Analysis of dilatancy relation and shear‐band formation in granular materials based on Eshelby‐Mandel tensor
Bibliographic record
Abstract
Abstract The theory of configurational or material forces based on the Eshelby stress tensor (also called energy‐momentum tensor) has provided a general and efficient way to describe the motion of material defects and other inhomogeneities within the framework of continuum mechanics. In this paper, we explore how to use the configurational forces to describe the behavior of homogeneous granular materials by considering the material characteristics on both continuum and discrete particle levels. In particular, dissipative driving forces based on the Eshelby‐Mandel stress tensor are utilized as the driving force of the configuration variations in the form of shear‐induced volume change. The energy dissipation induced by the relative sliding at particle contacts is considered in the configurational forces. To characterize the dilation of a homogeneous granular material with uniform deformation, a virtual plane is introduced to facilitate the analysis and to derive the dilatancy formulation. With the consideration of the shear‐band geometry and the requirement of configurational force equilibrium across the boundary of a shear‐band, the condition for the onset of a shear band is derived. For granular specimens subjected to biaxial compression, the analyses recover the well‐known Rowe's dilatancy formulation and yield the shear‐band orientation identical to that obtained from the classical bifurcation analysis within the framework of elasto‐plasticity.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".