If the matrix is elastically isotropic and both precipitate and matrix have equal elastic moduli, the total elastic strain energy is independent of which of the following?

Question

If the matrix is elastically isotropic and both precipitate and matrix have equal elastic moduli, the total elastic strain energy is independent of which of the following?

BlackTom AI · Accepted Answer

The question asks about the dependence of total elastic strain energy on the precipitate shape under specific material conditions.
First, consider the given scenario: the matrix is elastically isotropic, and the precipitate and the matrix have equal elastic moduli. In this case, there is no elastic misfit energy arising from stiffness contrast between the precipitate and the surrounding matrix, because their moduli are identical and the material behaves uniformly under loading.
Under isotropy with identical moduli, the internal stress state is the same in all directions and does not favor one precipitate morphology over another. As a result, the elastic strain energy stored due to a misfit or mismatch is not influenced by how the precipitate is shaped, since there is no elastic contrast to concentrate or redirect stress around different geometries.
Because the provided answer options are missing in the data, I cannot analyze alternative choices. If options were available, I would assess each one by asking whether a given feature would alter the elastic energy when there is no modulus mismatch and isotropy; typically, shapes that create different stress concentrations might matter only when there is anisotropy or modulus contrast. In this specific case, the shape does not change the energy contribution arising from elastic mismatch, so any option asserting energy independence from shape would be correct while others implying shape-dependence would be incorrect.
In summary, with elastic isotropy and equal moduli, the total elastic strain energy does not depend on the precipitate shape, because there is no differential stiffness or directional dependence to cause energy variations across shapes.

2251-1_20MTEN6070001 Lecture 16 Pre-Class Reading Quiz

If the matrix is elastically isotropic and both precipitate and matrix have equal elastic moduli, the total elastic strain energy is independent of which of the following?

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