Pure cross-anisotropy for geotechnical elastic potentials

Acta Geotechnica ◽

10.1007/s11440-021-01284-9 ◽

2021 ◽

Author(s):

Andrzej Niemunis ◽

Katarzyna Staszewska

Keyword(s):

Elastic Stiffness ◽

Elastic Potential ◽

Graphic Representation ◽

Second Law ◽

Dynamic Calibration ◽

Induced Anisotropy ◽

Elastic Potentials ◽

Alternative Approaches ◽

Stress Induced Anisotropy ◽

Cross Anisotropy

AbstractThe 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.

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A hyperelastic model for soils with stress-induced and inherent anisotropy

Acta Geotechnica ◽

10.1007/s11440-021-01159-z ◽

2021 ◽

Author(s):

Marcin Cudny ◽

Katarzyna Staszewska

Keyword(s):

Small Strain ◽

Induced Anisotropy ◽

Dynamic Simulations ◽

Inherent Anisotropy ◽

Directional Model ◽

Model Response ◽

Hyperelastic Model ◽

Stress Induced Anisotropy ◽

Stress Invariant ◽

Independent Model

AbstractIn this paper, modelling of the superposition of stress-induced and inherent anisotropy of soil small strain stiffness is presented in the framework of hyperelasticity. A simple hyperelastic model, capable of reproducing variable stress-induced anisotropy of stiffness, is extended by replacement of the stress invariant with mixed stress–microstructure invariant to introduce constant inherent cross-anisotropic component. A convenient feature of the new model is low number of material constants directly related to the parameters commonly used in the literature. The proposed description can be incorporated as a small strain elastic core in the development of some more sophisticated hyperelastic-plastic models of overconsolidated soils. It can also be used as an independent model in analyses involving small strain problems, such as dynamic simulations of the elastic wave propagation. Various options and features of the proposed anisotropic hyperelastic model are investigated. The directional model response is compared with experimental data available in the literature.

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Stress induced anisotropy in sandstone reservoir and shale overburden ‐ AVO modeling

Beijing 2009 International Geophysical Conference and Exposition, Beijing, China, 24–27 April 2009 ◽

10.1190/1.3603719 ◽

2009 ◽

Cited By ~ 1

Author(s):

Miroslav Brajanovski ◽

Dariush Nadri ◽

Boris Gurevich ◽

Andrej Bona

Keyword(s):

Induced Anisotropy ◽

Stress Induced Anisotropy ◽

Sandstone Reservoir

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The Magnetic Anisotropy of Co-Base Amorphous Alloys

MRS Proceedings ◽

10.1557/proc-232-201 ◽

1991 ◽

Vol 232 ◽

Author(s):

Wu-Xin Zhang ◽

Xi-Ming Li ◽

Nan-Ping Chen

Keyword(s):

Magnetic Anisotropy ◽

Amorphous Alloys ◽

Induced Anisotropy ◽

Pair Model ◽

Mn Content ◽

Stress Induced Anisotropy

ABSTRACT4 Co–base amorphous alloys prepared by rapid quenchling are stress–annealed under different temperature (Ta) balow its crytalline temperature Tcry, after pre–annealing. The effect of magnetic anisotropy with Ta shows the mechanism of stress–induced anisotropy is changed from single ionic modal to pair model as Ta inereases. The effect of Mn content may exaggerate the model changing.

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Anisotropy Energies and Critical Behavior of Ultrathin Ni(111) Films Grown on Smooth and Rough W(110) (invited)

MRS Proceedings ◽

10.1557/proc-231-289 ◽

1991 ◽

Vol 231 ◽

Cited By ~ 3

Author(s):

Yi Li ◽

K. Baberschke

Keyword(s):

Magnetic Properties ◽

Curie Temperature ◽

Film Thickness ◽

Critical Exponent ◽

Critical Behavior ◽

Induced Anisotropy ◽

Effective Anisotropy ◽

Stress Induced Anisotropy ◽

Surface Crystal

Abstract6 to 80 Å thin Ni(111) films were prepared on smooth and rough W(110) substrates in UHV and characterized by LEED and Auger spectroscopies. The measurements of the magnetic properties were carried out in situ by ferromagnetic resonance at 9 GHz between 300 and 600 K. We found that the effective anisotropies, which consist of surface, crystal, and stress induced anisotropy, increase with decreasing film thickness and temperature. The roughness of the substrate results in the drastic decrease of the effective anisotropy. This is attributed to the change of the surface structure and the stress within the Ni films. Furthermore we found that the Curie temperature Tc and the critical exponent β of Ni films on the smooth and rough substrates show no change.

