Physical meaning of nonholonomic strain measure

Abstract

The paper overviews the main approaches to the introduction of strain measures. It has been concluded that the physical meaning of certain measures is insufficiently clear. Problems concerning the definition of the physical meaning of the nonholonomic asymmetric strain measure introduced in the framework of a multiscale model, which is based on the physical theory of plasticity, are discussed. This measure is calculated using the corotational integration of the asymmetric and frame-independent strain rate measure equal to the relative velocity gradient. The integration is carried in terms of the corotational coordinate system whose instantaneous motion is determined by averaging the spins of mesoscale elements. It is shown that if elastic distortions are neglected, the introduced mesoscale strain measure is equal to the sum (over all slip systems of the crystallite) of products of accumulated shear multiplied by the basis dyads of the slip systems. The averaging reveals that additional contribution to the value of the macroscale strain measure is attributed, along with elastic distortions, to corotational terms that appear due to different rotation rates of the introduced macroscale corotational frame and crystallite lattices. In view of the absence of analytical expressions for the meso- and macroscale spins, the physical meaning of the macroscale nonholonomic measure is defined in numerical experiments for several strain paths. Calculations have shown that contributions of the elastic and corotational components to the macroscale nonholonomic strain measure are negligible for strain paths of different complexity.