Bulk Modulus

therefore,

we can expand the determinant of the tensor det[I + 2E] to find det[I + 2E] = 1 + 2Ie + 4IIE + 8IIIE

but for small strains, IE ^ IIE ^ IIIE since the first term is linear in E, the second is quadratic, and the third is cubic. Therefore, we can approximate det[I + 2E] « 1 + 2IE, hence we define the volumetric dilatation as

this quantity is readily measurable in an experiment.

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