European Journal of Applied Mathematics

Research Article

Laminates and microstructure

Pablo Pedregala1

a1 Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain


This paper deals with the mathematical characterization of microstructure in elastic solids. We formulate our ideas in terms of rank-one convexity and identify the set of probability measures for which Jensen's inequality for this type of functions holds. This is the set of laminates. We also introduce generalized convex hulls of sets of matrices and investigate their structure.

(Revised March 17 1992)