Isogeometric Static Analysis of Gradient-Elastic Plane Strain/Stress Problems

2016 ◽  
pp. 229-235 ◽  
Author(s):  
Sergei Khakalo ◽  
Viacheslav Balobanov ◽  
Jarkko Niiranen
Keyword(s):  
Plane Strain ◽  
Static Analysis ◽  
Elastic Plane ◽  
Strain Stress

Plane strain/stress solutions for piezoelectric solids

1997 ◽  
Vol 28 (4) ◽  
pp. 385-396 ◽  
Author(s):  
R.K.N.D. Rajapakse
Keyword(s):  
Plane Strain ◽  
Strain Stress ◽  
Piezoelectric Solids

Evaluation of a Modified Monotonic Neuber Relation

1991 ◽  
Vol 113 (1) ◽  
pp. 1-8 ◽  
Author(s):  
W. N. Sharpe ◽  
K. C. Wang
Keyword(s):  
Plane Strain ◽  
Notch Root ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Predictive Capability ◽  
Stress Strain Curve ◽  
Interferometric Technique ◽  
Strain Stress ◽  
Concentration Factors ◽  
Elastoplastic Strains

It has been proposed in the literature that the Neuber relation be modified to read Kε/Kt×(Kσ/Kt)m=1 in order to improve its predictive capability when plane strain loading conditions exist. Kε, Kσ, and Kt are respectively the strain, stress, and elastic concentration factors. The exponent m is proposed to be 1 for plane stress and 0 for plane strain. This paper reports the results of biaxial notch root strain measurements on three sets of double-notched aluminum specimens that have different thicknesses and root radiuses. Elastoplastic strains are measured over gage lengths as short as 150 micrometers with a laser-based in-plane interferometric technique. The measured strains are used to compute Kε directly and Kσ using the uniaxial stress-strain curve. The exponent m can then be determined for each amount of constraint. The amount of constraint is defined as the negative ratio of lateral to longitudinal strain at the notch root and determined from elastic finite element analyses. As this ratio decreases for the three cases, the values of m are found to be 0.65, 0.48, and 0.36. The modified Neuber relation is an improvement, but discrepancies still exist when plastic yielding begins at the notch root.

Singularities at Grain Triple Junctions in Two-Dimensional Polycrystals With Cubic and Orthotropic Grains

1996 ◽  
Vol 63 (2) ◽  
pp. 295-300 ◽  
Author(s):  
R. C. Picu ◽  
V. Gupta
Keyword(s):  
Grain Boundary ◽  
Plane Strain ◽  
Anisotropic Elasticity ◽  
Symmetric Case ◽  
Elastic Plane ◽  
Two Dimensional ◽  
Triple Junctions ◽  
Stress Singularities ◽  
Plane Strain Deformation ◽  
Singular Configuration

Stress singularities at grain triple junctions are evaluated for various asymmetric grain boundary configurations and random orientations of cubic and orthotropic grains. The analysis is limited to elastic plane-strain deformation and carried out using the Eshelby-Stroh formalism for anisotropic elasticity. For both the cubic and orthotropic grains, the most singular configuration corresponds to the fully symmetric case with grain boundaries 120 deg apart, and with symmetric orientations of the material axes. The magnitude of the singularities are obtained for several engineering polycrystals.

Analytical Solutions to Axisymmetric Plane Strain Porous Media-Transport Models in Large Arteries

2008 ◽  
Author(s):  
Jonathan P. Vande Geest ◽  
Bruce R. Simon
Keyword(s):  
Plane Strain ◽  
Analytical Solutions ◽  
Soft Tissues ◽  
Fluid Pressure ◽  
Convective Transport ◽  
Species Transport ◽  
Mobile Species ◽  
Starting Point ◽  
Strain Stress ◽  
Numerical Finite Element

Theoretical and numerical finite element models (FEMs) have been developed for analysis of coupled structural-fluid-species transport in soft tissues [1–3]. Here analytical solutions for coupled diffusive-convective transport of a single, neutral species in soft tissues are presented. Based on experimental observations [4], osmotic pressure and partial Onsager coupling of species transport can be neglected for large mobile species in rabbit carotid arteries. These analytical solutions provide a starting point for development of solutions to more complex problems and allow verification of the associated FEMs under development in our laboratory. The analytical solutions will allow comparison of elastic and poroelastic-species transport for axisymmetric, plane strain in thick-walled arteries including expressions for displacement, strain, stress, pore fluid pressure, and concentration fields. The initial models considered here will be steady state (SS) solutions for compressible, linear, isotropic materials undergoing small strains.

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