Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law
Bibliographic record
Abstract
Two numerical algorithms for solving elastoplastic problems with the finite element method are presented. The first deals with the implementation of the return mapping algorithm and is based on a fixed-point algorithm. This method rewrites the system of elastoplasticity non-linear equations in a form adapted to the fixed-point method. The second algorithm relates to the computation of the elastoplastic consistent tangent matrix using a simple finite difference scheme. A first validation is performed on a nonlinear bar problem. The results obtained show that both numerical algorithms are very efficient and yield the exact solution. The proposed algorithms are applied to a two-dimensional rockfill dam loaded in plane strain. The elastoplastic tangent matrix is calculated by using the finite difference scheme for Mohr–Coulomb’s constitutive law. The results obtained with the developed algorithms are very close to those obtained via the commercial software PLAXIS. It should be noted that the algorithm’s code, developed under the Matlab environment, offers the possibility of modeling the construction phases (i.e., building layer by layer) by activating the different layers according to the imposed loading. This algorithmic and implementation framework allows to easily integrate other laws of nonlinear behaviors, including the Hardening Soil Model.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.014 | 0.007 |
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".