Rheology and Nonlinear Elasticity

摘要: This first specialized chapter deals with the awaited generalization to mechanical behaviours that deviate from linear elasticity and standard Newtonian viscous fluids, is, in large deformations rheology of complex fluids. These extensions were kindled by mechanics rubber artificial fabrics fluids high viscosity visco-plastic response. It happens same scientists involved these two lines as a result required focus on bases continuum mechanics, particular theory finite rational geometric background, need account for flow features some Ronald Rivlin, his incommensurable contributions, is great hero this adventure. Other whose work was seminal are initially E. Bingham, M. Reiner, L.G.R. Treloar, P. J. Flory, M.A. Mooney, F.D. Murnaghan, more recently J.G. Oldroyd, A.E. Green, J.L. Ericksen, C.A. Truesdell, B.D. Coleman, W. Noll. The survey includes models neo-Hookean materials, Mooney-Rivlin Rivlin-Ericksen unsuccessful attempts such those Reiner-Rivlin hypoelasticity. Appropriately introduced tools have been tensors, Oldroyd Jaumann time derivatives, invariant representations scalar tensorvalued functions. Through Rivlin co-workers whole carries strong print British applied mathematics although Italian Russian contributions nonlinear cannot be overlooked. soft living tissues has now become best field application developments.