On a class of non-coaxial plasticity models for granular soils

2005 ◽  
Vol 462 (2067) ◽  
pp. 725-748 ◽  
Author(s):  
H.S Yu ◽  
X Yuan
Keyword(s):  
Simple Shear ◽  
Shear Loading ◽  
Granular Soils ◽  
Strain Rates ◽  
Principal Stresses ◽  
Constitutive Theories ◽  
Strain Behaviour ◽  
Plastic Potential ◽  
Stress States ◽  
Soil Behaviour

The non-coaxiality of the directions of principal stresses and principal plastic strain rates in granular soils under stress rotations has long been observed and recognized in soil tests using both simple shear and hollow cylinder apparatuses. A few constitutive theories have also been proposed in the literature to account for the effect of stress rotations and the subsequent non-coaxial soil behaviour, particularly in the context of shear band analysis. However, the lack of corresponding general numerical methods makes it difficult to investigate the influence of non-coaxial stress–strain behaviour on the results of geotechnical boundary value problems. This paper presents a numerical evaluation of a class of non-coaxial, elastic–plastic models that are developed by combining the conventional plastic potential theory and the double shearing theory. The general non-coaxial constitutive theories are first formulated and then a finite element implementation of the theories is carried out. To evaluate the non-coaxial theories, the problem of simple shear of soils is chosen to investigate the predicted behaviour of soils under simple shear loading conditions where the axes of principal stresses rotate. In particular, the influence of initial stress states and the degree of non-coaxiality are examined. It is found that the numerical results predicted using the non-coaxial model are in general agreement with the experimental observations reported in the literature.

scholarly journals Triaxial tests on snow at low strain rate. Part I. Experimental device

2003 ◽  
Vol 49 (164) ◽  
pp. 81-90 ◽  
Author(s):  
Markus von Moos ◽  
Perry Bartelt ◽  
Adrian Zweidler ◽  
Ernst Bleiker
Keyword(s):  
Compressive Strain ◽  
Swiss Federal Institute ◽  
Triaxial Tests ◽  
Research Station ◽  
Strain Rates ◽  
Constitutive Theories ◽  
Triaxial Apparatus ◽  
Federal Institute ◽  
Strain Behaviour ◽  
Snow Samples

AbstractA deformation-controlled triaxial apparatus has been developed in order to investigate the mechanical behaviour of alpine snow. Cylindrical specimens (58 mm in diameter, 126 mm in height) can be axially deformed by applying tensile or compressive strain rates between 2.4 × 10−7s−1and 2.4 × 10−2s−1. Compressed air is used to laterally load the snow specimens with pressures of up to 40 k Pa.The volumetric deformation is found by carefully encapsulating the snow samples in an airtight Mylar foil and measuring the expelled pore air during sample deformation. The multidimensional stress–strain behaviour can therefore be determined, and constitutive theories of snow advanced. The device is located in the cold rooms of the Weissfluhjoch research station of the Swiss Federal Institute for Snow and Avalanche Research. Some 180 tests have been performed over the last four winters. The density of the snow specimens varied between 190 and 435 kg m−3. Part I of this two-part paper discusses the development of the apparatus and the applied testing methodology. Qualitative results are provided. In Part II, a detailed analysis of the results is presented and the viscoelastic properties of snow quantified.

scholarly journals On Phenomenological Failure Loci of Metals under Constant Stress States of Combined Tension and Shear: Issues of Coaxiality and Non-Uniqueness

Metals ◽  
2019 ◽  
Vol 9 (10) ◽  
pp. 1052
Author(s):  
Cliff Butcher ◽  
Armin Abedini
Keyword(s):  
Stress State ◽  
Plane Stress ◽  
Simple Shear ◽  
Stress Triaxiality ◽  
Failure Surface ◽  
Equivalent Strain ◽  
Shear Loading ◽  
Stress Conditions ◽  
Failure Locus ◽  
Stress States

The present study investigates how the choice of characterization test and the composition of the stress state in terms of tension and shear can produce a non-unique failure locus in terms of stress triaxiality under plane stress conditions. Stress states that are composed of tensile and simple shear loadings result in a loss of proportionality between the cumulative strain and stress such that the principal frames become non-coaxial despite a constant stress triaxiality. Consequently, it is shown that the conventional interpretation of a failure locus in plane stress is based upon an implicit assumption of proportional coaxial loading. The use of simple shear tests along with traditional in-plane tensile tests for fracture characterization is only one “path” that can be taken in terms of the stress triaxiality, which may produce a bifurcation at uniaxial tension while the tension–torsion path does not. In general, the failure locus in terms of the equivalent strain is a failure surface and must consider the composition of the stress state that produces a given triaxiality. A comprehensive review of phenomenological fracture loci within a modified Mohr-Coulomb (MMC) framework is performed to highlight how the choice of stress states obtained using different characterization tests can change the apparent fracture locus of a material. The finite strain solutions for the work conjugate equivalent strain are derived for various loading paths that produce the same stress triaxiality. It is then shown that accounting for non-coaxiality leads to equivalent failure strains that are even higher than previously reported in tension–torsion tests within the literature. The equivalent plastic strains integrated from finite-element simulations are work-conjugate by definition. The equivalent strains estimated from the cumulative principal strains using DIC strain measurement depend upon a coaxial or non-coaxial assumption. Finally, an analytical solution for the onset of diffuse necking that accounts for the stabilizing influence of shear loading against a tensile instability is considered. Even under plane stress conditions, a failure surface arises in terms of the equivalent strain at necking, the stress triaxiality, and the severity of shear loading.

