An alternative stress boundary condition in small deformations and its application to soft elastic composites and structures
Bibliographic record
Abstract
• Enhanced stress condition for soft elastic perforated structure in linear elasticity. • Incorporating a small change in the normal to the boundary during deformation. • Predicting the influence of initial or residual stress in a perforated structure. • Large-deformation-based finite element simulations to verify accuracy. • Accurate referential analytic results for soft elastic structures and composites. Linear elasticity theory has been used extensively in the study of the elastic behavior of various perforated structures and composite materials requiring the accompaniment of appropriate boundary conditions to derive qualitatively correct and quantitatively referential solutions. When incorporating conventional boundary conditions, however, linear elasticity theory fails to predict certain essential phenomena associated with perforate structures and composite materials even when they undergo small deformations. For example, a soft elastic porous medium is appreciably stiffened when inflated despite the fact that the internal air pressure is significantly lower than the modulus of the medium itself. In this paper, we propose an improved stress boundary condition by simply incorporating a small change in the normal to the boundary during deformation. We show via numerical examples that in the context of linear elasticity theory, the use of this improved boundary condition offers the possibility of predicting the influence of initial or residual stress in a perforated structure on the elastic response of the structure to external loadings (which can never be captured with the use of conventional boundary conditions). We perform also large-deformation-based finite element simulations to verify the accuracy of the closed-form results obtained from the improved boundary condition for a soft elastic perforated structure with initial internal pressure. We believe that the idea presented in this paper will extend the applicability of linear elasticity theory and yield more accurate referential analytic results for soft elastic structures and composites.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".