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首页> 外文期刊>Journal of thermal stresses >IMPORTANCE OF INERTIA TERM IN DYNAMIC CRACK PROBLEMS CONSIDERING LORD-SHULMAN THEORY OF THERMOELASTICITY
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IMPORTANCE OF INERTIA TERM IN DYNAMIC CRACK PROBLEMS CONSIDERING LORD-SHULMAN THEORY OF THERMOELASTICITY

机译：惯性术语在考虑热弹性劳德-舒尔曼理论的动态裂纹问题中的重要性

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摘要

A numerical technique is presented for the accurate calculation of stress intensity factors as a function of time for generalized coupled thermoelastic problems. In this task, the effect of the inertia term is investigated, considering different theories of thermoelasticity, and its importance is shown. A boundary element method using the Laplace transform in time domain is developed for the analysis of fracture mechanics; dynamic coupled thermoelasticity problems with relaxation time are considered in the two-dimensional finite domain. The Laplace transform method is applied to the time domain and the resulting equations in the transformed field are discretized using the boundary element method. Actual physical quantities in the time domain are obtained using the numerical inversion of the Laplace transform method. The singular behavior of the temperature and displacement fields in the vicinity of the crack tip is modeled by quarter-point elements. The thermal dynamic stress intensity factor for mode I is evaluated using the J-integral method. The accuracy of the method is investigated through comparison of the results with the data available in literature. The J integral, which represents the dynamic energy release rate for propagating cracks, contains a boundary integral and a domain integral. The boundary integral contains strain energy, tractions, and strains whereas the domain integral contains inertia and strains. The J-integral method allows these two terms to be calculated separately. In this way, the importance of each term may be investigated by considering different theories of dynamic thermoelasticity.
机译：提出了一种数值技术，用于精确计算广义耦合热弹性问题随时间变化的应力强度因子。在此任务中，考虑了不同的热弹性理论，研究了惯性项的影响，并显示了其重要性。提出了使用时域拉普拉斯变换进行边界元分析的方法。在二维有限域中考虑了具有松弛时间的动力耦合热弹性问题。将Laplace变换方法应用于时域，并使用边界元方法离散化变换后的字段中的方程。使用Laplace变换方法的数值反演可获得时域中的实际物理量。裂纹尖端附近温度场和位移场的奇异行为由四分之一点元素建模。使用J积分方法评估模式I的热动应力强度因子。通过将结果与文献中可用的数据进行比较，研究了该方法的准确性。代表裂纹扩展的动态能量释放速率的J积分包含边界积分和域积分。边界积分包含应变能，牵引力和应变，而区域积分包含惯性和应变。 J积分方法允许分别计算这两个项。这样，可以通过考虑动态热弹性的不同理论来研究每个术语的重要性。

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