Bounds on the volume fraction of 2-phase, 2-dimensional elastic bodies and on (stress, strain) pairs in composites

摘要

Bounds are obtained on the volume fraction in a two-dimensional bodycontaining two elastically isotropic materials with known bulk and shearmoduli. These bounds use information about the average stress and strainfields, energy, determinant of the stress, and determinant of the displacementgradient, which can be determined from measurements of the traction anddisplacement at the boundary. The bounds are sharp if in each phase certaindisplacement field components are constant. The inequalities we obtain alsodirectly give bounds on the possible (average stress, average strain) pairs ina two-phase, two-dimensional, periodic or statistically homogeneous composite