A thermomechanical constitutive model for cemented granular materials with quantifiable internal variables. Part II – Validation and localization analysis

Das, Arghya; Tengattini, Alessandro; Nguyen, Giang D.; Viggiani, Gioacchino; Hall, Stephen A.; Einav, Itai

doi:10.1016/j.jmps.2014.05.022

Cited by 65 publications

(29 citation statements)

References 51 publications

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“…Specifically, stationary compaction bands with localized intense volumetric strain rate have been frequently observed in a wide range of brittle porous materials, including rocks 1-3 , foams 4 and honeycomb materials 11 . The formation of such bands has been rationalized mathematically using continuum models of viscoplasticity 12,13 or breakage mechanics 14,15 , with the latter connecting the process directly to the physics of grain breakage and pore collapse.The formation of oscillatory propagating compaction bands in porous media was discovered more recently by Valdes et al5 , via uniaxially confined compression experiments on puffed rice packs (Fig. 1a).…”

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confidence: 99%

Dynamic patterns of compaction in brittle porous media

et al. 2015

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Here, using a new heuristic lattice spring model undergoing repeated crushing events, we first predict the possible emergence of new types of dynamic compaction; we then discover and confirm these new patterns experimentally in compressed cereal packs. In total, we distinguish three observed compaction patterns: short-lived erratic compaction bands, multiple oscillatory propagating compaction bands reminiscent of critical phenomena near phase transitions, and di used irreversible densification. The manifestation of these three di erent patterns is mapped in a phase diagram using two dimensionless groups that represent fabric collapse and external dissipation.Compaction of brittle porous media is of central importance in industry and science, and has many ramifications, from destruction waves during meteoritic impacts 7 to the formation of density heterogeneities in pharmaceutical pills 8 and permeability barriers in rocks 9,10 . Previous work on brittle porous media has generally revealed two forms of compaction patterns: stationary and oscillatory propagating compaction bands. Specifically, stationary compaction bands with localized intense volumetric strain rate have been frequently observed in a wide range of brittle porous materials, including rocks 1-3 , foams 4 and honeycomb materials 11 . The formation of such bands has been rationalized mathematically using continuum models of viscoplasticity 12,13 or breakage mechanics 14,15 , with the latter connecting the process directly to the physics of grain breakage and pore collapse.The formation of oscillatory propagating compaction bands in porous media was discovered more recently by Valdes et al.5 , via uniaxially confined compression experiments on puffed rice packs (Fig. 1a). Similar to stationary compaction bands, the material within these bands experienced high volumetric strain rates accommodated by severe grain breakage and pore collapse. By comparing experiments on material placed in containers with different boundary roughness, this work motivated a connection between compaction dynamics to how energy is dissipated outside.More recently, similar experiments on dry foamy snow 6 also revealed oscillatory propagating compaction bands, although with only one or two oscillations per test (this will be discussed later, in Fig. 2g-i). This form of compaction was captured using a phenomenological continuum model for snow, with an assumed elastoplastic yield function, power-law density dependence, shearinduced bond failure, strength recovery due to sintering, and nonlocality of damage 6 . The need for these assumptions indicates that the underlying mechanisms that control the emergence of oscillatory compaction bands are not clear yet.In this paper we present experiments that unfold novel compaction patterns in brittle porous media. We show that all the observed patterns can be explained using a simple lattice spring model. We then map the manifested patterns in terms of a phase diagram that covers system and material parameters, applicable for brittle porous...

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Dynamic patterns of compaction in brittle porous media

et al. 2015

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“…An excellent illustration of this failure pattern can be found in experiments on mudstones (Oka et al, 2011, Fig. 6) as well as in the theoretical work of and Das et al (2014). In these works the material can be seen to go from pure shear to pure compaction with increasing confinement.…”

Section: Introductionmentioning

confidence: 79%

Cnoidal waves in solids

Veveakis

Regenauer-Lieb

2015

Journal of the Mechanics and Physics of Solids

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“…To be more descriptive, combined isotropic/kinematic hardening of the cap model is visualized by the schematic diagram in Figure . It should be mentioned that, although the softening‐induced localization behavior is also of importance in many geological and geophysical problems [43, 47–50], it is beyond the scope of the present paper and will be discussed in the future work.…”

Section: Elasto/viscoplastic Constitutive Equations: Rate Sensitive mentioning

confidence: 99%

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

Motamedi

Foster

2015

Num Anal Meth Geomechanics

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Summary The Sandia GeoModel is a continuum elastoplastic constitutive model that captures many features of the mechanical response for geological materials over a wide range of porosities and strain rates. Among the specific features incorporated into the formulation are a smooth compression cap, isotropic/kinematic hardening, nonlinear pressure dependence, strength differential effect, and rate sensitivity. This study attempts to provide enhancements regarding computational tractability, domain of applicability, and robustness of the model. A new functional form is presented for the yield and plastic potential functions. This reformulation renders a more accurate, robust, and efficient model as it eliminates spurious solutions attributed to the original form. In addition, we achieve a high‐performance implementation, because the local iterative method is allowed to recast residual vectors with a uniform dimensionality. The model is also furnished with a smooth, elliptical tension cap to account for the tensile yielding. Moreover, an efficient algorithm is introduced, which decreases the computational cost by differentiating the updated shear yield surface from the cap surface based on the trial relative stress state. Finally, various numerical examples including a large‐scale boundary value problem are presented to demonstrate the fidelity of the modified model and to analyze its numerical performance. Copyright © 2015 John Wiley & Sons, Ltd.

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A thermomechanical constitutive model for cemented granular materials with quantifiable internal variables. Part II – Validation and localization analysis

Cited by 65 publications

References 51 publications

Dynamic patterns of compaction in brittle porous media

Dynamic patterns of compaction in brittle porous media

Cnoidal waves in solids

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

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