On the strain-energy density in linear elasticity

Abstract

Standard results from matrix theory are used to derive optimal upper and lower bounds for the strain-energy density in terms of the norm of the stress tensor in two and three dimensions. The approach also yields directly necessary and sufficient conditions for positive-definiteness.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42704/1/10665_2005_Article_BF01535284.pd