弹性各向异性体的接触模型及其在离散元法中的有效实现
Contact model for elastically anisotropic bodies and efficient implementation into the discrete-element method
摘要：
我们介绍了一个接触定律的法向力之间产生的两个接触，弹性各向异性体的任意几何形状。唯一的要求是它们的表面光滑无摩擦。这种各向异性接触定律是从连续弹性问题的精确解的简化中获得的，并且采用了赫兹接触定律的常见形式，唯一的区别是材料特定接触模量的取向依赖性。对于各种材料和表面几何形状，与精确解相比，接触定律非常准确。我们描述了一个计算效率高的实施接触法到离散元方法代码，利用所有可能的方向上的接触模量的预先计算。最后，我们展示了两个应用实例的基础上，实际材料中的颗粒的弹性各向异性诱导宏观行为的显着影响。值得注意的是，第二个例子证明了在一维粒状晶体中仅通过组成球形颗粒的旋转来设计可调谐振动带隙的能力。
英文摘要：
We introduce a contact law for the normal force generated between two contacting, elastically anisotropic bodies of arbitrary geometry. The only requirement is that their surfaces be smooth and frictionless. This anisotropic contact law is obtained from a simplification of the exact solution to the continuum elasticity problem and takes the familiar form of Hertz' contact law, with the only difference being the orientation-dependence of the material-specific contact modulus. The contact law is remarkably accurate when compared with the exact solution, for a wide range of materials and surface geometries. We describe a computationally efficient implementation of the contact law into a discrete element method code, taking advantage of the precomputation of the contact modulus over all possible orientations. Finally, we showcase two application examples based on real materials where elastic anisotropy of the particles induces noticeable effects on macroscopic behavior. Notably, the second example demonstrates the ability to engineer tunable vibrational band gaps in a one-dimensional granular crystal by mere rotation of the constituent spherical particles.
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