Application of Critical State Approach to Liquefaction Resistance of Sand–Silt Mixtures under Cyclic Simple Shear Loading

2021 ◽  
Vol 147 (3) ◽  
pp. 04020177
Author(s):  
Daniela Dominica Porcino ◽  
Theodoros Triantafyllidis ◽  
Torsten Wichtmann ◽  
Giuseppe Tomasello
Keyword(s):  
Simple Shear ◽  
Critical State ◽  
Shear Loading ◽  
Liquefaction Resistance

Effects of Stress Path and Stress History on the Stiffness of Reconstituted London Clay

1986 ◽  
Vol 2 (1) ◽  
pp. 139-144 ◽  
Author(s):  
J. H. Atkinson ◽  
J. S. Evans ◽  
D. Richardson
Keyword(s):  
Stress Path ◽  
Triaxial Tests ◽  
Soil Parameters ◽  
Stress History ◽  
Strain Behaviour ◽  
Reconstituted Soil ◽  
Path Dependent ◽  
London Clay ◽  
Soil Behaviour

AbstractSoil behaviour is stress history dependent and stress path dependent and soil parameters, particularly those for stress-strain behaviour, measured in conventional triaxial tests may not represent the behaviour of soil in many civil engineering works.To obtain more realistic parameters it may be necessary to conduct laboratory tests which more closely represent in situ conditions before and during construction.The paper describes equipment developed at The City University to carry out stress path tests simply and economically. A series of CU triaxial tests and stress path tests on reconstituted soil illustrate the dependence of measured soil parameters on stress history and stress path.

scholarly journals Benefits of Using Lode Angle Dependent Fracture Models to Predict Ballistic Limits of Armor Steel

2018 ◽  
Vol 183 ◽  
pp. 01052
Author(s):  
Christian C. Roth ◽  
Teresa Fras ◽  
Norbert Faderl ◽  
Dirk Mohr
Keyword(s):  
Fracture Initiation ◽  
Strain Rates ◽  
Plastic Response ◽  
Rate Dependent ◽  
Gas Gun ◽  
Fracture Models ◽  
Armor Steel ◽  
Stress States ◽  
Impact Experiments ◽  
Single Material

Ductile fracture experiments are carried out at different stress states, strain rates and temperatures on a range of flat Mars 300 steel specimens to calibrate both a plasticity and a fracture model. To predict the onset of fracture a stress state and strain rate-dependent Hosford–Coulomb fracture initiation model is used. Single material impact experiments are performed on targets of homogenous and perforated Mars 300 plates by accelerating cylindrical Mars 300 impactors in a single-stage gas gun. It is shown that the chosen modeling approach allows accurate modeling of the plastic response as well as the fracture patterns.

scholarly journals A Study on Modelling the Plane Strain Behaviour of Sand and its Stability

2012 ◽  
Vol 59 (3-4) ◽  
pp. 85-100 ◽  
Author(s):  
Andrzej Sawicki ◽  
Justyna Sławinska
Keyword(s):  
Plane Strain ◽  
3D Model ◽  
Original Model ◽  
Governing Equations ◽  
Principal Stresses ◽  
Full System ◽  
Incremental Model ◽  
Strain Behaviour ◽  
Incremental Equations ◽  
Principal Strains

Abstract The plane strain behaviour of sand is studied using, previously proposed, incremental model describing its pre-failure deformations. Original model has been formulated for the tri-axial configuration, and then generalized for 3D conditions. This 3D model was subsequently adapted to study deformations of sand in the plane strain conditions, in the x1; x3 plane. There are three unknowns in such a configuration, namely the principal strains "1; "3 and the principal stress σ2. Respective equations were derived, and then applied to study deformations of sand for chosen stress paths. The governing incremental equations were integrated numerically, and it was shown, for some loading paths, that σ2 epends linearly on the other principal stresses, so introduction of apparent Poisson’s ratio is justified, as a kind of approximation. Subsequent analysis of deformations of sand was performed using this concept, as well as using full system of governing equations.

scholarly journals Strain rate and thermal softening effects in shear testing of AA7075-T6 sheet

2018 ◽  
Vol 183 ◽  
pp. 02037 ◽  
Author(s):  
Taamjeed Rahmaan ◽  
Ping Zhou ◽  
Cliff Butcher ◽  
Michael J. Worswick
Keyword(s):  
Strain Rate ◽  
High Speed ◽  
Rate Sensitivity ◽  
Thermal Conditions ◽  
Shear Loading ◽  
Image Correlation ◽  
High Rate ◽  
Strain Rates ◽  
Shear Testing ◽  
Plane Shear

Shear tests were performed at strain rates ranging from quasi-static (0.01 s-1) to 500 s-1 for AA7075-T6 sheet metal alloy at room temperature. A miniature sized shear specimen was used in this work to perform high strain rate shear testing. Digital image correlation (DIC) techniques were employed to measure the strains in the experiments. At maximum in-plane shear strains greater than 20%, the AA7075-T6 alloy demonstrated a reduced work hardening rate at elevated strain rates. At lower strains, the AA7075-T6 alloy showed mild positive rate sensitivity. The strain to localization (using the Zener-Holloman criterion), measured using the DIC technique, decreased with strain rate in shear loading. The strain at complete failure, however, exhibited an increase at the highest strain rate (500 s-1). The current work also focused on characterization of the thermal conditions occurring during high rate loading in shear with in situ high speed thermal imaging. Experimental results from the highest strain rate (500 s-1) tests showed a notable increase in temperature within the specimen gauge region as a result of the conversion of plastic deformation energy into heat.

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