Asymptotic bounds on overall moduli of cracked bodies. (English) Zbl 0961.74055

Summary: The interactions among multiple parallel microcracks in an elastic body are examined asymptotically in an explicit and quantitative manner in order to reveal fully their so-called shielding and magnification effects on the overall moduli of the body. Based upon this asymptotic analysis, we derive analytical upper and lower bounds for the overall moduli of bodies containing randomly distributed multiple parallel unbridged/bridged microcracks. The bounds are used to assess the accuracy of the approximate methods – the dilute distribution approximation, the differential scheme and the self-consistent model – that are commonly used to determine the overall moduli of bodies with multiple microcracks.


74Q20 Bounds on effective properties in solid mechanics
74R10 Brittle fracture
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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