Deformation of inhomogeneous elastic solids with two-dimensional damage

A general correlation is derived between macroscopic stresses/strains and m icroscopic deformation on the damage surfaces for inhomogeneous elastic sol ids with two-dimensional damage. Assuming linear elastic behavior for the u ndamaged materials, the macroscopic deformation associated with nonlinear s trains, or damage strains, is shown to be the weighted sum of the microscop ic deformations on the damage surfaces. For inhomogeneous materials with pe riodic, structures (laminated composites, for example) and various identifi able damage modes, simple relations are derived between the macroscopic def ormation and microscopic damage. When the number of identifiable damage mod es is less than or equal to the number of relevant measurable macroscopic s trains, the correlation can be used to evaluate the damage progression from simple macroscopic stress and strain measurements. The simple case of a un idirectional fiber-reinforced composite under longitudinal load is used to show how the results can help detect and characterize the damage using macr oscopic measurements, without resorting to assumptions of detailed microsco pic deformation mechanisms.