Second-order work criterion: from material point to boundary value problems

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Summary Within the framework of the second‐order work theory, the onset of instabilities is explored numerically in loose granular materials through three‐dimensional DEM simulations. Stress controlled directional analysis are performed in Rendulic's plane, and a particular attention is paid to transient evolutions at the microscale. Thanks to a micromechanical analysis, the onset and development of transient mechanical instabilities is explored. It is shown that these instabilities result from the unjamming and bending of a few force chains associated with a local burst of kinetic energy. This burst of kinetic energy propagates to the whole sample and provokes a generalized unjamming of force chains. As force chains buckle, a phase transition from a quasi‐static to an inertial regime is observed. At the macroscopic scale, this results in a transient softening and a loss of controllability. After the collapse of existing force chains, the development of plastic strain is eventually stopped as new stable force chains are built.

Section: Macroscopic Assessment Of Bifurcation Pointsmentioning

confidence: 99%

Micro‐inertia origin of instabilities in granular materials

Wautier

Bonelli²,

Nicot

2018

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“…With the finite element method, the global second‐order work can be calculated as

W_{2} = \int_{V_{el}} d ε^{t} normaldσ {dV}_{el} = \int_{V_{el}} {(italicBdq)}^{t} D^{ep} {BdqdV}_{el} = {dq}^{t} ((), \int_{V_{el}} B^{t} D^{ep} {BdV}_{el}) italicdq = {dq}^{t} k_{el} italicdq,

where k el is the elementary consistent tangent stiffness matrix and dq is the vector of nodal displacement. Once all the meshes are assembled, we obtain

W_{2} = \int_{V} d ε^{t} d σ d V = {dQ}^{t} italicKdQ = {dQ}^{t} italicdF,

in which dQ and dF are the global nodal incremental displacement and force and K is the global consistent tangent matrix …”

Section: Second‐order Work As a Failure Criterionmentioning

confidence: 99%

“…Therefore, it is of crucial importance to improve understanding of the mechanism of material instability to improve the safety of geotechnical structures. Several researchers have attempted to give precise definitions of material failure . Lyapunov, in particular, was a pioneer in defining instability in solid mechanics within a mathematical framework.…”

Section: Introductionmentioning

confidence: 99%

“…Nicot et al answered this question from the perspective of energy and, in so doing, demonstrated that, for a quasistatic system, the second‐order work can be a uniform quantity in capturing the bifurcation point in granular materials . More recently, the second‐order work criterion has been applied to investigate material instability from the particle scale to boundary value problems …”

Section: Introductionmentioning

confidence: 99%

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A multiscale approach for investigating the effect of microstructural instability on global failure in granular materials

Zhao

Yin

Hicher

2018

Summary This paper aims to develop a multiscale approach that has the ability to characterise the influence of microstructural instabilities on global failures in granular materials. For this purpose, the Chang‐Hicher multiscale constitutive relation has been implemented into a finite element code, and the expression of the second‐order work, as an indicator of the material instability, has been computed at the interparticle contact scale, at the representative element volume scale, and at the boundary value problem scale. At the global scale, the second‐order work can be obtained through the integration of that obtained at interparticle contacts. Hence, it becomes possible to analyse the range of instability from the microstructure to the macrostructure. Drained and undrained triaxial tests were numerically simulated. With this method, it was demonstrated that the grain‐scale origin of the specimen instability was well captured. Additionally, biaxial tests were conducted and the onsets of localised and diffuse failure in granular assemblies were successfully predicted. The transition from diffuse to localised failure was demonstrated at different scales, whereby the coincidence between the direction of local instabilities and the direction of the shear band became evident. The influence of the boundary conditions and of the heterogeneity of the initial porosity on the failure mode of granular materials was also analysed. All these examples demonstrate that the developed multiscale approach can characterise in a satisfactory manner the influence of instability at the inter‐grain contacts upon the global failure of granular assemblies.

“…It is noted that the second‐order work criterion does not provide a sufficient condition for failure but the instabilities may occur with the system transforming from a quasistatic regime toward a dynamic regime when the second‐order work vanishes along a given loading path . This regime transformation usually relates to the occurrence of an outburst in kinetic energy, which can be detected by the vanishing of the second‐order work …”

Section: Introductionmentioning

confidence: 99%

A multiscale work‐analysis approach for geotechnical structures

Xiong

Yin

Nicot

2019

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Summary This paper presents a second‐order work analysis in application to geotechnical problems by using a novel effective multiscale approach. To abandon complicated equations involved in conventional phenomenological models, this multiscale approach employs a micromechanically‐based formulation, in which only four parameters are involved. The multiscale approach makes it possible a coupling of the finite element method (FEM) and the micromechanically‐based model. The FEM is used to solve the boundary value problem (BVP) while the micromechanically‐based model is utilized at the Gauss point of the FEM. Then, the multiscale approach is used to simulate a three‐dimensional triaxial test and a plain‐strain footing. On the basis of the simulations, material instabilities are analyzed at both mesoscale and global scale. The second‐order work criterion is then used to analyze the numerical results. It opens a road to interpret and understand the micromechanisms hiding behind the occurrence of failure in geotechnical issues.