Knowles, J.K.: On the representation of the elasticity tensor for isotropic materials. J. Elast. 39 (2), 175–180 (1995)Knowles J. On the representation of the elasticity tensor for isotropic materials. J. Elast
This assumption allows us to use the contracted photoelastic tensor for isotropic materials, with inverse symmetry rotation simplifications applied in the Pockel's c oefficients27. Application of longitudinal strain through the sup- porting optical fiber beam to the silk fibroin cylindrical micro-...
For the case of complete symmetry where all directions have the same constitutive response, the material is referred to as isotropic. For this case, the fourth-order elasticity tensor must reduce to an isotropic tensor and this form has been previously given in Table 2.15.1 as (6.2.17)Cijkl...
However, relying on the data shown in Figure 3.7b it can be well accepted that phase transformation strain tensor direction conforms very well to the direction of inducing its stress tensor direction at maximum loading stress; dashed lines indicate loading stress directions and arrows indicate pseudo...
Thus, we take C13 = λ and C33 = λ + 2μ and finally define the stiffness tensor of a nearly-incompressible transversely isotropic (NITI) material as: $$C=\left[\begin{array}{cccccc}\lambda +2\mu & \lambda & \lambda & & & \\ \lambda & \lambda +2\mu & \lambda...
Kröner, E.: 1955 Die inneren Spannungen und der Inkompatibilitätstensor in der Elastizitätstheorie. Z. Angew. Phys. 7, 249–257. (17). MATH Google Scholar Lodge, A. S.: 1955 The transformation to isotropic form of the equilibrium equations for a class of anisotropic elastic so...
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 ...
is the elastic tensor for a linear isotropic solid, and where u ij ≡ (∂ i u j +∂ j u i )/2 (8) is the strain tensor. The purpose of this paper is to point out that these boundary conditions, (2) and (3), while quite appro- priate for the geophysical application mention...
The dynamical matrices were calculated using the density functional perturbation theory [Baroni et al., 2001] with a 2 × 2 × 2 q points mesh and were interpolated to obtain the vibrational frequency for an 8 × 8 × 8 q points mesh. The static elastic tensors were calculated from ...
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...