A micro-mechanical investigation of bifurcation in granular materials

Nicot, François; Darve, Félix

doi:10.1016/j.ijsolstr.2007.03.002

Cited by 79 publications

(78 citation statements)

References 36 publications

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“…An everyday illustration of a bifurcation point is the vaporization temperature of water. Nevertheless, within our framework, Nicot and Darve [28] have shown that negative values of second-order work are related to a burst of kinetic energy, which is in agreement with the proposed definition. Under constant loading conditions, the mechanical state of the sample changes suddenly from a static regime to a dynamic one.…”

Section: Second-order Work Criterion Analysis Within a Phenomenologicsupporting

confidence: 88%

Bifurcation modeling in geomaterials: From the second‐order work criterion to spectral analyses

Prunier

Laouafa

Lignon

et al. 2008

Num Anal Meth Geomechanics

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SUMMARYThe present paper investigates bifurcation analysis based on the second-order work criterion, in the framework of rate-independent constitutive models and rate-independent boundary-value problems. The approach applies mainly to nonassociated materials such as soils, rocks, and concretes. The bifurcation analysis usually performed at the material point level is extended to quasi-static boundary-value problems, by considering the stiffness matrix arising from finite element discretization. Lyapunov's definition of stability (Annales de la faculté des sciences de Toulouse 1907; 9:203-274), as well as definitions of bifurcation criteria (Rice's localization criterion (Theoretical and Applied Mechanics. Fourteenth IUTAM Congress, Amsterdam, 1976; 207-220) and the plasticity limit criterion are revived in order to clarify the application field of the second-order work criterion and to contrast these criteria. The first part of this paper analyses the second-order work criterion at the material point level. The bifurcation domain is presented in the 3D stress space as well as 3D cones of unstable loading directions for an incrementally nonlinear constitutive model. The relevance of this criterion, when the nonlinear constitutive model is expressed in the classical form (d = Mdε) or in the dual form (dε = N d ), is discussed. In the second part, the analysis is extended to the boundary-value problems in quasi-static conditions. Nonlinear finite element computations are performed and the global tangent stiffness matrix is analyzed. For several examples, the eigenvector associated with the first vanishing eigenvalue of the symmetrical part of the stiffness matrix gives an accurate estimation of the failure mode in the homogeneous and nonhomogeneous boundary-value problem.

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Section: Second-order Work Criterion Analysis Within a Phenomenologicsupporting

confidence: 88%

Bifurcation modeling in geomaterials: From the second‐order work criterion to spectral analyses

Prunier

Laouafa

Lignon

et al. 2008

Num Anal Meth Geomechanics

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“…According to the evolutions of q and ε v against ε 1 under axial strain controlled drained compression, and as reported in Table 2, both numerical test specimens D 1 and D 2 confirm a typical behavior of a dense dry sand characterized by a dilatant change in volumetric behavior and a well marked peak. The peak in q indicates that a limit stress state is reached which also coincides with the vanishing of the second order work [18,30].…”

Section: Non-effective Versus Effective Localized Failurementioning

confidence: 78%

“…Both proportional paths led to the total liquefaction (more severe when stress-controlled) of the granular assembly marked by the vanishing of the principal stresses. As shown in [20,31], the passing of (σ 1 − σ 2 /R) through a peak with ε 1 indicates that a generalized limit state has been reached,at which the second order work [18,30] vanishes and pinpoints the occurrence of failure inside the Mohr-Coulomb limit.…”

Section: Non-effective Versus Effective Diffuse Failurementioning

confidence: 95%

Failure in granular media from an energy viewpoint

Hadda

Sibille

Nicot³

et al. 2016

Granular Matter

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The present paper examines failure in discrete granular media with respect to its mode and nature based on energetic considerations through a comprehensive discrete element modelling computational analysis. The mode of failure refers to whether deformations will localize into an intense shear band or be diffuse. More subtly, a given failure mode can be effective with a burst of kinetic energy, or noneffective with a more controlled release of kinetic energy, depending on the control parameter. Physical quantities based on energy considerations with elementary decompositions of externally applied energy into elastic, plastic and kinetic contributions at the particle level are computed for a number of granular assemblies under a variety of failure scenarios. With the picture of a particle system experiencing macroscopic deformations according to underlying microand meso-mechanisms, it is concluded that computed grainenergy components depend on the microstructural detail that emerges as a function of loading program and control parameter. The relationship between elastic unloading outside a shear band and plastic dissipation inside it under both strain and stress control modes determines the genesis of shear banding in terms of plastic work dissipation minimization. Most interestingly, it is found that the energy signature inside the shear band in a dense granular packing is germane to This article is part of the Topical Collection on Micro origins for macro behavior of granular matter.B Nejib Hadda energy characteristics of diffuse failure in a loose assembly, suggesting some similarities in microscopic failure processes between shear banding and diffuse failure.

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“…Likewise, the consideration of microscopic aspects in the formulation of non-local constitutive theories for porous and granular materials are due to Nicot and Darve (2007); Yin et al (2009);Zhu et al (2010) and Xie et al (2011). Other remarkable works related to this matter were performed by Bonelli et al (2012); Jiang and Shao (2012); Shen et al (2012); Tran et al (2012); Shen et al (2013) and Shojaei et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic gradient-based poroplastic theory for concrete under high temperatures

Ripani

Etse

Vrech

et al. 2014

International Journal of Plasticity

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Concrete materials subjected to long term exposures to high temperatures suffer severe degradations in its mechanical properties (cohesion, friction, strength and stiffness) and changes in their failure mechanisms. These degradations may lead to irreversible damage or sudden collapse of the related structures. From the predictive analysis stand point, accurate constitutive theories are required to simulate the variations of concrete mechanical failure behavior under high and durable temperature fields. In the realm of the smeared crack approach, non-local model strategies are required to objectively reproduce failure behaviors under coupled thermo-mechanical loading conditions, while realistic descriptions of the involved characteristic lengths are needed to objectively reproduce the variation from ductile to brittle failure modes depending on the acting confining pressure and temperature. In this work, a thermodynamically consistent gradient poroplastic model for concrete subjected to high temperatures is proposed. A particular and simple form of gradient-based poroplasticity is considered whereby the state variables are the only ones of non-local character. The degradations of these variables due to coupled thermo-mechanical effects are described in the framework of the thermodynamic approach. After describing the material formulation, numerical analyses are presented which demonstrate the predictive capabilities of the proposed constitutive theory for different stress paths and thermal conditions.

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A micro-mechanical investigation of bifurcation in granular materials

Cited by 79 publications

References 36 publications

Bifurcation modeling in geomaterials: From the second‐order work criterion to spectral analyses

Bifurcation modeling in geomaterials: From the second‐order work criterion to spectral analyses

Failure in granular media from an energy viewpoint

Thermodynamic gradient-based poroplastic theory for concrete under high temperatures

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