Finite plane strain problems for compressible elastic solids: General solution and volume changes

1977 ◽  
Vol 16 (2) ◽  
pp. 113-122 ◽  
Author(s):  
D. A. Isherwood ◽  
R. W. Ogden
Keyword(s):  
General Solution ◽  
Plane Strain ◽  
Finite Plane ◽  
Elastic Solids ◽  
Volume Changes

Finite Plane Strain of Incompressible Elastic Solids by the Finite Element Method

1968 ◽  
Vol 19 (3) ◽  
pp. 254-264 ◽  
Author(s):  
J. Tinsley Oden
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plane Strain ◽  
Simple Shear ◽  
Finite Elasticity ◽  
The Finite Element Method ◽  
Finite Plane ◽  
Elastic Solids ◽  
Non Linear ◽  
Element Method

SummaryThe finite element method is extended to the problem of finite plane strain of elastic solids. A highly elastic body subjected to two-dimensional deformations is represented by an assembly of triangular elements of finite dimension. The displacement fields within each element are approximated by linear functions of the local coordinates. Non-linear stiffness relations involving generalised node forces and displacements are derived from energy considerations. For demonstration purposes, the non-linear stiffness equations are applied to the problems of finite simple shear and generalised shear. For finite simple shear, it is shown that these relations are in exact agreement with finite elasticity theory. Convergence rates of finite element representations of these problems are briefly examined.

scholarly journals Finite Plane Strain Bending under Tension of Isotropic and Kinematic Hardening Sheets

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1166
Author(s):  
Stanislav Strashnov ◽  
Sergei Alexandrov ◽  
Lihui Lang
Keyword(s):  
Plane Strain ◽  
Kinematic Hardening ◽  
Tensile Force ◽  
Plastic Region ◽  
Equivalent Plastic Strain ◽  
Isotropic Hardening ◽  
Finite Plane ◽  
Present Solution ◽  
Bending Under Tension ◽  
Elastic Unloading

The present paper provides a semianalytic solution for finite plane strain bending under tension of an incompressible elastic/plastic sheet using a material model that combines isotropic and kinematic hardening. A numerical treatment is only necessary to solve transcendental equations and evaluate ordinary integrals. An arbitrary function of the equivalent plastic strain controls isotropic hardening, and Prager’s law describes kinematic hardening. In general, the sheet consists of one elastic and two plastic regions. The solution is valid if the size of each plastic region increases. Parameters involved in the constitutive equations determine which of the plastic regions reaches its maximum size. The thickness of the elastic region is quite narrow when the present solution breaks down. Elastic unloading is also considered. A numerical example illustrates the general solution assuming that the tensile force is given, including pure bending as a particular case. This numerical solution demonstrates a significant effect of the parameter involved in Prager’s law on the bending moment and the distribution of stresses at loading, but a small effect on the distribution of residual stresses after unloading. This parameter also affects the range of validity of the solution that predicts purely elastic unloading.

Volume Changes in Triaxial and Plane Strain Tests

1967 ◽  
Vol 93 (6) ◽  
pp. 297-308
Author(s):  
W. D. Liam Finn ◽  
Neil H. Wade ◽  
Kenneth L. Lee
Keyword(s):  
Plane Strain ◽  
Volume Changes

scholarly journals Plane-strain waves in nonlinear elastic solids with softening

Wave Motion ◽  
2019 ◽  
Vol 89 ◽  
pp. 65-78 ◽  
Author(s):  
Harold Berjamin ◽  
Bruno Lombard ◽  
Guillaume Chiavassa ◽  
Nicolas Favrie
Keyword(s):  
Plane Strain ◽  
Elastic Solids ◽  
Strain Waves ◽  
Nonlinear Elastic

Thermal Stresses in Plane Strain of Porous Elastic Solids

Meccanica ◽  
2004 ◽  
Vol 39 (2) ◽  
pp. 125-138 ◽  
Author(s):  
D. Ieşan ◽  
L. Nappa
Keyword(s):  
Plane Strain ◽  
Thermal Stresses ◽  
Elastic Solids

Magnetic Fields Generated by a Mechanical Singularity in a Magnetized Elastic Half Plane

1989 ◽  
Vol 56 (1) ◽  
pp. 89-95 ◽  
Author(s):  
Chau-Shioung Yeh
Keyword(s):  
Fourier Transform ◽  
Magnetic Fields ◽  
Exact Solutions ◽  
Closed Form ◽  
Plane Strain ◽  
Half Plane ◽  
Elastic Solids ◽  
Soft Ferromagnetic ◽  
Single Force ◽  
The Fourier Transform

The induced magnetic fields generated by a line mechanical singularity in a magnetized elastic half plane are investigated in this paper. One version of linear theory for soft ferromagnetic elastic solids which has been developed by Pao and Yeh (1973) is adopted to analyze the plane strain problem undertaken. By applying the Fourier transform technique, the exact solutions for the generated magnetic inductions due to various mechanical singularities such as a single force, a dipole, and single couple are obtained in a closed form. The distributions of the generated inductions on the surface are shown with figures.

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