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Published January 1994 | metadata_only
Journal Article

Restrictions on microstructure


We consider the following question: given a set of matrices ⊁ with no rank-one connections, does it support a nontrivial Young measure limit of gradients? Our main results are these: (a) a Young measure can be supported on four incompatible matrices; (b) in two space dimensions, a Young measure cannot be supported on finitely many incompatible elastic wells; (c) in three or more space dimensions, a Young measure can be supported on three incompatible elastic wells; and (d) if ⊁ supports a nontrivial Young measure with mean value 0, then the linear span of ⊁ must contain a matrix of rank one.

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© 1994 Royal Society of Edinburgh. Received February 10 1993. Accepted June 12 1993.

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August 20, 2023
August 20, 2023