Shear localization is a frequent feature of granular materials. While the discrete element method can properly simulate such a phenomenon as long as the grain representation is accurate, it is computationally intractable when there are a large number of grains. The continuum-based finite element method is computationally tractable, yet struggles to capture many grain-scale effects, e.g., shear band thickness, because of mesh dependence, unless the constitutive model has a length scale. We propose a hybrid discrete-continuum technique that combines the speed of the continuum method with the grain-scale accuracy of the discrete method. In the case of shear localization problems, we start the simulation using the continuum-based material point method. As the simulation evolves, we monitor an adaptation oracle to identify the onset of shear bands and faithfully enrich the macroscopic continuum shear bands into the microscopic-scale grains using the discrete element method. Our algorithm then simulates the shear band region with the discrete method while continuing to simulate the rest of the domain with the continuum method so that the computational cost remains significantly cheaper than a purely discrete solution. We validate our technique in planar shear, triaxial compression, and plate indentation tests for both dry and cohesive granular media. Our method is as accurate as a purely discrete simulation but over 100 times faster than a discrete simulation that would require tens of millions of grains.

剪切局部化是粒状材料的常见特征。尽管只要晶粒表示准确，离散元方法就可以正确地模拟这种现象，但是当存在大量晶粒时，它在计算上是棘手的。基于连续体的有限元方法在计算上是易于处理的，但是由于网格依赖性，除非本构模型具有长度尺度，否则它很难捕获许多晶粒尺度的影响，例如剪切带厚度。我们提出了一种混合离散连续谱技术，该技术结合了连续谱方法的速度和离散方法的粒度精度。在剪切局部化问题的情况下，我们使用基于连续体的材料点方法开始模拟。随着模拟的发展，我们监测一个适应性预言机，以识别剪切带的出现，并使用离散元方法将宏观连续体剪切带忠实地丰富到微观尺度的晶粒中。然后，我们的算法使用离散方法模拟剪切带区域，同时继续使用连续介质方法模拟其余区域，从而使计算成本比纯离散解决方案便宜得多。我们在平面剪切，三轴压缩和平板压痕测试中验证了我们的技术，适用于干性和粘性粒状介质。我们的方法与纯离散模拟一样精确，但比需要数千万个晶粒的离散模拟快100倍以上。