K., On the representation of the elasticity tensor for isotropic materials, J. Elasticity, 39, 175-180, 1995.Knowles J. On the representation of the elasticity tensor for isotropic materials. J. Elast. 1995;39:175-180.Knowles, J.K.: On the representation of the elasticity tensor for ...
The constitutive equations for linear isotropic elastic materials with voids provide relations for the stress tensor, equilibrated stress vector, and intrinsic body force of the form (15.5.6)σij=λekkδij+2μeij+βϕδijhi=αϕ,ig=−ωϕ˙−ξϕ−βekk where the material constan...
The localization tensor for the matrix phase is conveniently determined from Eq. (10):(14)Aaest=1fa[I−fbAbest]Since both phases and the homogenized material are isotropic, the stiffness tensors cr=a,b and Cpest take the form:(15)cr=3krK+2μrJ;Cpest=3kpestK+2μpestJwhere kr=a,...
The elasticity tensor of a single-grain quasicrystal of composition AlCuLihas been determined. The longitudinal and transverse mode velocities have been obtained at ultrasonic frequencies (20 MHz) for several propagation and polarization directions. We find that the quasicrystal is elastically isotropic ...
We used this measure to calculate the exfoliability of 10,812 crystals having a first-principles calculated elastic tensor. By setting the threshold values for easy and potential exfoliation based on already-exfoliated materials, we predicted 58 easily exfoliable bulk crystals and 90 potentially exfo...
the fluid-like property can be perfectly accounted for by effective medium. Here TMs have dipolar symmetry hence they introduce anomalous effective mass densities6,37,46,47. Owing to the mismatched eigenfrequencies of TM(z) and TM(x, y), the effective mass density tensor is extremely anisotropi...
We prove that there are eight subgroups of the orthogonal group O(3) that determine all symmetry classes of an elasticity tensor. Then, we provide the necessary and sufficient conditions that allow us to determine the symmetry class to which a given elasticity tensor belongs. We also give a ...
1-21 Expression for Differential Length in Orthogonal Curvilinear Coordinates. 1-22 Gradient and Laplacian in Orthogonal Curvilinear Coordinates. Part III Elements of Tensor Algebra. 1-23 Index Notation: Summation Convention. 1-24 Transformation of Tensors under Rotation of Rectangular Cartesian Coordinate...
The ranges were obtained from the three diagonal terms of the tensors of Young's modulus and permeability. Owing to increasing effective stresses with depth, Young's moduli increase rapidly while permeabilities and porosities decrease rapidly with depth. Note that matrix porosities were not included...
The chapter also discusses response function, principle of coordinate invariance, and isotropic tensor function. The principle of coordinate invariance is trivially fulfilled when the constitutive law is written as a tensor relation and the principle of coordinate invariance follows trivially from tensor ...