Generalized Continuum Mechanics: What Do We Mean by That?

Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 21)


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).


Couple Stress Generalize Continuum Gradient Theory Nonlocal Theory Virtual Power 
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Authors and Affiliations

  1. 1.UMR 7190 CNRS, Institut Jean Le Rond d’AlembertUPMC Univ Paris 6ParisFrance

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