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Is the trunk of your tree girdled (bark missing all the way around the circumference of the tree)?
Below are some articles that will help you determine a course of treatment for your damaged bark:
https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-fix-girdled-trees.htm
https://www.gardeningknowhow.com/ornamental/trees/tgen/repairing-tree-bark-damage.htm
For more information on the care of eucalyptus trees, please visit the following link:
https://www.gardeningknowhow.com/ornamental/trees/eucalyptus/tips-growing-eucalyptus.htm