Comparison of Continuum Stresses in Granular Material Computed by Volume Average Approach and Boundary Average Approach Under Static and Quasi-Static Conditions
Bibliographic record
Abstract
Averaging approaches have been widely used to estimate continuum stress in granular materials to facilitate the assimilation of granular materials’ behavior into a continuum mechanics framework. At present, selection criteria for the appropriate averaging approach are still poorly understood. This paper compares the stresses computed by two popular averaging approaches, i.e., volume average approach (VAA) and boundary average approach (BAA) in order to investigate relative errors between the two approaches under various conditions. The comparisons between VAA and BAA under a static condition were first carried out based on the rigid particle analytical framework proposed by Rothenburg, L. [1980] “Micromechanics of idealized granular systems,” Ph.D. thesis, Carleton University, Ottawa, followed by discrete element modelling (DEM) simulations using PFC3D under a quasi-static condition. The results of theoretical comparison suggested that the relative error in the computed stresses by VAA with an omission of overlap could be grossly estimated by the ratio of overlap to length of contact branch, while the relative error in the computed stresses by VAA with an omission of external contacts could be grossly estimated by the ratio of maximum particle diameter to specimen size. At the ratio of maximum particle diameter to specimen size of 5, which is usually taken as the minimum recommended ratio to minimize boundary effect, the relative error caused by omitting the external contacts was as high as 20%. Numerical comparisons suggested that the relative errors of the two approaches under a quasi-static condition were significantly influenced by the strain energy ratio defined in this study. The VAA was recommended as a preferred computation method over the BAA when the strain energy ratio was considerably lower than unity.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".