By Stephen G. Brush
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44)1 A A ϕxxx = utt − c2uxx xx , ϕttx = utt − c2 uxx tt . (47) ρ0 ρ0 Inserting the results into the balance of linear momentum (44)1 , we obtain a more general equation 28 A. Berezovski, J. A. Maugin utt = c2 uxx + C utt − c2uxx B xx − I utt − c2 uxx B tt − A2 uxx . ρ0 B (48) It is easy to see, identifying A2 = c2A Bρ0 ,C = Ic21 , B = I/p2 , that the obtained equation is nothing else but the general model of the dispersive wave propagation (6). Acknowledgements. B. ) is gratefully acknowledged.
Material Inhomogeneities in Elasticity. Chapman and Hall, London (1993) 9. : Nonlinear Waves in Elastic Crystals. Oxford University Press, Oxford (1999) 10. : Pseudo-plasticity and pseudo-inhomogeneity effects in materials mechanics. J. Elasticity 71, 81–103 (2003) 11. : On the thermomechanics of continuous media with diffusion and/or weak nonlocality. Arch. Appl. Mech. 75, 723–738 (2006) 12. : Thermodynamics with internal variables. J. Non-Equilib. Thermodyn. 19, 217–249 (1994) 13. : One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure–part 1: generic formulation.
Ganghoffer, F. ): Mech. of Microstru. Solids, LNACM 46, pp. 39–46. com 40 D. Durville or textile composite structures. Other approaches concentrate on the finite element simulation at the scale of yarns, representing yarns by means of 3D elements with appropriate constitutive laws [1]. Going down to the scale of fibers requires a description of the geometry of fibers in the initial configuration. Such a geometry is a priori unknown, and therefore needs to be computed, for example by simulating the weaving process.