BODY TENSOR FORMALISM IN FINITE DEFORMATION ELASTICITY AND APPLICATION TO THE TORSION OF A CIRCULAR CYLINDER
In this work one develops the body tensor formalism for homogenous, isotropic elastic materials. This formalism is general and not limited to small deformations. One examines the physical laws and the constitutive equation which relates the stress to the strain with the help of the two Lame coefficients and the three third order elastic constants. Although the body tensor formalism has been used before to describe finite deformation elasticity, it has not been used to generalize the constitutive equation for the stress-strain relationship. The body tensor formalism and the generalised constitutive equation are applied to the torsion of a right circular cylinder whose length is prevented from changing by the application of an end force. The solution of the torsion problem leads to a new second order non-linear differential equation which is valid to all orders in the torsion parameter. When linearized this equation can be solved to the first two orders in a dimensionless torsion parameter. Using the values of the third order elastic constants found in the ultrasonic literature new values are calculated to first order for the radius, the torque and the force at the end of the cylinder for six metallic compounds and three non metallic ones.
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