Corrigendum: “Band-gaps in electrostatically controlled dielectric laminates subjected to incremental shear motions” (Journal of the Mechanics and Physics of Solids (2012) 60(11) (1970-1981) (S0022509612001159) (10.1016/j.jmps.2012.05.006))

摘要

There is a typo in Eq. (47), where λ should be raised to the power 4. We also fix typos in Eqs. (62)-(64), where the correct form of these equations, respectively, is [Formula presented] should read [Formula presented]. Eq. (59) contains associated errors, and its corrected version is [Formula presented]. Following these corrections, the figures are reproduced as follows. Figs. 1-4 revise Figs. 3-7, respectively. In the examples considered in Fig. 1, we observe that larger volume fractions of the soft phase result in gaps at higher frequencies. The width of the gaps increases when the contrast parameters are larger. The dependency on the volume fraction is highlighted in Fig. 2. Therein, we conclusively observe how as the volume fraction of the softer phase increases, the frequencies of the gaps are shifted towards higher frequencies. Conversely, Figs. 3 and 4 show that as the contrast parameters α and β increase, the frequency of the gaps are shifted towards lower frequencies. However, depending on the specific combination of α and β and the number of the gap, its width can either increase or decrease. The quantities in the dispersion relation that affect the width and the location of the gaps are γ, which serves as a measure of the mismatch in the impedance of the phases, and the ratio [Formula presented] and 2. We observe that in general γ does not depend monotonically on α and β, and different values of [Formula presented] demonstrate different dependency on the contrast parameters. Fig. 6 herein revises Fig. 7 of the original paper. Figs. 7 and 8 revise Figs. 8 and 9 of the original paper, respectively, taking H = 100 µm. The revised Figs show that the gaps are shifted towards higher frequencies as functions of the bias field, in agreement with the results of Shmuel (2013).