Modeling fracture in the context of a strain-limiting theory of elasticity: A single plane-strain crack

• Published in: International journal of engineering science Vol. 88; pp. 73 - 82
• Main Authors: Gou, K., Mallikarjuna, M., Rajagopal, K.R., Walton, J.R.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-03-2015
• Subjects: Asymptotic analysis; Asymptotic properties; Constitutive relationships; Elastic limit; Elasticity; Finite elasticity; Fracture; Fracture mechanics; Mathematical analysis; Mathematical models; Strain; Strain-limiting theories; Stresses; Fracture; Finite elasticity; Strain-limiting theories; Asymptotic analysis
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/j.ijengsci.2014.04.018

Implicit constitutive relations afford a logically consistent framework for formulating strain-limiting, nonlinear elastic constitutive models utilizing the classical linearized strain tensor. This is in marked contrast to traditional Cauchy or Green elastic formulations which give rise to customary linear elasticity in the infinitesimal strain limit. Within this strain-limiting elastic constitutive setting, the present paper investigates the asymptotic behavior of the stress field at the tip of a straight plane-strain fracture. It is shown that within the general class of crack-tip asymptotic expansions considered, the only cases satisfying the required boundary conditions correspond to bounded stresses. This is in agreement with previous results for the corresponding anti-plane shear fracture problem.