Strain Rates and Material Spins

@article{citeulike:1224313, author = {Xiao, Heng and Bruhns, Otto T. and Albert}, citeulike-article-id = {1224313}, comment = {SIMILAR to @article{citeulike:1212450, abstract = {In this paper, we prove a general result on objective corotational rates and their defining spin tensors: let [Omega]* be a spin tensor that is associated with the rotation and deformation of a deforming material body in an arbitrary manner indicated by [Omega]* = Y(B. D. W), where B and D and W are the left Cauchy Green tensor and the stretching tensor and the vorticity tensor, respectively. Then the corotational rate of [sigma] defined by the spin [Omega]*, i.e., the tensor field [sigma]* = [sigma]+[sigma][Omega]*--[Omega]*[sigma], is objective for every time-differentiable objective Eulerian symmetric tensor field a if and only if the spin tensor [Omega]* assumes the form [Omega]* = W+ Y(B, D). where Y(B,D) is an antisymmetric tensor-valued isotropic function. Furthermore, by virtue of certain necessary or reasonable requirements, it is found that a single antisymmetric function of two positive real variables can be introduced to characterize a general class of spin tensors defining objective corotational rates. Accordingly, a general explicit basis-free expression for the latter is established in terms of the left Cauchy-Green tensor B, the vorticity tensor W and the stretching tensor D as well as the introduced antisymmetric function. By choosing several particular forms of the latter, it is shown that all commonly-used spin tensors are incorporated into this general expression in a natural way.}, author = {Xiao, H. and Bruhns, O. T. and Meyers, A. }, citeulike-article-id = {1212450}, doi = {10.1016/S0020-7683(97)00267-9}, journal = {International Journal of Solids and Structures}, keywords = {elasticity similar\_paper}, month = {October}, number = {30}, pages = {4001--4014}, priority = {2}, title = {On objective corotational rates and their defining spin tensors}, url = {http://www.sciencedirect.com/science/article/B6VJS-3TP0Y4T-9/2/8fe6ccb16af5658f1d568e8d333a3f9a}, volume = {35}, year = {1998} }}, doi = {10.1023/A:1007570827614}, journal = {Journal of Elasticity}, keywords = {elasticity, nonlinear, similar\_paper}, month = {July}, number = {1}, pages = {1--41}, posted-at = {2007-04-13 16:49:58}, priority = {2}, title = {Strain Rates and Material Spins}, url = {http://dx.doi.org/10.1023/A:1007570827614}, volume = {52}, year = {1998} }

TY - JOUR ID - citeulike:1224313 L3 - citeulike-article-id:1224313 TI - Strain Rates and Material Spins JF - Journal of Elasticity VL - 52 IS - 1 SP - 1 EP - 41 KW - elasticity KW - nonlinear KW - similar_paper N1 - SIMILAR to @article{citeulike:1212450, abstract = {In this paper, we prove a general result on objective corotational rates and their defining spin tensors: let [Omega]* be a spin tensor that is associated with the rotation and deformation of a deforming material body in an arbitrary manner indicated by [Omega]* = Y(B. D. W), where B and D and W are the left Cauchy Green tensor and the stretching tensor and the vorticity tensor, respectively. Then the corotational rate of [sigma] defined by the spin [Omega]*, i.e., the tensor field [sigma]* = [sigma]+[sigma][Omega]*--[Omega]*[sigma], is objective for every time-differentiable objective Eulerian symmetric tensor field a if and only if the spin tensor [Omega]* assumes the form [Omega]* = W+ Y(B, D). where Y(B,D) is an antisymmetric tensor-valued isotropic function. Furthermore, by virtue of certain necessary or reasonable requirements, it is found that a single antisymmetric function of two positive real variables can be introduced to characterize a general class of spin tensors defining objective corotational rates. Accordingly, a general explicit basis-free expression for the latter is established in terms of the left Cauchy-Green tensor B, the vorticity tensor W and the stretching tensor D as well as the introduced antisymmetric function. By choosing several particular forms of the latter, it is shown that all commonly-used spin tensors are incorporated into this general expression in a natural way.}, author = {Xiao, H. and Bruhns, O. T. and Meyers, A. }, citeulike-article-id = {1212450}, doi = {10.1016/S0020-7683(97)00267-9}, journal = {International Journal of Solids and Structures}, keywords = {elasticity similar_paper}, month = {October}, number = {30}, pages = {4001--4014}, priority = {2}, title = {On objective corotational rates and their defining spin tensors}, url = {http://www.sciencedirect.com/science/article/B6VJS-3TP0Y4T-9/2/8fe6ccb16af5658f1d568e8d333a3f9a}, volume = {35}, year = {1998} } AU - Xiao, Heng AU - Bruhns, Otto AU - Albert PY - 1998/07/16/ UR - http://dx.doi.org/10.1023/A:1007570827614 ER -