Generalized formulation for strip yielding model with variable cohesion and its analytical solutions Wei Wang a , Cheng-Tzu Thomas Hsu b, * , Denis Blackmore c a HLW International, LLP. 115 5th Avenue New York, NY 10003, USA b Department of Civil and Environmental Engineering, New Jersey Institute of Technology, University Heights, Newark, NJ 07102-1982, USA c Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102-1982, USA Received 22 November 1998; in revised form 16 July 1999 Abstract A generalized plastic zone theory based on the ParisÕ displacement formula is presented to study inelastic fracture properties. This theory is capable of analyzing inelastic fracture characteristics of engineering materials in general. The so-called size eect is predicted for softening materials. A brittleness index is also discussed based on this theory. It is illustrated that the brittleness index may be used to characterize the inelastic fracture properties of the structures. Ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Formulation; Strip yielding model; Cohesion; Analytical solutions 1. Introduction The plastic zone size may be estimated by IrwinÕs (1960) eective crack length method for metallic structures. This eective crack length concept is based on the fact that most metallic materials are con- siderably ductile and have a nearly constant yield strength after the stress in the material reaches its peak value. His plastic zone formula is based on the concept of force balance near the crack tip and is con- siderably accurate in small scale yielding cases when compared with the more accurate DugdaleÕs strip yielding model. However, extension of this theory to cementitious material, such as mortar and concrete may initiate technical problems due to the softening properties of the material. Concrete and mortar are known to be softening materials and have a descending cohesive force. Pre- vious researches have shown dierences in the fracture properties between cementitious materials and metals (Carpinteri, 1985; Bazant, 1985; Shah, 1984; Sih, 1984). Several researchers concluded that this softening cohesive force plays a key role in determining the fracture properties of the concrete structures, especially in the case of non-linear fracture mechanics. International Journal of Solids and Structures 37 (2000) 7533±7546 www.elsevier.com/locate/ijsolstr * Corresponding author. 0020-7683/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII:S0020-7683(99)00293-0