The chapter by Zdeněk P. Bazant and B. H. Oh presents a fracture theory for concrete, focusing on Mode I cracks in heterogeneous aggregate materials. The theory models the fracture as a blunt smeared crack band, justified by the random microstructure of concrete. It derives simple triaxial stress-strain relations to describe strain-softening and the effect of microcracking. The theory uses compliance matrices and characterizes material properties with three parameters: fracture energy, uniaxial strength limit, and width of the crack band. The method for determining fracture energy from stress-strain relations is provided, and the theory is verified against experimental data, showing satisfactory fits. The width of the crack band is found to be about 3 aggregate sizes, which is the minimum acceptable for continuum modeling. The theory is also implemented in finite element codes, and a formula is derived to predict fracture energy and strain-softening modulus from tensile strength and aggregate size. The statistical analysis of errors shows significant improvement over linear fracture theory. The applicability of fracture mechanics to concrete is thus established, addressing the structural size effect and the challenges of elastic finite element analysis.The chapter by Zdeněk P. Bazant and B. H. Oh presents a fracture theory for concrete, focusing on Mode I cracks in heterogeneous aggregate materials. The theory models the fracture as a blunt smeared crack band, justified by the random microstructure of concrete. It derives simple triaxial stress-strain relations to describe strain-softening and the effect of microcracking. The theory uses compliance matrices and characterizes material properties with three parameters: fracture energy, uniaxial strength limit, and width of the crack band. The method for determining fracture energy from stress-strain relations is provided, and the theory is verified against experimental data, showing satisfactory fits. The width of the crack band is found to be about 3 aggregate sizes, which is the minimum acceptable for continuum modeling. The theory is also implemented in finite element codes, and a formula is derived to predict fracture energy and strain-softening modulus from tensile strength and aggregate size. The statistical analysis of errors shows significant improvement over linear fracture theory. The applicability of fracture mechanics to concrete is thus established, addressing the structural size effect and the challenges of elastic finite element analysis.