Uniform elastic field inside an elliptical inhomogeneity with Neuber’s nonlinear stress–strain law under generalized plane strain deformations
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Bibliographic record
Abstract
We prove the uniformity of the in-plane and anti-plane elastic field of stresses and strains inside an incompressible nonlinear elastic elliptical inhomogeneity embedded in an infinite linear isotropic elastic matrix subjected to uniform remote in-plane and anti-plane stresses. The elastic material occupying the elliptical inhomogeneity obeys Neuber’s special nonlinear stress-strain law. The original boundary value problem is finally reduced to a single non-linear equation for the constant effective strain within the inhomogeneity, which is rigorously proved to have a unique solution. Once the non-linear equation is solved numerically, we establish the uniform elastic field within the elliptical inhomogeneity and the non-uniform elastic field in the linear elastic matrix.
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Full frame distilled prediction
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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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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