Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Stochastic Singularity Analysis in Multi-Material Domains: Effects of Randomness in Isotropic Material Properties. |
| Συγγραφείς: |
Omer, Netta1 (AUTHOR) |
| Πηγή: |
Mathematics (2227-7390). Aug2026, Vol. 14 Issue 15, p2689. 20p. |
| Θεματικοί όροι: |
*Eigenanalysis, *Polynomial chaos, *Young's modulus, *Poisson's ratio, *Isotropic properties, *Inhomogeneous materials |
| Περίληψη: |
The singularity level near a bi-material interface crack is crucial for failure prediction. Unlike a crack in a homogeneous material with a fixed eigenvalue of 1/2, interface crack eigenvalues are complex. Their fixed real part is 1/2, while the stochastic imaginary part depends explicitly on the material properties, governing the stress field's oscillatory nature. Consequently, deterministic approximations may underestimate the severity of the singularity. This paper presents a stochastic approximation of the eigenvalue's imaginary component for a bi-material interface crack. Both materials are isotropic, involving stochastic Young's modulus and stochastic Poisson's ratio, yielding four independent random variables. The generalized Polynomial Chaos (gPC) method is used to construct a multidimensional polynomial expansion via tensor products of orthogonal bases that are dictated by the material distributions. The deterministic coefficients are derived from evaluations at selected quadrature points. The methodology is demonstrated and directly validated on a benchmark problem of a crack between bonded half-planes, utilizing its exact closed-form analytical solution. The gPC approximation converges rapidly as the polynomial order increases, achieving relative differences below 1% in all statistical moments compared to the exact analytical solution, using only 4% of the computational effort typically required for such statistical characterization These findings underscore that accounting for material stochasticity is essential for accurate failure criteria. [ABSTRACT FROM AUTHOR] |
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