A New 3D Empirical Plastic and Damage Model for Simulating the Failure of Concrete Structure

Yan-Tao Jiao,Zhen-Zhong Shen,Bo Wang

doi:10.1186/s40069-019-0362-z

Abstract

A new plastic–damage constitutive model based on the combination of damage mechanics and classical plastic theory was developed to simulate the failure of concrete. In order to explain different material behaviors of concrete under tensile and compressive loadings, the plastic yield criterion, the different kinematic hardening rule for tension and compressive and the isotropic flow rule were established in the effective stress space. Meanwhile, two different empirical damage evolution equations were adopted: one for compression and the other for tension. A multi-axial damage influence factor was also introduced to fully describe the anisotropic damage of concrete. Finally, the model response was compared with a wide range of experiment results. The results showed that the model could well describe the nonlinear behavior of concrete in a complex stress state.

Highlights

Existing plastic–damage models (PDMs) of concrete are usually based on sound thermodynamic principles (Hesebeck 2001; Mahnken 2002; Voyiadjis and Deliktas 2000; Cicekli et al 2007; Taqieddin et al 2012; Voyiadjis et al 2008; Abu Al-Rub and Kim 2010; Wu et al 2006; Liu et al 2013; Mazars and Pijaudier-Cabot 1989; Lee and Fenves 1998)
With inspirations from all the previous works and understandings mentioned above, this paper presented a new PDM for concrete with two different empirical and strain-based damage evolution equations: one for tensile damage and the other for compressive damage
By substituting wi+ and wi− into M± defined in Eq (73), the damage-effect matrix for cyclic loading can be rewritten as follows: 2.2 Plasticity Part Concrete has different material behaviors under tensile and compressive loadings, the yield criterion proposed by Lubliner et al (1989) that accounts for both tension and compression plasticity was adopted in this work

Summary

Introduction

This study mainly aimed to formulate a new plastic–damage constitutive model for concrete as completely and as as possible. Given the complex anisotropic damage in concrete, some authors adopted a single damage variable for both tension and compression (Grassl and Jir Sek 2006a, b; Yu et al 2010; Kitzig and Häußler-Combe 2011; Valentini and Hofstetter 2013). This is sufficient for monotonic loading with unloading, but it is not suitable. A simple and effective method which needs the uniaxial cyclic loading stress–strain experimental curves to identify the material parameters was proposed by Abu Al-Rub and Kim (2010). To demonstrate the capability of the proposed model, the model response was compared with a wide range of experimental results

Theoretical Basics of Plastic‐Damage Model

Definition of Damaged Elastic Stiffness with Cyclic Loading Neglected

Definition of damaged elastic stiffness for cyclic loading

Conclusions