Kinematics

Abstract

This chapter is concerned with the kinematics of deformations and motions of micromorphic, microstretch, and micropolar (3M) continua. In Section 1.1 we present a physical picture to show how microdeformation of bodies gives rise to extra degrees of freedom necessary to characterize microstructural continua. To this end, examples are chosen from lattice dynamics of crystalline solids, liquid crystals, suspensions, animal blood, and composites. Definitions are then given for the microcontinua based on this picture. In Section 1.2, motion and micromotions are defined. Micromorphic continua are then characterized by the macromotions of a particle and a set of deformable directors that represent the mathematical model of a deformable particle. The rotation is the subject of Section 1.3, where finite macrorotation of directors is introduced and the fundamental theorem of rotation is given. In Section 1.4 we define microstretch and micropolar continua and show that they arise as special subcontinua,by means of constraints placed on micromorphic continua. Possible applications of these continua are mentioned briefly. Section 1.5 is devoted to strain measures of micromorphic, microstretch, and micropolar continua. To eliminate repetitions, we shall also call them 3M continua.

Arguments against new ideas generally pass through distinct stages from:

“It’s not true” to

“Well it may be true, but not important” to

“It’s true and it’s important, but it’s not new-we knew it all along.”

From The Artful Universe

by John D. Barron