Wang, Xu; Schiavone, Peter Uniform stress state inside a non-elliptical inhomogeneity near an irregularly shaped hole in antiplane shear. (English) Zbl 1446.74100 Math. Mech. Solids 25, No. 2, 362-373 (2020). Summary: Analytic continuation and conformal mapping techniques are applied to establish that the state of stress inside a non-elliptical elastic inhomogeneity can remain uniform despite the presence of a nearby irregularly shaped hole when the surrounding matrix is subjected to uniform remote antiplane shear stresses. The hole boundary is assumed to be either traction-free or subjected to antiplane line forces. Detailed numerical results are presented to demonstrate the resulting analytical solutions. Our results indicate that in maintaining a uniform stress distribution inside the inhomogeneity, it is permissible for the stresses in the matrix to exhibit either a square root singularity at sharp corners of a hole boundary or a high level of stress concentration at rounded corners of a hole. Cited in 1 Document MSC: 74E05 Inhomogeneity in solid mechanics 74B05 Classical linear elasticity 74S70 Complex-variable methods applied to problems in solid mechanics 74G05 Explicit solutions of equilibrium problems in solid mechanics Keywords:uniform stress state; elastic inhomogeneity; hole; concentrated surface force; antiplane elasticity; conformal mapping PDFBibTeX XMLCite \textit{X. Wang} and \textit{P. Schiavone}, Math. Mech. Solids 25, No. 2, 362--373 (2020; Zbl 1446.74100) Full Text: DOI References: [1] Sendeckyj, GP. Elastic inclusion problem in plane elastostatics. Int J Solids Struct 1970; 6: 1535-1543. · Zbl 0218.73021 [2] Ru, CQ, Schiavone, P. On the elliptical inclusion in anti-plane shear. Math Mech Solids 1996; 1: 327-333. · Zbl 1001.74509 [3] Lubarda, VA, Markenscoff, X. On the absence of Eshelby property for non-ellipsoidal inclusions. Int J Solids Struct 1998; 35: 3405-3411. · Zbl 0918.73015 [4] England, AH. Complex variable methods in elasticity. London: Wiley, 1971. · Zbl 0222.73017 [5] Liu, LP. Solution to the Eshelby conjectures. Proc R Soc Lond A 2008; 464: 573-594. · Zbl 1132.74010 [6] Kang, H, Kim, E, Milton, GW. Inclusion pairs satisfying Eshelby’s uniformity property. SIAM J Appl Math 2008; 69: 577-595. · Zbl 1159.74387 [7] Wang, X. Uniform fields inside two non-elliptical inclusions. Math Mech Solids 2012; 17: 736-761. [8] Dai, M, Gao, CF, Ru, CQ. Uniform stress fields inside multiple inclusions in an elastic infinite plane under plane deformation. Proc R Soc Lond A 2015; 471: 20140933. [9] Dai, M, Ru, CQ, Gao, CF. Uniform strain fields inside multiple inclusions in an elastic infinite plane under anti-plane shear. Math Mech Solids 2017; 22: 114-128. · Zbl 1371.74027 [10] Antipov, YA. 2019. Method of Riemann surfaces for an inverse antiplane problem in an n-connected domain. Complex Variables Elliptic Equations. Epub ahead of print 1 March 2019. DOI: 10.1080/17476933.2019.1585429. · Zbl 1457.74022 [11] Ting, TCT. Anisotropic elasticity: theory and applications. New York: Oxford University Press, 1996. [12] Milton, G, Serkov, SK. Neutral coated inclusions in conductivity and anti-plane elasticity. Proc R Soc Lond A 2001; 457: 1973-1997. · Zbl 1090.74558 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.