A Discussion of Multiplicative Decompositions and Strain Measures

2021 ◽  
Author(s):  
James Casey
Keyword(s):  
Strain Measures

A new approach to curvature measures in linear shell theories

2020 ◽  
pp. 108128652097275
Author(s):  
Miroslav Šilhavý
Keyword(s):  
Strain Tensor ◽  
Middle Surface ◽  
Surface Strain ◽  
Affine Function ◽  
Shear Deformations ◽  
Strain Measure ◽  
Bending Strain ◽  
Curvature Measures ◽  
Tensor Formula ◽  
Strain Measures

The paper presents a coordinate-free analysis of deformation measures for shells modeled as 2D surfaces. These measures are represented by second-order tensors. As is well-known, two types are needed in general: the surface strain measure (deformations in tangential directions), and the bending strain measure (warping). Our approach first determines the 3D strain tensor E of a shear deformation of a 3D shell-like body and then linearizes E in two smallness parameters: the displacement and the distance of a point from the middle surface. The linearized expression is an affine function of the signed distance from the middle surface: the absolute term is the surface strain measure and the coefficient of the linear term is the bending strain measure. The main result of the paper determines these two tensors explicitly for general shear deformations and for the subcase of Kirchhoff-Love deformations. The derived surface strain measures are the classical ones: Naghdi’s surface strain measure generally and its well-known particular case for the Kirchhoff-Love deformations. With the bending strain measures comes a surprise: they are different from the traditional ones. For shear deformations our analysis provides a new tensor [Formula: see text], which is different from the widely used Naghdi’s bending strain tensor [Formula: see text]. In the particular case of Kirchhoff–Love deformations, the tensor [Formula: see text] reduces to a tensor [Formula: see text] introduced earlier by Anicic and Léger (Formulation bidimensionnelle exacte du modéle de coque 3D de Kirchhoff–Love. C R Acad Sci Paris I 1999; 329: 741–746). Again, [Formula: see text] is different from Koiter’s bending strain tensor [Formula: see text] (frequently used in this context). AMS 2010 classification: 74B99

Constitutive inequalities for isotropic elastic solids under finite strain

1970 ◽  
Vol 314 (1519) ◽  
pp. 457-472 ◽  
Keyword(s):  
Scalar Product ◽  
Finite Strain ◽  
Strain Analysis ◽  
Stress And Strain ◽  
Elastic Solids ◽  
Intrinsic Interest ◽  
Typical Member ◽  
Rates Of Change ◽  
Constitutive Inequalities ◽  
Strain Measures

Possible restrictions on isotropic constitutive laws for finitely deformed elastic solids are examined from the standpoint of Hill (1968). This introduced the notion of conjugate pairs of stress and strain measures, whereby families of contending inequalities can be generated. A typical member inequality stipulates that the scalar product of the rates of change of certain conjugate variables is positive in all circumstances. Interrelations between the various inequalities are explored, and some statical implications are established. The discussion depends on several ancillary theorems which are apparently new; these have, in addition, an intrinsic interest in the broad field of basic stress—strain analysis.

Experimental Determination of Wheel and Guiding Forces on the Tracks

2015 ◽  
Vol 732 ◽  
pp. 203-206
Author(s):  
Lubos Pazdera ◽  
Jaroslav Smutny ◽  
Libor Topolář
Keyword(s):  
Experimental Determination ◽  
Vertical Direction ◽  
Railway Track ◽  
Experimental Basis ◽  
Force Interaction ◽  
Dynamic Forces ◽  
Passing Train ◽  
Strain Measures

Force interaction between a railway track and a vehicle affects the safety, comfort, and last but not least, economical maintenance. Train of wagons incidence on track in both transversal and vertical direction is simplified by qualifying of force wheel (FQ), guiding (FY) and perpendicular and transverse acceleration. An experimental basis for dynamic determination of vertical, FQ, and lateral, FY, forces at the wheel using strain measures in the foot of the rail is given. Measurements of the dynamic forces during passing train are normally very costly and uneasy. These method consists of measuring strains at selected points of the rail profile is very simple and therefore interesting.

Bodies, Deformations, and Strain Measures

2015 ◽  
pp. 1-67
Author(s):  
Paolo Maria Mariano ◽  
Luciano Galano
Keyword(s):  
Strain Measures
Sign in / Sign up

Export Citation Format

Share Document