脆性材料统一断裂相场方法及其裂缝宽度的确定

UNIFIED FRACTURE PHASE-FIELD METHOD AND DETERMINATION OF CRACK WIDTH FOR BRITTLE MATERIALS

岩石、混凝土等脆性材料的开裂问题一直是国内外关注的热点和难点,裂缝的演化使得脆性材料的力学性能难以预测。针对脆性材料的拉、剪和拉剪复合开裂问题,将统一拉伸断裂准则引入到相场理论,进而基于谱分解技术提出了统一断裂相场方法,并通过交错算法在商业有限元软件中实现了该方法。拉伸断裂试验和拉剪复合断裂试验数值模拟结果表明:统一断裂相场方法具有热力学一致性,该方法不仅能准确模拟裂缝演化过程中脆性材料的力学性能,还能精准预测拉剪复合裂缝的扩展路径。此外,运用水平集理论构建了一个相场函数,识别了相场裂缝的分界面,进而通过理论推导得出了相场裂缝宽度的计算公式,并对其进行了验证。该研究旨在提出精准预测脆性材料拉、剪和拉剪复合开裂的相场方法,以保障土木工程结构的安全。

The cracking of brittle materials such as rock and concrete has always been a hot and difficult issue at home and abroad,and the evolution of cracks makes it difficult to predict the mechanical behavior of brittle materials.As for the tensile,shear and tensile-shear mixed-mode cracking problem of brittle materials,a unified fracture phase-field method was presented based on spectral decomposition with the unified tensile fracture criterion in hand,and implemented in commercial finite element software by the staggered algorithm.The numerical simulation results of tensile fracture test and tensile-shear mixed-mode fracture test show that the unified fracture phase-field method is thermodynamic consistency,and can not only accurately simulate the mechanical behavior of brittle materials during crack evolution,but also accurately predict the propagation path of tensile-shear mixed-mode crack.In addition,a phase-field function was constructed by using the level-set theory to identify the interface of the phase-field crack,and the calculation formula of the phase-field crack width was deduced theoretically and then verified.This study aims to develop a phase-field method to accurately predict the tensile,shear and tensile-shear mixed-mode cracking of materials,so as to ensure the safety of civil engineering structures.