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Thermal Stability of Field- and Stress-Induced Anisotropy in Nanocrystalline Fe-Based and Amorphous Co-Based Alloys

Textures and Microstructures ◽

10.1155/tsm.32.281 ◽

1999 ◽

Vol 32 (1-4) ◽

pp. 281-287 ◽

Cited By ~ 1

Author(s):

N. V. Dmitrieva ◽

V. A. Lukshina ◽

G. V. Kurlyandskaya ◽

A. P. Potapov

Keyword(s):

Thermal Stability ◽

Magnetic Anisotropy ◽

Amorphous Alloys ◽

Nanocrystalline Alloy ◽

Induced Anisotropy ◽

External Effects ◽

Nanocrystalline And Amorphous ◽

Induced Magnetic Anisotropy ◽

Stress Induced Anisotropy ◽

Thermal Stability Of

Thermal stability of induced magnetic anisotropy (IMA) was studied in a course of subsequent annealings without any external effects for already field- or stress-annealed specimens of the nanocrystalline Fe73.5Cu1Nb3Si13.5B9 and amorphous Fe3Co67Cr3Si15B12 alloys. For these alloys the dependence of IMA thermal stability on the magnitude of the IMA constant (Ku) and temperature of stress-annealing was investigated. For the nanocrystalline alloy thermal stability of field- and stress-induced anisotropy with identical Ku was compared. It was shown that nanocrystalline specimens with identical Ku values after field- or stress-annealing have identical thermal stability of IMA. This can point to a similarity of the mechanisms of IMA formation after field- or stress-annealings. Thermal stability of stress-induced anisotropy in the nanocrystalline alloy with Ku value less than 1000 J/m3 and the amorphous alloy with Ku less than 100 J/m3 depends on the value of Ku. For both stress-annealed nanocrystalline and amorphous alloys magnetic anisotropy induced at higher temperatures is more stable because more long-range and energy-taking processes take place at these temperatures.

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Stress-Induced Anisotropy and the Propagation of Seismic Waves

International Geophysics - An Introduction to Mining Seismology ◽

10.1016/b978-0-12-282120-2.50011-x ◽

1994 ◽

pp. 105-127

Keyword(s):

Seismic Waves ◽

Induced Anisotropy ◽

Stress Induced Anisotropy

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Undrained Shear Characteristics of Normally Consolidated Clays with Stress Induced Anisotropy

SOILS AND FOUNDATIONS ◽

10.3208/sandf1972.28.2_196 ◽

1988 ◽

Vol 28 (2) ◽

pp. 196-204 ◽

Cited By ~ 1

Author(s):

Hisao Hara ◽

Hōsei Uehara

Keyword(s):

Induced Anisotropy ◽

Shear Characteristics ◽

Stress Induced Anisotropy ◽

Undrained Shear

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Anisotropic Behavior of Geomaterial under Three-Dimensional Stress States

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.160-162.1425 ◽

2010 ◽

Vol 160-162 ◽

pp. 1425-1431

Author(s):

Kun Yong Zhang ◽

Yan Gang Zhang ◽

Chi Wang

Keyword(s):

Stress State ◽

Principal Stress ◽

Three Dimensional ◽

Complex Stress State ◽

Triaxial Tests ◽

Induced Anisotropy ◽

Principal Stresses ◽

True Triaxial ◽

Stress Effects ◽

Stress Induced Anisotropy

Most soil constitutive models were developed based on the traditional triaxial tests with isotropic assumption, in which the load is applied as the major principal stress direction and the other two principal stresses are symmetric. When such isotropic models are applied to practical analysis, stress induced anisotropy under complex stress state and the middle principal stress effects are often neglected, thus there are many disagreements between the calculated results and the infield testing data. To simulate the practical loading process, true triaxial tests were carried out on geomaterial under three-dimensional stress state. It was found that the stress induced anisotropy effects are remarkable and the middle principal stress effects are obvious because of the initial three-dimensional stress state. Such kind of stress-induced anisotropy could have important impact on the numerical analysis results and should be taken into consideration when developing the constitutive model.

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