Aspects of Differential Geometry and Tensor Calculus in Anholonomic Configuration Space

作者: John D Clayton

DOI:

关键词: HolonomicClassical mechanicsTangentCovariant transformationDifferential geometryTensor calculusConfiguration spaceFinite strain theoryMathematical analysisMathematicsMotion (geometry)

摘要: Abstract : In the context of finite deformation mechanics, a tangent mapping is anholonomic over some domain when it not gradient motion; conversely, holonomic integrable to motion field everywhere in that domain. This brief report addresses covariant differentiation for four possible choices basis vectors space. As an example from continuum physics, theory applied towards description divergence heat flux.

参考文章(4)
John D. Clayton, Nonlinear Mechanics of Crystals ,(2010)
Walter Noll, Materially uniform simple bodies with inhomogeneities Archive for Rational Mechanics and Analysis. ,vol. 27, pp. 211- 242 ,(1967) , 10.1007/BF00276433
J.D. Clayton, D.J. Bammann, D.L. McDowell, Anholonomic Configuration Spaces and Metric Tensors in Finite Elastoplasticity International Journal of Non-linear Mechanics. ,vol. 39, pp. 1039- 1049 ,(2004) , 10.1016/S0020-7462(03)00095-7
J.D Clayton, A continuum description of nonlinear elasticity, slip and twinning, with application to sapphire Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 465, pp. 307- 334 ,(2009) , 10.1098/RSPA.2008.0281