TY - JOUR
T1 - Restrictions on microstructure
AU - Bhattacharya, Kaushik
AU - Firoozye, Nikan B.
AU - James, Richard D.
AU - Kohn, Robert V.
N1 - Funding Information:
Section 2 draws from the Ph.D. thesis of Firoozye (New York University, 1990). The 'four-gradient example' was worked out while James was visiting the Mathematical Sciences Institute at Cornell University during the spring of 1988. Firoozye held a postdoctoral position at the Institute for Mathematics and its Applications in 1990-91, and a visiting position at Universitat Bonn in 1992-3. Firoozye and James were affiliated with the Mathematics Department of Heriot-Watt University during 1991-2. Bhattacharya was a graduate student at the University of Minnesota (Ph.D. 1991) then a Visiting Member at the Courant Institute (1991-3) during the execution of this research. Partial support from the following agencies is gratefully acknowledged: AFOSR (K.B., R.D.J., R.V.K.), ARO (K.B., R.D.J., R.V.K.), NSF (K.B., N.B.F., R.D.J., R.V.K.), ONR (R.D.J.), and SERC (N.B.F, R.D.J.).
PY - 1994
Y1 - 1994
N2 - We consider the following question: given a set of matrices Jf 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 k supports a nontrivial Young measure with mean value 0, then the linear span of Jf must contain a matrix of rank one.
AB - We consider the following question: given a set of matrices Jf 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 k supports a nontrivial Young measure with mean value 0, then the linear span of Jf must contain a matrix of rank one.
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U2 - 10.1017/S0308210500022381
DO - 10.1017/S0308210500022381
M3 - Article
AN - SCOPUS:84971928488
SN - 0308-2105
VL - 124
SP - 843
EP - 878
JO - Proceedings of the Royal Society of Edinburgh: Section A Mathematics
JF - Proceedings of the Royal Society of Edinburgh: Section A Mathematics
IS - 5
ER -