Higher stage polar materials and the application to thin-walled members.

Abstract

Polar materials or oriented media are typical examples of generalized continua. These materials, to some extent, are composed of particles that behave like rigid bodies or deformable particles, unlike the geometrical points of the classical continuum theory. Extending these theories in this paper, higher stage innner structures are further introduced successively in the microstructure. This continuum model can be called "higher stage polar materials". The kinematics of the 2nd stage polar materials are studied as an example of the n-th stage polar materials, and 2nd stage strain measures are obtained in addition to the conventional 1st stage strain measures. Applying this model, cross-sectional distortions of thin-walled open cross-section members are analyzed. Constitutive equations and balance equations are obtained, which have the same form as the conventional formula. We can regard the concept of "bimoment" in the theory of thin-walled structures as the couple-stress of the 2nd stage polar materials.