Abstract
The pure cross-anisotropy is understood as a special scaling of strain (or stress). The scaled tensor is used as an argument in the elastic stiffness (or compliance). Such anisotropy can be overlaid on the top of any elastic stiffness, in particular on one obtained from an elastic potential with its own stress-induced anisotropy. This superposition does not violate the Second Law. The method can be also applied to other functions like plastic potentials or yield surfaces, wherever some cross-anisotropy is desired. The pure cross-anisotropy is described by the sedimentation vector and at most two constants. Scaling with more than two purely anisotropic constants is shown impossible. The formulation was compared with experiments and alternative approaches. Static and dynamic calibration of the pure anisotropy is also discussed. Graphic representation of stiffness with the popular response envelopes requires some enhancement for anisotropy. Several examples are presented. All derivations and examples were accomplished using the algebra program Mathematica.
Highlights
Elastic response is an essential part of most constitutive models for soils
Borja et al [4] proposed a hyperelastic model based on elastic potential formulated in terms of the strain invariants, WðeÞ 1⁄4 c3 exp ðevol =c2 Þ
Anisotropic elastic parameters can be determined from the measurements of wave velocities in different direction of propagation n
Summary
Elastic response is an essential part of most constitutive models for soils. It is important for soil dynamics, for stability analysis [2] and for material response in the range of small strains. EA 1⁄4 QT : Eiso : Q; ð1Þ wherein the elastic properties are given in the isotropic stiffness Eiso and all pure anisotropic properties are moved to the anisotropy tensor Q. The advantage of such separated description follows from the fact that the same Q can be applied to any hyperelastic (and barotropic) stiffness without violating the Second Law. The advantage of such separated description follows from the fact that the same Q can be applied to any hyperelastic (and barotropic) stiffness without violating the Second Law Any basic tangential stiffness (or compliance), possibly with its own induced anisotropy, can be superposed by the pure inherent anisotropy This pure cross-anisotropy is denoted as AM wherein M is the number of constants required for the anisotropy tensor Q. All relevant packages and notebooks for the algebra program Mathematica are available from the authors
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