The research in this area concerns the mechanical properties of materials, notably those of metals, elastomers, biological materials, functionally-graded materials and granular materials. The understanding and modeling of the role of inhomogeneities in the linear and nonlinear domains, those arising in connection with volume and surface (interface or wear) damage are the important issues at stake. They involve theoretical work ( in particular, in connection with homogenization theory, large transformation formulations or the study of constitutive instabilities), numerical investigations ( multiscale methods, Fourier transforms, parallel computations) and targeted experimental programs ( fatigue tests, mechanical and ultrasonic measurements, measurements of mechanical properties by X-ray scanning).