A Neutral Nonlinear Elastic Circular Inhomogeneity Obeying Neuber’s Stress–Strain Law in Anti-Plane Shear
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Bibliographic record
Abstract
Summary We consider a three-phase composite in which the internal circular inhomogeneity obeying Neuber’s nonlinear stress-strain law is bonded to an infinite linear isotropic elastic matrix via a middle linear isotropic elastic annular coating when the matrix is subjected to uniform remote anti-plane stresses. A neutral circular inhomogeneity that does not disturb the prescribed uniform stress field in the matrix is identified by numerically solving the resulting two coupled nonlinear equations via iteration or equivalently by solving a single sextic equation to arrive at the constant effective strain within the inhomogeneity and the ratio of the shear modulus of the matrix to that of the coating. The upper bound of the shear modulus ratio is the classical Hashin–Shtrikman formula while the lower bound is the classical Hashin–Shtrikman formula for a cavity. A neutral coated nonlinear spherical inhomogeneity in conductivity obeying Neuber’s law is also designed.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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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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