A cohesion-friction combined hardening plastic model of concrete with the nonorthogonal flow rule: Theory and numerical implementation

Abstract

A cohesion-friction combined hardening model of concrete was developed. Combined with the Mohr-Coulomb strength criterion, the yield curve is determined directly by the test data of concrete. Then, a method to determine the hardening law from the evolutionary process of the yield curve is elaborated. To consider the influence of the multiaxial stress state on the ductility of concrete, a stress dependent plastic internal variable is proposed. Based on the nonorthogonal flow rule implemented by fractional order derivative, the direction of plastic strain increment is directly determined by the nonorthogonal gradient of the yield function without the need for plastic potential function. The comparison with the test data shows that the proposed model can capture the strength and deformation characteristics of concrete reasonably. Finally, the model is implemented into ABAQUS via an open-source user defined material subroutine UMAT (https://github.com/zhouxin615/CFCH_model.git) based on the implicit return mapping algorithm. In particular, the integral-type nonlocal approach was adopted to regularise FE solution. Moreover, through the structural analysis of reinforced concrete columns, the operation process of the friction and cohesion mechanism of concrete materials is well reproduced.