Simulations of characteristic mesoscale processes in a solid require a computational domain with a large number of structural elements (grains, inclusions, pores, etc.) and a sufficiently detailed mesh for their approximation. Reasoning that the computer power needed for such simulation increases nonlinearly with the number of structural elements, it is desirable to minimize the computational costs without loss of information and accuracy, for example, by solving quasi-static problems in a dynamic statement. Here we analyze the applicability of dynamic methods to quasi-static micro- and mesomechanical problems with explicit account of microstructure by the example of dynamic and static finite element computations of uniaxial tension for materials insensitive to strain rates. The analysis shows that the main parameter influencing the coincidence of dynamic and static solutions is the time in which the loading rate rises to its amplitude. If this rise time is longer than two travels of an elastic wave through a material, the dynamic and static problem solutions deviate by no more than 0.1% while the random access memory and the computation time needed for the static case is about ten times those for the dynamic one. Thus, explicit dynamic methods can be applied to advantage to quasi-static problems of micro- and mesomechanics.

中文翻译：

---

关于动态公式中准静态微机械和力学问题的解答

固体中特征中尺度过程的模拟需要一个具有大量结构元素（晶粒，内含物，孔等）的计算域，并需要足够详细的网格对其进行逼近。推理这种模拟所需的计算机能力随结构元素的数量非线性增加，因此希望在不损失信息和准确性的情况下，例如通过解决动态语句中的准静态问题，将计算成本降至最低。在这里，我们以对应变速率不敏感的材料的单轴张力的动态和静态有限元计算为例，分析了动态方法对准静态微观和细观力学问题的适用性，并明确说明了微观结构。分析表明，影响动态和静态解同时发生的主要参数是加载速率上升到其振幅的时间。如果此上升时间大于弹性波穿过材料的两次传播时间，则动态和静态问题解决方案的偏差将不超过0.1％，而静态情况下所需的随机存取存储器和计算时间大约是静态情况下的十倍。动态的。因此，显式动力学方法可以应用于微力学和细观力学的准静态问题。1％，而静态情况下的随机存取存储器和计算时间大约是动态情况下的十倍。因此，显式动力学方法可以应用于微力学和细观力学的准静态问题。1％，而静态情况下的随机存取存储器和计算时间大约是动态情况下的十倍。因此，显式动力学方法可以应用于微力学和细观力学的准静态问题。