热磁电弹性体非线性裂纹模型及其求解方法研究

The novel magnetoelectric coupling effects of piezo-magneto-electric materials can offer a physical basis for the design of the smart devices and structures. The physical and mechanical behavior of magnetoelectroelastic should be modelled and studied. The corresponding study can be used as a solid theory for understanding the operating mechanism, the stability and the reliability of the smart devices. The project focuses on the modelling of the crack with a medium interior presented in the practical cases. The nonlinear crack models will be made for thermo-magneto-electro-elastic solids and their solving methods will be studied. The main contents are given as follows. (1) Based on Fourier and Non-Fourier thermal transformation theory, the nonlinear crack models for thermo-magneto-electro-elastic solids are made by considering the effects of medium inside crack. The closed-form solutions of crack tip fields are derived by using the Fourier transform technique. (2) Under the practical cases of the dynamical propagation of crack, the fractal crack models are given. The variations of the fracture criteria such as the stress intensity factors and the energy release rate are studied. The novel fracture criterion may be proposed under the multiple field coupling effects. (3) By considering the effects of the scale, the static and dynamical nonlinear crack problems for finite thermo-magneto-electro-elastic solids are investigated. The novel numerical methods will be given and lay a solid foundation for the development of computational programs. The research results will enrich the theory and methods of the fracture mechanics under multiple field effects. The novel idea and computational methods will be offered for modelling the physical and mechanical problems. Some theoretical basis will be made for understanding the physical and mechanical behavior of materials.

磁电材料新型的磁电耦合效应为智能器件及结构的设计提供了新的物理基础，磁电体物理力学行为的模拟及分析方法研究能为理解器件的运行机制、稳定性和可靠性等构建坚实的理论基石。本项目模拟客观实际的热介质裂纹情形，建立热磁电弹性体非线性裂纹模型并研究其求解方法，主要有：（1）基于Fourier或非Fourier热传导定律，提出考虑裂纹内部介质影响的热磁电弹性体非线性裂纹模型，采用Fourier变换方法研究其解析解。（2）基于裂纹动态扩展的实际情形，建立热磁电弹性体分形裂纹模型，研究应力强度因子和能量释放率等断裂判断的变化规律，探索多场耦合作用下的新型断裂判据。（3）考虑尺度效应，研究有限热磁电弹性体静态和动态非线性裂纹问题，建立新的数值求解算法并为计算程序开发奠定基础。研究成果将丰富多场耦合断裂力学的理论与方法，为模拟客观物理力学问题提供新的思路和计算策略，为理解材料物理力学行为建立一定的理论基础。

材料和结构在外加荷载下可能导致破坏或失效，不同荷载下材料及结构的力学行为研究具有重要理论及实际意义。本项目开展积分方程近似求解驱动的热介质裂纹尖端场近似结构、数值计算方法驱动的断裂判断分析和数据驱动的金属疲劳寿命预测研究，主要创新性研究成果如下：. （1）针对热介质裂纹尖端热弹性场，考虑裂纹面的非规则性和裂纹内部介质的物理特性，建立非线性裂纹模型。以热弹性带型内含圆形裂纹为研究代表性模型，建立了导出的Fredholm积分方程近似求解方法，获得了积分方程的近似解，推导了热介质圆形裂纹前沿的热弹性场的近似解，揭示了其结构特征，填补了热介质裂纹尖端场结构特征刻画的空白。发展的研究方法能推广到热电弹性体和热磁电弹性体中介质裂纹问题的研究。. （2）针对热介质裂纹的起裂行为及断裂判据，把热弹性和热电弹性带型中Griffith裂纹问题作为研究对象，导出了奇异积分方程及其离散格式，建立了非线性代数方程组的求解策略，获得了裂纹尖端场的数值解，分析了应力强度因子、热应力强度因子和能量密度因子等的变化规律，揭示了裂纹内部介质的物理特性等对裂纹扩展的影响。. （3）针对循环荷载下金属疲劳寿命的预测问题，考虑同样条件下金属疲劳寿命实验结果的不确定性，提出了环境数据、几何数据和过程数据的随机分布区间化方法，发展了区间型数据驱动的机器学习模型，为金属疲劳寿命的预测提供了新方法，揭示了材料和结构循环200次特征数据对疲劳寿命预测的关键性作用，为工程应用奠定了理论和技术基础。. 本项目研究成果创新性发展了热电弹性体断裂力学理论，揭示了热介质裂纹尖端场的近似结构，推动了人工智能驱动的材料及结构疲劳寿命预测方法的发展，为量化实际工程中材料及结构破坏的不确定性提供了可行的方法。在国际主流学术期刊发表高水平学术论文，培养优秀的毕业研究生，产生了一定的国际影响力。