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.

The Strain-Energy Density of Rubber-Like Shells of Revolution Undergoing Torsionless, Axisymmetric Deformation (Axishells)

1986 ◽  
Vol 53 (3) ◽  
pp. 593-596 ◽  
Author(s):  
J. G. Simmonds
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Three Dimensional ◽  
Axisymmetric Deformation ◽  
Shells Of Revolution ◽  
Characteristic Wavelength ◽  
Transverse Shearing ◽  
Shearing Strain

We consider a shell of revolution made of an incompressible elastically isotropic material. Assuming a torsionless, axisymmetric three-dimensional displacement field that permits large normal strains (i.e., large thickness changes) but small transverse shearing strains, we construct a two-dimensional strain-energy density for a first-approximation shell theory in which the extensional strains may be O(1). The bending strains, however, are small, as in Reissner’s nonlinear theory. An error estimate is given that depends on the undeformed thickness and curvatures, the bending strains, the transverse shearing strain, and the characteristic wavelength of the shell theory solutions.

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 Strain Energy Density of Compressible, Rubber-Like Shells of Revolution

1996 ◽  
Vol 63 (2) ◽  
pp. 419-423 ◽  
Author(s):  
R. F. Yu¨kseler
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Density Functions ◽  
Two Dimensional ◽  
Circular Plates ◽  
Shells Of Revolution ◽  
Large Rotations ◽  
Shear Strains ◽  
Transverse Shear Strains

An approach for the derivation of two-dimensional strain energy density functions of compressible, rubber-like shells of revolution which undergo axisymmetric, arbitrarily large rotations and strains including transverse normal and transverse shear strains is proposed. The proposed method is applied to polyurethane rubber, circular plates and numerical results for the flexural buckling of polyurethane circular plates are obtained for an illustrative comparison with a method presented previously.

Data-Driven Design Optimization for Composite Material Characterization

2011 ◽  
Vol 11 (2) ◽  
Author(s):  
John G. Michopoulos ◽  
John C. Hermanson ◽  
Athanasios Iliopoulos ◽  
Samuel G. Lambrakos ◽  
Tomonari Furukawa
Keyword(s):  
Energy Density ◽  
Design Optimization ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Polymer Matrix Composites ◽  
Large Strain ◽  
Surface Strain ◽  
Structural Shape ◽  
Material Systems ◽  
The Difference

The main goal of the present paper is to demonstrate the value of design optimization beyond its use for structural shape determination in the realm of the constitutive characterization of anisotropic material systems such as polymer matrix composites with or without damage. The approaches discussed are based on the availability of massive experimental data representing the excitation and response behavior of specimens tested by automated mechatronic material testing systems capable of applying multiaxial loading. Material constitutive characterization is achieved by minimizing the difference between experimentally measured and analytically computed system responses as described by surface strain and strain energy density fields. Small and large strain formulations based on additive strain energy density decompositions are introduced and utilized for constructing the necessary objective functions and their subsequent minimization. Numerical examples based on both synthetic (for one-dimensional systems) and actual data (for realistic 3D material systems) demonstrate the successful application of design optimization for constitutive characterization.

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.

scholarly journals Volume free strain energy density method for applications to blunt V-notches

2020 ◽  
Vol 28 ◽  
pp. 734-742
Author(s):  
Pietro Foti ◽  
Seyed Mohammad Javad Razavi ◽  
Liviu Marsavina ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Density Method ◽  
Free Strain

scholarly journals On the application of the volume free strain energy density method to blunt V-notches under mixed mode condition

2021 ◽  
Vol 230 ◽  
pp. 111716
Author(s):  
Pietro Foti ◽  
Seyed Mohammad Javad Razavi ◽  
Majid Reza Ayatollahi ◽  
Liviu Marsavina ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Mixed Mode ◽  
Strain Energy ◽  
Density Method ◽  
Free Strain

scholarly journals A numerical analysis of skin–PPE interaction to prevent facial tissue injury

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Rikeen D. Jobanputra ◽  
Jack Hayes ◽  
Sravani Royyuru ◽  
Marc A. Masen
Keyword(s):  
Strain Energy Density ◽  
Strain Energy ◽  
Tissue Injury ◽  
Soft Materials ◽  
Element Model ◽  
Healthcare Systems ◽  
Skin Injury ◽  
Energy Density Distribution ◽  
The World ◽  
The Face

AbstractThe use of close-fitting PPE is essential to prevent exposure to dispersed airborne matter, including the COVID-19 virus. The current pandemic has increased pressure on healthcare systems around the world, leading to medical professionals using high-grade PPE for prolonged durations, resulting in device-induced skin injuries. This study focuses on computationally improving the interaction between skin and PPE to reduce the likelihood of discomfort and tissue damage. A finite element model is developed to simulate the movement of PPE against the face during day-to-day tasks. Due to limited available data on skin characteristics and how these vary interpersonally between sexes, races and ages, the main objective of this study was to establish the effects and trends that mask modifications have on the resulting subsurface strain energy density distribution in the skin. These modifications include the material, geometric and interfacial properties. Overall, the results show that skin injury can be reduced by using softer mask materials, whilst friction against the skin should be minimised, e.g. through use of micro-textures, humidity control and topical creams. Furthermore, the contact area between the mask and skin should be maximised, whilst the use of soft materials with incompressible behaviour (e.g. many elastomers) should be avoided.

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

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