Generalized Measures for Large Deformations

Abstract

In engineering materials, even in the largest purely elastic deformations, the strain is small even though the displacement gradients and rotations may be large. In such cases there is very little gained in altering classical linear strain-stress tensor constitutive equations. In 1935, a paper by B.R. Sethi renewed interest in such problems, and then followed a host of papers by prominent workers in the field of continuum mechanics. A number of them wanted to consider incompressible materials like rubber and produced complicated constitutive equations, for which many adhoc approximations had to be made to get an agreement with experimental results. But with the advent of soft alloys and high polymers the problem of large deformations, involving severe strains, has again put the constitutive equations in the melting pot. Even though all branches of science have adopted Generalized Measures for problems both at the micro and macro levels, the engineer has been reluctant to change his concepts. He does not want to go beyond the Cauchy and Hencky measures. It should also be appreciated that high speed computation of engineering problems can give reliable results only if the order of strain measure is prescribed in advance. Thus arises the need of adopting generalized measures to simplify constitutive equations and to get better agreement with experimental results.