Extrema of Young's modulus for cubic and transversely isotropic solids

@article{citeulike:915872, abstract = {For a homogeneous anisotropic and linearly elastic solid, the general expression of Young's modulus E(n), embracing all classes that characterize the anisotropy, is given. A constrained extremum problem is then formulated for the evaluation of those directions n at which E(n) attains stationary values. Cubic and transversely isotropic symmetry classes are dealt with, and explicit solutions for such directions n are provided. For each case, relevant properties of these directions and corresponding values of the modulus are discussed as well. Results are shown in terms of suitable combinations of elements of the elastic tensor that embody the discrepancy from isotropy. On the basis of such material parameters, for cubic symmetry two classes of behavior can be distinguished and, in the case of transversely isotropic solids, the classes are found to be four. For both symmetries and for each class of behavior, some examples for real materials are shown and graphical representations of the dependence of Young's modulus on direction n are given as well.}, author = {Cazzani, Antonio and Rovati, Marco }, citeulike-article-id = {915872}, doi = {10.1016/S0020-7683(02)00668-6}, journal = {International Journal of Solids and Structures}, keywords = {anisotropy, elasticity, poisson}, month = {April}, number = {7}, pages = {1713--1744}, posted-at = {2006-10-28 16:03:23}, priority = {2}, title = {Extrema of Young's modulus for cubic and transversely isotropic solids}, url = {http://dx.doi.org/10.1016/S0020-7683(02)00668-6}, volume = {40}, year = {2003} }

TY - JOUR ID - citeulike:915872 L3 - citeulike-article-id:915872 TI - Extrema of Young's modulus for cubic and transversely isotropic solids JF - International Journal of Solids and Structures VL - 40 IS - 7 SP - 1713 EP - 1744 N2 - For a homogeneous anisotropic and linearly elastic solid, the general expression of Young's modulus E(n), embracing all classes that characterize the anisotropy, is given. A constrained extremum problem is then formulated for the evaluation of those directions n at which E(n) attains stationary values. Cubic and transversely isotropic symmetry classes are dealt with, and explicit solutions for such directions n are provided. For each case, relevant properties of these directions and corresponding values of the modulus are discussed as well. Results are shown in terms of suitable combinations of elements of the elastic tensor that embody the discrepancy from isotropy. On the basis of such material parameters, for cubic symmetry two classes of behavior can be distinguished and, in the case of transversely isotropic solids, the classes are found to be four. For both symmetries and for each class of behavior, some examples for real materials are shown and graphical representations of the dependence of Young's modulus on direction n are given as well. KW - anisotropy KW - elasticity KW - poisson AU - Cazzani, Antonio AU - Rovati, Marco PY - 2003/04// UR - http://dx.doi.org/10.1016/S0020-7683(02)00668-6 ER -