsion

1996 ◽  
Vol 63 (2) ◽  
pp. 539-542 ◽  
Author(s):  
J. G. Simmonds
Keyword(s):  
Equations Of Motion ◽  
Shell Of Revolution ◽  
Shells Of Revolution ◽  
Elastic Shells ◽  
Axisymmetric Bending ◽  
Nonlinearly Elastic

By appropriately defining two displacements and a rotation, it is shown that the equations of motion of a shell of revolution undergoing combined axisymmetric bending and torsion, in which the extensional strains and the rotations may be arbitrarily large, can be given a form in which there are three effective extensional strains and two effective bending strains, each of which is only linear or quadratic in the displacements and rotation.

On a Nonlinear Theory for Muscle Shells: Part I—Theoretical Development

1991 ◽  
Vol 113 (1) ◽  
pp. 56-62 ◽  
Author(s):  
L. A. Taber
Keyword(s):  
Muscle Activation ◽  
Large Strain ◽  
Axisymmetric Deformation ◽  
Theoretical Development ◽  
Nonlinear Material ◽  
Shells Of Revolution ◽  
Strain Behavior ◽  
Strain Energy Density Function ◽  
Lines Of Curvature ◽  
Transverse Shear Strains

This paper presents a theory for studies of the large-strain behavior of biological shells composed of layers of incompressible, orthotropic tissue, possibly muscle, of arbitrary orientation. The intrinsic equations of the laminated-shell theory, expressed in lines-of-curvature coordinates, account for large membrane [O(1)] and moderately large bending and transverse shear strains [O(0.3)], nonlinear material properties, and transverse normal stress and strain. An expansion is derived for a general two-dimensional strain-energy density function, which includes residual stress and muscle activation through a shifting zero-stress configuration. Strain-displacement relations are given for the special case of axisymmetric deformation of shells of revolution with torsion.

The Strain-Energy Density of Compressible, Rubber-Like Axishells

1987 ◽  
Vol 54 (2) ◽  
pp. 453-454 ◽  
Author(s):  
J. G. Simmonds
Keyword(s):  
Strain Energy Density ◽  
Strain Energy ◽  
Large Strain ◽  
Axisymmetric Deformation ◽  
Strain Theory ◽  
Three Dimensions ◽  
Compressible Material ◽  
Shells Of Revolution ◽  
First Approximation ◽  
Recent Method

A recent method for deriving, by descent from three dimensions, strain-energy densities in a first-approximation, large-strain theory of incompressible, elastically isotropic shells of revolution undergoing torsionless, axisymmetric deformation (axishells) is adapted to axishells made of compressible material. Application is made to the Blatz-Ko strain-energy densities for a polyurethane (“continuum”) rubber and a foam rubber.

Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

1990 ◽  
Vol 57 (2) ◽  
pp. 298-306 ◽  
Author(s):  
K. W. Neale ◽  
S. C. Shrivastava
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Flow Theory ◽  
Constitutive Laws ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Inelastic Behavior ◽  
Rate Dependent

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

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.

Numerical Modelling of Plastic Deformation and Subsequent Recrystallization in Polycrystalline Materials, Based on a Digital Material Framework

2007 ◽  
Vol 558-559 ◽  
pp. 1133-1138 ◽  
Author(s):  
Roland E. Logé ◽  
M. Bernacki ◽  
H. Resk ◽  
H. Digonnet ◽  
T. Coupez
Keyword(s):  
Level Set ◽  
Large Strain ◽  
Voronoi Tessellation ◽  
Constitutive Law ◽  
Polycrystalline Materials ◽  
Large Strains ◽  
Element Mesh ◽  
Digital Material ◽  
Digital Sample ◽  
Level Set Approach

The development of a digital material framework is presented, allowing to build virtual microstructures in agreement with experimental data. The construction of the virtual material consists in building a multi-level Voronoï tessellation. A polycrystalline microstructure made of grains and sub-grains can be obtained in a random or deterministic way. A corresponding finite element mesh can be generated automatically in 3D, and used for the simulation of mechanical testing under large strain. In the examples shown in this work, the initial mesh was non uniform and anisotropic, taking into account the presence of interfaces between grains and sub-grains. Automatic remeshing was performed due to the large strains, and maintained the non uniform and anisotropic character of the mesh. A level set approach was used to follow the grain boundaries during the deformation. The grain constitutive law was either a viscoplastic power law, or a crystallographic formulation based on crystal plasticity. Stored energies and precise grain boundary network geometries were obtained directly from the deformed digital sample. This information was used for subsequent modelling of grain growth with the level set approach, on the same mesh.

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