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I expect the following approach works.

The original cell vector before deformation: $A = [\boldsymbol{a}_1, \boldsymbol{a}_2, \boldsymbol{a}_3]$
The cell vector after deformation: $A' = [\boldsymbol{a}'_1, \boldsymbol{a}'_2, \boldsymbol{a}'_3]$

$A' = FA$

where $F$ is defined as $F_{\mu\nu} = \delta_{\mu\nu} + u_{\mu\nu}$.

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@RicardoCecconello
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