Torsional strain definition

Like many other chemical concepts the concept of strain is only semi-quantitative and lacks precise definition. Molecules are considered strained if they contain internal coordinates (interatomic distances (bond lengths, distances between non-bonded atoms), bond angles, torsion angles) which deviate from values regarded as normal and strain-free . For instance, the normal bond angle at the tetra-coordinated carbon atom is close to the tetrahedral value of 109.47°. In the course of force field calculations these normal values are defined more satisfactorily, though in a somewhat different way, as force field parameters. 

The problem of definition of modulus applies to all tests. However there is a second problem which applies to those tests where the state of stress (or strain) is not uniform across the material cross-section during the test (i.e. to all beam tests and all torsion tests - except those for thin walled cylinders). In the derivation of the equations to determine moduli it is assumed that the relation between stress and strain is the same everywhere, this is no longer true for a non-linear material. In the beam test one half of the beam is in tension and one half in compression with maximum strains on the surfaces, so that there will be different relations between stress and strain depending on the distance from the neutral plane. For the torsion experiments the strain is zero at the centre of the specimen and increases toward the outside, thus there will be different torque-shear modulus relations for each thin cylindrical shell. Unless the precise variation of all the elastic constants with strain is known it will not be possible to obtain reliable values from beam tests or torsion tests (except for thin walled cylinders). 

The conventional definition of equivalent strain is based on the proposition that samples should be compared on which the same amount of plastic work has been spent. For comparison of two specimens deformed in compression and torsion this would read... 

As structured fluids such as liquid crystals are at least partially fluid, we also need to consider the forces and torques produced by friction. The frictional forces are given by a dissipative stress tensor, which is most conveniently derived from the dissipative function (j)F It is a homogeneous positive definite quadratic function of the time derivatives of the strains and rotations (the time derivatives of the torsions can be generally ignored) giving ... 

Among variorrs properties, mechanical properties probably are the most important properties of fibers. There are many different types of mechanical properties, including tensile, torsional, bending, and compressional properties. Among them, tensile properties are the most intensively studied for fibers, probably because of their unique shape. However, other types of mechanical properties also are important. Chapter 15 first deseribes the basic definitions of Hooke s law, stress, strain, and tensile, bulk and shear moduli, and then gives more detailed discussion on the tensile, torsional, bending, and compressional properties of fibers. 

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