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Correction to: Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials

  • The original article was published in Advanced Modeling and Simulation in Engineering Sciences 2020 7:19

Correction to: Adv. Model. and Simul. (2020) 7:19 https://doi.org/10.1186/s40323-020-00152-7

Following publication of the original article [1], the authors reported the errors in the equations. In Eqs. (2), (3) and (22), at the end of all integrals, \(\hbox {d}\vec {X}_{\mathrm{md}}\vec {X}\) has been changed to \(\hbox {d}\vec {X}_\mathrm{m}\hbox { d}\vec {X}\). The corrected equations are given below:

$$\begin{aligned} \mathcal {E}(\vec {u}) = \frac{1}{|\Omega _\mathrm {m}|} \int _\Omega \int _{\Omega _\mathrm {m}} W(\vec {X},{{\varvec{F}}}) \, \mathrm {d}\vec {X}_\mathrm {m}\hbox { d}\vec {X}. \end{aligned}$$
(2)
$$\begin{aligned} \delta {\mathcal {E}}(\vec {u};\delta \vec {u}) = \frac{1}{|\Omega _\mathrm {m}|} \int _\Omega \int _{\Omega _\mathrm {m}} {{\varvec{P}}} : \vec {\nabla }_\mathrm {m}\delta \vec {u}(\vec {X},\vec {X}_\mathrm {m}) \, \mathrm {d}\vec {X}_\mathrm {m}\hbox { d}\vec {X}, \end{aligned}$$
(3)
$$\begin{aligned} \delta ^2{\mathcal {E}}(\vec {u};\delta \vec {u}) = \frac{1}{|\Omega _\mathrm {m}|} \int _\Omega \int _{\Omega _\mathrm {m}} \vec {\nabla }_\mathrm {m}\delta \vec {u}(\vec {X},\vec {X}_\mathrm {m}) : \mathbb {C} : \vec {\nabla }_\mathrm {m}\delta \vec {u}(\vec {X},\vec {X}_\mathrm {m}) \, \mathrm {d}\vec {X}_\mathrm {m}\hbox { d}\vec {X}, \end{aligned}$$
(22)

The original article [1] has been updated.

Reference

  1. 1.

    Rokoš O, Zeman J, Doškář M, Krysl P. Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials. Adv Model Simul Eng Sci. 2020;7:19. https://doi.org/10.1186/s40323-020-00152-7.

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Correspondence to Ondřej Rokoš.

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Rokoš, O., Zeman, J., Doškář, M. et al. Correction to: Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials. Adv. Model. and Simul. in Eng. Sci. 7, 25 (2020). https://doi.org/10.1186/s40323-020-00160-7

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