However, for higher noise levels (3%), the quality of the reconstructions deteriorates for the parameter C12 of the orthotropic elasticity tensor. A theoretical analysis is performed and we demonstrate that this may be due to small gradients of the objective function with respect to C12. Overall...
It should be apparent that laboratory testing methods attempting to characterize anisotropic materials would have to be more complicated than those used for isotropic solids. 6.2.2 General Formulation We now wish to establish the general formulation of the linear elasticity model. This process combines...
Intuitively, one could expect that “linear elasticity” means that there is a linear relation between force and displacement in a simple tensile test. This will not be the case, since both stresses and strains depend on the deformation. To see this, consider a bar with a square cross sectio...
The numerical homogenization of anisotropic linear elastic materials with strongly heterogeneous microstructure is studied. The developed algorithm is applied to the case of trabecular bone tissue. In our previous work [1], the orthotropic case was considered. The homogenized anisotropic tensor is transfor...
Linear elasticity is one of the more successful theories of mathematical physics. Its pragmatic success in describing the small deformations of many materials is uncontested. The origins of the three-dimensional theory go back to the beginning of the 19t
Conditions are derived that show the integrals exhibit alternative behavior and in particular for the semi-infinite cylinder that there is either at least exponential growth or at most exponential decay, provided the elasticity tensor is positive definite or satisfies a strong ellipticity condition.doi:...
►anisotropicFilter ►APIdiffCoefFunc ►Ar ►areaMesh ►areaWrite ►argList ►ArmijoConditions ►arraySet ►ArrheniusReactionRate ►ash ►aspectRatioModel ►ATCModel ►ATCstandard ►ATCUaGradU ►atmAlphatkWallFunctionFvPatchScalarField ►atmBoundaryLayer ►atmBoundaryLayerInletEpsi...
►anisotropicFilter ►APIdiffCoefFunc ►Ar ►areaMesh ►areaWrite ►argList ►ArmijoConditions ►arraySet ►ArrheniusReactionRate ►ash ►aspectRatioModel ►ATCModel ►ATCstandard ►ATCUaGradU ►atmAlphatkWallFunctionFvPatchScalarField ►atmBoundaryLayer ►atmBoundaryLayerInletEpsi...
σ:S:σ+ɛ0n−1n+1.σ:N:σ,where in the first and the second term we introduce compliance tensors S and N, associated with the linear and the non-linear anisotropic material response, respectively. Both tensors have the properties of minor and major symmetry (shown using index ...
The theory for anisotropic elasticity is covered in detail in numerous textbooks [4–6], here we will simply summarize some of the more important and useful results for engineering analysis. As is shown in Equations (5.11) and (5.12), the stiffness and compliance tensors have 3 × 3 × 3...