Erratum: “Effective Electromechanical Properties of 622 Piezoelectric Medium With Unidirectional Cylindrical Holes” [ASME J. Appl. Mech., 2013, 80(5), p. 050905; DOI 10.1115/1.4023475

Abstract

This erratum concerns the replacement of expressions (39)–(42) in the original article by the expressions listed below:(39)M=(p0s00p0−ss0−t00−s0−t)(40)E=(1/20s/2p001/20−s/2p−s/2t01/200s/2t01/2)(41)M¯=(p¯10s¯100p¯20−s¯2s¯30−t¯100−s¯40−t¯2)(42)p¯p=(1−V12)(σ+1)(1−V1)2σ+(1+V1)2, s¯s=(1−V1)2(σ+1)(1−V1)2σ+(1+V1)2, t¯t=(1−V12)(σ+1)(1−V1)2σ+(1+V1)2In view of the above replacements, parts of the text in Secs. 5 and 6 of the original article were revised and are presented below.where V1+V2=1, which means that l=1, V1 is the area fraction of the circular hole, and we recall from Eq. (3) that σ is the electromechanical coupling factor of the piezoelectric matrix.In Fig. 2(a), we show the ratios pe/p and te/t versus V1, where pe/p=te/t using either the AHM expressions (36) (first expression) and (37) (second expression) or the Mori–Tanaka expressions (42) (first and third expressions).Observe also that the curves for pe/p and te/t using the AHM and considering N0=0 are indistinguishable from the curves for pe/p and te/t using the Mori–Tanaka approach.The curves obtained via the AHM become indistinguishable for large values of N0, and the curve obtained via the AHM together with N0=0 is indistinguishable from the curve obtained via the Mori–Tanaka approach.Observe from this figure that the curves obtained via the AHM become indistinguishable for large values of N0, and the curve obtained via the AHM together with N0=0 is indistinguishable from the curve obtained via the Mori–Tanaka approach.The third author gratefully acknowledges the financial support from Coordination for the Improvement of Higher Education Personnel (CAPES) and São Paulo Research Foundation (FAPESP), Grant No. 2014/21836-2, and the second author gratefully acknowledges the financial support from Cátedra Extraordinaria IIMAS-UNAM.