Scale-dependent constitutive relations and the role of scale on nominal properties

Size effects in strength and fracture energy of heterogeneous materials is considered within a context of scale-dependent constitutive relations. Usin g tools of wavelet analysis, and considering the failure state of a one-dim ensional solid, constitutive relations which include scale as a parameter a re derived from a 'background' gradient formulation. In the resulting theor y, scale is not a fixed quantity independent of deformation, but rather dir ectly dependent on the global deformation field. It is shown that strength or peak nominal stress (maximum point at the engineering stress-strain diag ram) decreases with specimen size while toughness or total work to fracture per nominal area (area under the curve in the engineering stress-strain di agram integrated along the length of the considered one-dimensional specime n) increases. This behavior is in agreement with relevant experimental find ings on heterogeneous materials where the overall mechanical response is de termined by variations in local material properties. The scale-dependent co nstitutive relations are calibrated from experimental data on concrete spec imens. (C) 2001 Editions scientifiques et medicales Elsevier SAS.