A new thermal-mechanical coupled numerical model was proposed based on the lattice discrete element method (LDEM), aiming at the heat conduction and thermal cracking of quasi-brittle materials. In LDEM, in order to simulate the numerical test of the temperature conduction and crack propagation, the equivalent conversion of the heat transfer process between the lattice discrete system and the continuum was carried out, combined with the linear expansion formula of the lattice element. Taking the heat conduction and thermoelastic stress of the plate, and the cracking caused by the temperature gradient and thermal mismatch as examples, the model was verified. In addition, the model was applied to the numerical simulation of the meso-level concrete temperature-stress test. Results show that the LDEM thermal-mechanical coupling model can simulate the heat conduction process of quasi-brittle materials, as well as the crack initiation and propagation under the influence of temperature effectively, which provides a powerful tool for studying the thermal cracking process and mechanism of quasi-brittle materials.
Fig.1Discrete mode and basic structure of lattice discrete element method
Fig.2Schematic diagram of lattice discrete element method mesh and crack simulation
Fig.3Equivalent parallel section of continuum and basic module
Fig.4Bilinear constitutive model of load-strain
Fig.5Comparison of LDEM solution and analytical solution of plate temperature and stress at different times
Fig.6Comparison of plate temperature distribution under different grid sizes
Fig.7Comparison of stress results between LDEM solution and analytical solutions under different mesh sizes
Fig.8Comparison of finite element solution and LDEM solution for temperature distribution of flat plate
Fig.9Comparison of LDEM solution and analytical solution of plate temperature and stress at different times
Fig.10Thermal cracking experiment on non-uniformity of reinforced concrete materials
参数
数值
混凝土保护层 （b≥r≥a）
钢筋内芯 （r＜a）
半径/m
b=0.15
a=0.03
厚度 h/m
0.002
0.002
弹性模量 E/GPa
20
40
泊松比 μ
0.2
0.3
密度 ρ/(kg·m?3)
2300
7850
抗拉强度 ft/MPa
3
235
断裂能 Gf/(N·m?1)
100
—
线膨胀系数 α/ K?1
7.00×10?6
2.20×10?5
初始温度 θ0/℃
0
0
温升幅度 Δθ /℃
100
100
Tab.1Thermal and mechanical parameters of reinforced concrete
Fig.11Comparison between LDEM solution and analytical solutions of concrete circumferential stress
Fig.12Crack morphology of reinforced concrete at different temperature rise times
参数
数值
参数
数值
弹性模量 E/GPa
69
比热 c/ (J·kg?1·K?1)
920
泊松比 μ
0.25
线膨胀系数 α/K?1
1×10?5
密度 ρ/(kg·m?3)
2600
初始温度 θ0/℃
20
抗拉强度 ft/MPa
9
边界温度 θc/℃
20
断裂能 Gf/(N·m?1)
500
中心孔温度 θh/℃
20~200
导热系数 k/(W·m?1·K?1)
1.2
—
—
Tab.2Thermal and mechanical parameters of granite
Fig.13Temperature distribution and crack morphology of granite at different times
Fig.14Experimental results and numerical simulation results of granite thermal cracking
Fig.15Mesoscopic models of concrete with different aggregate volume fractions
参数
数值
砂浆基质
骨料
界面过渡区
弹性模量 E/GPa
4
50
2.4
泊松比 μ
0.20
0.16
0.20
密度 ρ/(kg·m?3)
2440
2620
2440
抗拉强度 ft/MPa
2.06
20.00
1.24
断裂能 Gf/(N·m?1)
60
500
40
导热系数 k//(W·m?1·K?1)
1.106
2.440
0.940
线膨胀系数 α/K?1
1.2×10?5
0.5×10?5
1.2×10?5
比热 c/ (J·kg?1·K?1)
762.3
719.8
762.3
Tab.3Thermal and mechanical parameters of concrete components
Fig.16Temperature and deformation distribution of specimens with different aggregate volume fraction
Fig.17Shrinkage comparison of concrete specimens with different aggregate volume fraction
Fig.18Comparison of constraint stresses of concrete specimens with different aggregate volume fraction
Fig.19Cracking pattern of specimens with different aggregate volume fractions
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