TY - JOUR

T1 - An implicit stress update algorithm for the plastic nonlocal damage model of concrete

AU - Su, Cancan

AU - Lu, Dechun

AU - Zhou, Xin

AU - Wang, Guosheng

AU - Zhuang, Xiaoying

AU - Du, Xiuli

N1 - Funding Information: Support for this study is provided by the National Natural Science Foundation of China (Grant Nos., 52238011 , 52008231 , and 52025084 ), China Postdoctoral Science Foundation (Grant Nos., 2022M721884 ) and National Key R&D Program of China (Grant Nos., 2022YFC3800901 ).

PY - 2023/9/1

Y1 - 2023/9/1

N2 - The numerical implementation of advanced plastic damage models has been challenging due to the diverse computational difficulties caused by material nonlinearity. In this study, firstly, a plastic damage model is developed by a nonsmoothed Mohr–Coulomb yield criterion. The nonorthogonal flow rule without plastic potential function is employed to describe the dilatancy behavior of concrete. The stiffness degradation is considered through two tensile and compressive damage variables. Subsequently, an implicit stress update algorithm incorporating several advanced numerical methods is proposed to tackle difficulties arising in the numerical calculation of the plastic damage model. In the model implementation, the Mohr–Coulomb yield function with corners is replaced by a single smooth expression to ensure the stability of the numerical calculation. A line search method is used to solve nonlinear systems of integral stress equations to obtain better convergence than Newton method. The complex step derivative approximation is used to evaluate the consistent tangent operator to provide quadratic convergence speed of the global equilibrium iterations, thus avoiding tedious analytical derivative operations. The integral nonlocal method is also used to regularize the finite element solution. At the material point scale, the ability of the proposed model to describe the complex mechanical behavior of concrete is verified by utilizing nine sets of monotonic and cyclic loading and unloading tests. Finally, the algorithm and model's performance is well tested by the failure analysis of five numerical examples. The code of this work will be freely available at https://github.com/zhouxin615/PD_model.

AB - The numerical implementation of advanced plastic damage models has been challenging due to the diverse computational difficulties caused by material nonlinearity. In this study, firstly, a plastic damage model is developed by a nonsmoothed Mohr–Coulomb yield criterion. The nonorthogonal flow rule without plastic potential function is employed to describe the dilatancy behavior of concrete. The stiffness degradation is considered through two tensile and compressive damage variables. Subsequently, an implicit stress update algorithm incorporating several advanced numerical methods is proposed to tackle difficulties arising in the numerical calculation of the plastic damage model. In the model implementation, the Mohr–Coulomb yield function with corners is replaced by a single smooth expression to ensure the stability of the numerical calculation. A line search method is used to solve nonlinear systems of integral stress equations to obtain better convergence than Newton method. The complex step derivative approximation is used to evaluate the consistent tangent operator to provide quadratic convergence speed of the global equilibrium iterations, thus avoiding tedious analytical derivative operations. The integral nonlocal method is also used to regularize the finite element solution. At the material point scale, the ability of the proposed model to describe the complex mechanical behavior of concrete is verified by utilizing nine sets of monotonic and cyclic loading and unloading tests. Finally, the algorithm and model's performance is well tested by the failure analysis of five numerical examples. The code of this work will be freely available at https://github.com/zhouxin615/PD_model.

KW - Complex step derivative approximation

KW - Concrete

KW - Line search method

KW - Nonlocal regularization method

KW - Plastic damage model

UR - http://www.scopus.com/inward/record.url?scp=85163847154&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2023.116189

DO - 10.1016/j.cma.2023.116189

M3 - Article

AN - SCOPUS:85163847154

VL - 414

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 116189

ER -