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The phrase "demonstrate the damage" is correct and perfectly usable in written English.
For example, you might use it in a sentence like this: "The photos taken after the storm demonstrate the damage that the high winds caused."
Exact(4)
Bulut et al. (2005) demonstrate the damage detection in civil structure using SVM classifier and wavelets.
Animal study was conducted in a rat brain surgery model to demonstrate the damage in cerebral neocortex/neopallium loss.
The analysis results are shown to demonstrate the damage caused by these radiation sources in the polymers.
"There has been a lot of work by HRW, Amnesty, the UN panel, to demonstrate the damage, find out what has occurred," said Roy Ibitser, an arms control expert at the UK charity Saferworld.
Similar(56)
Demonstrating the damage done, the prosecutors asked the judge at least three times to reconsider the ruling.
It demonstrates the damage caused by the hollowing out of industry since the 1970s.
At a council session in Hauppauge on Dec. 8, Councilman John Potente showed aerial photographs that he said demonstrated the damage ponds can cause in wetlands.
This demonstrated the damage tolerance capabilities of 3D woven composites.
The exceeding ISD from different damage threshold demonstrates the damage of structure at that earthquake level which can be observed in Figs. 4 and 5 (dotes over the horizontal lines).
It is demonstrated the damage induced by high-pressure air blasting around the hole enhances the gas drainage dramatically; however, the in-situ stress in coal seam may restrain the blasting-induced fractures and subsequent gas drainage, which should be paid attention to during the design of enhanced gas drainage with high-pressure air blasting.
Histological and molecular examination of the model demonstrated the damage and the Wnt pathway activation at 12 and 18 weeks after the surgery where we can mimic CKD.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com