Generalized Continuum Mechanics: What Do We Mean by That?

Discursive historical perspective on the developments and ramifications of generalized continuum mechanics from its inception by the Cosserat brothers (Théorie des corps déformables. Hermann,

1909

) with their seminal work of 1909 to the most current developments and applications is presented. The point of view adopted is that generalization occurs through the successive abandonment of the basic working hypotheses of standard continuum mechanics of Cauchy, that is, the introduction of a rigidly rotating microstructure and

couple stresses

(Cosserat continua or

micropolar

bodies, nonsymmetric stresses), the introduction of a truly deformable microstructure (

micromorphic

bodies), “weak”

nonlocalization

with

gradient theories

and the notion of

hyperstresses

, and the introduction of characteristic lengths, “strong nonlocalization” with space functional constitutive equations and the loss of the Cauchy notion of stress, and finally giving up the Euclidean and even Riemannian material background. This evolution is paved by landmark papers and timely scientific gatherings (e.g., Freudenstadt, 1967; Udine, 1970, Warsaw, 1977).