@Article{cmes.2020.07799,
AUTHOR = {Shixue Liang, Hankun Liu},
TITLE = {An Equivalent Strain Based Multi-Scale Damage Model of Concrete},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {122},
YEAR = {2020},
NUMBER = {3},
PAGES = {1015--1038},
URL = {http://www.techscience.com/CMES/v122n3/38384},
ISSN = {1526-1506},
ABSTRACT = {A multi-scale damage model of concrete is proposed based on the concept of 
energy equivalent strain for generic two- or three-dimensional applications. Continuum 
damage mechanics serves as the framework to describe the basic damage variables, 
namely the tensile and compressive damage. The homogenized Helmholtz free energy is 
introduced as the bridge to link the micro-cell and macroscopic material. The crack 
propagation in micro-cells is modeled, and the Helmholtz free energy in the cracked 
micro-structure is calculated and employed to extract the damage evolution functions in 
the macroscopic material. Based on the damage energy release rates and damage 
consistent condition, the energy equivalent strain is used to expand the uniaxial damage 
model to the multi-dimensional damage model. Agreements with existing experimental 
data that include uniaxial tensile and compressive tests, biaxial compression and biaxial 
peak stress envelop demonstrate the capacity of the multi-scale damage model in 
reproducing the typical nonlinear performances of concrete specimens. The simulation of 
precast laminated concrete slab further demonstrates its application to concrete structures.},
DOI = {10.32604/cmes.2020.07799}
}