Saint-Venant End Effects for Incremental Plane Deformations of Incompressible Nonlinearly Elastic Materials

1985 ◽  
Vol 52 (4) ◽  
pp. 847-852 ◽  
Author(s):  
R. Abeyaratne ◽  
C. O. Horgan ◽  
D.-T. Chung
Keyword(s):  
Plane Deformation ◽  
Tensile Load ◽  
Infinite Strip ◽  
End Effects ◽  
Short Side ◽  
Incompressible Materials ◽  
Constitutive Parameters ◽  
Small Deformations ◽  
Nonlinearly Elastic ◽  
Plane Deformations

This paper is concerned with assessing the extent of Saint-Venant end effects within the theory of small deformations superposed on a large deformation for plane strain of homogeneous, isotropic, incompressible materials. The problem considered is that of plane deformation of a body which in its undeformed configuration, occupies a semi-infinite strip. The long sides of the strip are free of traction while the short side is subjected to prescribed normal and shear tractions. A purely normal tensile traction is applied uniformly at the remote end. For the case of slightly nonuniform end tractions at the near end, it is shown that the resulting stress distribution differs from that of homogeneous uniaxial tension by an exponentially decaying function of the distance from the end of the strip. The decay rate is characterized explicitly in terms of the strip width, the remotely applied tensile load, and constitutive parameters. Numerical results are provided for the Mooney-Rivlin material and power-law materials which either harden or soften in tension.

scholarly journals In-Process Measurement of Three-Dimensional Deformations Based on Speckle Photography

2021 ◽  
Vol 11 (11) ◽  
pp. 4981
Author(s):  
Andreas Tausendfreund ◽  
Dirk Stöbener ◽  
Andreas Fischer
Keyword(s):  
Evaluation Method ◽  
Process Analysis ◽  
Plane Deformation ◽  
Three Dimensional ◽  
Machining Process ◽  
Image Correlation ◽  
Speckle Photography ◽  
Process Measurement ◽  
Out Of Plane ◽  
Plane Deformations

In the concept of the process signature, the relationship between a material load and the modification remaining in the workpiece is used to better understand and optimize manufacturing processes. The basic prerequisite for this is to be able to measure the loads occurring during the machining process in the form of mechanical deformations. Speckle photography is suitable for this in-process measurement task and is already used in a variety of ways for in-plane deformation measurements. The shortcoming of this fast and robust measurement technique based on image correlation techniques is that out-of-plane deformations in the direction of the measurement system cannot be detected and increases the measurement error of in-plane deformations. In this paper, we investigate a method that infers local out-of-plane motions of the workpiece surface from the decorrelation of speckle patterns and is thus able to reconstruct three-dimensional deformation fields. The implementation of the evaluation method enables a fast reconstruction of 3D deformation fields, so that the in-process capability remains given. First measurements in a deep rolling process show that dynamic deformations underneath the die can be captured and demonstrate the suitability of the speckle method for manufacturing process analysis.

scholarly journals Saint-Venant end effects for plane deformations of linear piezoelectric solids

2006 ◽  
Vol 43 (5) ◽  
pp. 943-956 ◽  
Author(s):  
Alessandra Borrelli ◽  
Cornelius O. Horgan ◽  
M. Cristina Patria
Keyword(s):  
End Effects ◽  
Piezoelectric Solids ◽  
Plane Deformations

Stress Analysis for a Nonlinear Viscoelastic Compressible Cylinder

1970 ◽  
Vol 37 (4) ◽  
pp. 1127-1133 ◽  
Author(s):  
E. C. Ting
Keyword(s):  
Large Deformations ◽  
Finite Deformations ◽  
Kernel Functions ◽  
Nonlinear Viscoelastic ◽  
Stress Strain Relation ◽  
Incompressible Materials ◽  
Small Deformations ◽  
Compressible Cylinder ◽  
Elastic Casing ◽  
Finite Difference Techniques

Real solids are not incompressible, although many viscoelastic materials which undergo large deformations show only small changes in volume under ordinary loading conditions. This paper is concerned with a pressurized isotropic viscoelastic hollow cylinder bonded to an elastic casing in which, during a finite deformation, the dilatational change in any element of the cylinder is a small quantity. The analysis is based in part upon the theory of small deformations superposed on finite deformations. Numerical calculations are evaluated by using finite-difference techniques and assuming particular forms of kernel functions in the stress-strain relation. The results for compressible and incompressible materials are compared.

An interference technique for the measurement of in-plane displacements of opaque surfaces

1974 ◽  
Vol 9 (1) ◽  
pp. 36-43 ◽  
Author(s):  
M Marchant ◽  
S M Bishop
Keyword(s):  
Carbon Fibre ◽  
Real Time ◽  
Fringe Pattern ◽  
Laser Interferometer ◽  
Tensile Load ◽  
Surface Displacements ◽  
Moiré Fringes ◽  
Fibre Composites ◽  
Carbon Fibre Composites ◽  
Plane Deformations

A laser interferometer system is used to record two mutually perpendicular diffraction gratings on a photoresist coated specimen. When either grating is re-illuminated by the fringe pattern used to form it, real-time observations can be made of moiré fringes corresponding to surface displacements which occur as a tensile load is applied to the specimen. The technique has been used to study the in-plane deformations of carbon-fibre composites, and typical results are given.

MODELING OF A MEMBRANE FOR NONLINEARLY ELASTIC INCOMPRESSIBLE MATERIALS VIA GAMMA-CONVERGENCE

2006 ◽  
Vol 04 (01) ◽  
pp. 31-60 ◽  
Author(s):  
KARIM TRABELSI
Keyword(s):  
Integral Representation ◽  
Internal Energy ◽  
Elastic Membrane ◽  
Gamma Convergence ◽  
Two Dimensional ◽  
Incompressible Materials ◽  
Plate Models ◽  
Γ Convergence ◽  
Nonlinearly Elastic

In this paper, we derive nonlinearly elastic membrane plate models for hyperelastic incompressible materials using Γ-convergence arguments. We obtain an integral representation of the limit two-dimensional internal energy owing to a result of singular functionals relaxation due to Ben Belgacem [6].

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