Multimaterial Topology Optimization of Adhesive Backing Layers via J-Integral and Strain Energy Minimizations
Bibliographic record
Abstract
Abstract Strong adhesives often rely on reduced stress concentrations obtained via specific functional grading of material properties. This can be seen in many examples in nature and engineering. Basic design principles have been formulated based on parametric optimization, but a general design tool is still missing. We propose here the use of topology optimization to achieve optimal stiffness distribution in a multimaterial adhesive backing layer, reducing stress concentration at selected (crack tip) locations. The method involves the minimization of a linear combination of (i) the J-integral around the crack tip and (ii) the strain energy of the structure. This combination is due to the compromise between numerical stability and accuracy of the method, where (i) alone is numerically unstable and (ii) alone cannot eliminate the crack tip stress singularity. We analyze three cases in plane strain conditions, namely, (1) double-edged crack and (2) center crack, in tension, as well as (3) edge crack under shear. Each case evidences a different optimal topology with (1) and (2) providing similar results. The optimal topology allocates stiffness in regions that are far away from the crack tip, and the allocation of softer materials over stiffer ones produces a sophisticated structural hierarchy. To test our solutions, we plot the contact stress distribution across the interface. In all observed cases, we eliminate the stress singularity at the crack tip, albeit generating (mild) stress concentrations in other locations. The optimal topologies are tested to be independent of the crack size. Our method ultimately provides the robust design of flaw tolerant adhesives where the crack location is known.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".