An improved implicit numerical integration of a non‐associated, three‐invariant cap plasticity model with mixed isotropic–kinematic hardening for geomaterials

Motamedi, M. H.; Foster, Craig D.

doi:10.1002/nag.2372

Cited by 23 publications

(11 citation statements)

References 57 publications

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“…where R ij is a second-order tensor and η is a scalar constant, which will be defined later. By equating Equation 14 to zero as there is no change in the mass during undrained condition, we obtain the following relationship between the strain rate and the pore water pressure rate:…”

Section: Undrained Conditionsmentioning

confidence: 99%

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Influence of Lode angle‐dependent failure criteria on shear localization analysis in sand

Sisodiya

Das

2018

Num Anal Meth Geomechanics

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Summary Geotechnical experiments show that Lode angle‐dependent constitutive formulations are appropriate to describe the failure of geomaterials. In the present study, we have adopted one such class of failure criteria along with a versatile constitutive relationship to theoretically analyze the effects of Lode angle on localized shear deformation or shear band formation in loose sand for both drained and undrained conditions. We determine the variation in the possible stress states for shear localization due to the introduction of Lode angle by considering the localized deformation as a bifurcation problem. Further, similar bifurcation analysis is performed for the stress states along a specific loading path, namely, plane strain compression at the constitutive level. In addition, the plane strain compression tests have been simulated as a boundary value finite element problem to see how Lode angle affects the post‐localization response. Results show that the inclusion of a Lode angle parameter within the failure criterion has considerable effects on the onset, plastic strain, and propagation of shear localization in loose sand specimens. For drained condition, we notice early inception of shear localization and multiple band formation when the Lode angle‐dependent failure criterion is used. Undrained localization characteristics, however, found to be independent of Lode angle consideration.

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Section: Undrained Conditionsmentioning

confidence: 99%

“…The expressions for η and R ij can be determined by differentiating m with respect to time and comparing it with Equation 14.…”

Section: Undrained Conditionsmentioning

confidence: 99%

Influence of Lode angle‐dependent failure criteria on shear localization analysis in sand

Sisodiya

Das

2018

Num Anal Meth Geomechanics

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“…Alternatively, to take the effect of high strain rates into account for both strength and stiffness, formulations of viscosity have been integrated with conventional plasticity, that is, resulting in the so-called viscoplasticity. There are two popular viscoplastic models to account for the high strain rate phenomenon in the literature, the viscoplastic formulations of Duvaut-Lions [90][91][92][93] and Perzyna [70,71,[76][77][78][79]94].…”

Section: 2mentioning

confidence: 99%

“…By multiplying the cap ellipse function by the shear surface function, the complete failure envelope would take on the same slope at such intersection. This model has been termed as a smooth cap model or a continuous surface cap model, and similar treatment for such an intersection point has been widely used . However, in this type of model, the product of a monotonically increasing shear yield function and a decreasing cap expression (with respect to I 1 ) would mean that the range of the cap is ambiguous, that is, the ratio of the major to the minor axis of the elliptic cap ( R ) will not be constant during the hardening process and will be different from the R value that is specified by the modeler.…”

Section: Formulation Of the Modelmentioning

confidence: 99%

A coupled chemo‐viscoplastic cap model for simulating the behavior of hydrating cemented tailings backfill under blast loading

Fall

2015

Num Anal Meth Geomechanics

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Summary Although the use of blasting has become a routine in contemporary mine operations, there is a lack of knowledge on the response of cement tailings backfills subjected to sudden dynamic loading. To rationally describe such a phenomenon, a new coupled chemo‐viscoplastic cap model is proposed in the present study to describe the behavior of hydrating cemented tailings backfill under blast loading. A modified Perzyna type of visco‐plasticity model is adopted to represent the rate‐dependent behavior of the cemented tailings backfill under blast loading. A modified smooth surface cap model is consequently developed to characterize the yield of the material, which also facilitates hysteresis and full compaction as well as dilation control. Then, the viscoplastic formulation is further augmented with a variable bulk modulus derived from a Mie–Gruneisen equation of state, in order to capture the nonlinear hydrostatic response of cemented backfills subjected to high pressure. Subsequently, the material properties required in the viscoplastic cap model are coupled with a chemical model, which captures and quantifies the degree of cement hydration. Thus, the behavior of hydrating cemented backfills under the impact of blast loading can be evaluated under any curing time of interest. The validation results of the developed model show a good agreement between the experimental and the predicted results. The authors believe that the proposed model will contribute to a better understanding of the performance of cemented backfills under mine blasting and contribute to evaluating and managing the risk of failure of backfill structures under such a dynamic condition. Copyright © 2015 John Wiley & Sons, Ltd.

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“…In the transition between granular and fully dense states of a given material, the constitutive formulation faces the challenging problem of granular and dense materials having completely different mechanical behaviors, e.g., nonlinear elastic properties, cohesion, interparticle friction, pressure-sensitive yielding, plastic flow, hardening laws, crack/fracture induced damage, differences in strength in triaxial extension versus compression, and the Bauschinger effect. Capturing these behaviors typically necessitates the use of fairly complicated and expensive nonlinear material models [2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Smooth Yield Surface Constitutive Modeling for Granular Materials

Hammi¹,

Stone

Paliwal³

et al. 2016

Journal of Engineering Materials and Technology

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In this paper, the authors present an internal state variable (ISV) cap plasticity model to provide a physical representation of inelastic mechanical behaviors of granular materials under pressure and shear conditions. The formulation is dependent on several factors: nonlinear elasticity, yield limit, stress invariants, plastic flow, and ISV hardening laws to represent various mechanical states. Constitutive equations are established based on a modified Drucker-Prager cap plasticity model to describe the mechanical densification process. To avoid potential numerical difficulties, a transition yield surface function is introduced to smooth the intersection between the failure and cap surfaces for different shapes and octahedral profiles of the shear failure yield surface. The ISV model for the test case of a linear-shaped shear failure surface with Mises octahedral profile is implemented into a finite element code. Numerical simulations using a steel metal powder are presented to demonstrate the capabilities of the ISV cap plasticity model to represent densification of a steel powder during compaction. The formulation is general enough to also apply to other powder metals and geomaterials.

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An improved implicit numerical integration of a non‐associated, three‐invariant cap plasticity model with mixed isotropic–kinematic hardening for geomaterials

Cited by 23 publications

References 57 publications

Influence of Lode angle‐dependent failure criteria on shear localization analysis in sand

Influence of Lode angle‐dependent failure criteria on shear localization analysis in sand

A coupled chemo‐viscoplastic cap model for simulating the behavior of hydrating cemented tailings backfill under blast loading

Smooth Yield Surface Constitutive Modeling for Granular Materials

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