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

The Original Article was published on 11 April 2020

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

Following publication of the original article , 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  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.

## Author information

Authors

### Corresponding author

Correspondence to Ondřej Rokoš. 