Purpose

The purpose of this paper is to propose a novel quasi-nonlocal coupling of the bond-based peridynamic model with the classical continuum mechanics model to fully take advantage of their merits and be free of ghost forces.

Design/methodology/approach

This study reconstructs a total energy functional by introducing a coupling parameter that alters only the nonlocal interactions in the coupling region rather than the whole region and a modified elasticity tensor that affects the local interactions. Then, the consistency of force patch test is enforced in the coupling region to completely eliminate the ghost force in a general energy-based coupling scheme. For a one-dimensional problem, these coupling parameters are further determined through an energy patch test to preserve the energy equivalence or through an l¹-regularization. And, for a two- or three-dimensional problem, depending on the existence of a solution to the discretized force patch test, they are determined through an l¹-minimization or l¹-regularization.

Findings

One- and two-dimensional numerical examples under affine deformation have been conducted to verify the accuracy of the quasi-nonlocal coupling method, which exhibits no ghost force. Moreover, the coupling model can reproduce almost the same deformation behaviors of points near the crack for a cracked plate under tension as that from a pure peridynamic model, the former with a rather low computational cost and an easier application of boundary conditions.

Originality/value

This work is aiming at getting over long-standing ghost force issues in the energy-based coupling scheme. The numerical results from the cracked plate problem are exhibited promising extension to dynamic problems.

中文翻译：

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基于键的近场动力学与经典连续介质力学的准非局域耦合方法

目的

本文的目的是提出一种新的基于键的近场动力学模型与经典连续介质力学模型的准非局部耦合，以充分利用它们的优点并消除鬼力。

设计/方法/方法

本研究通过引入一个仅改变耦合区域而非整个区域中的非局部相互作用的耦合参数和一个影响局部相互作用的修正弹性张量来重建总能量泛函。然后，在耦合区域强制执行力补丁一致性测试，以完全消除一般基于能量的耦合方案中的鬼力。对于一维问题，这些耦合参数通过能量补丁测试进一步确定，以保持能量等效性或通过 l ¹正则化。并且，对于二维或三维问题，取决于离散力补丁测试的解的存在，它们通过 l ¹ -最小化或 l ^1确定-正则化。

发现

已经进行了仿射变形下的一维和二维数值示例，以验证准非局部耦合方法的准确性，该方法不表现出鬼力。此外，该耦合模型可以再现几乎与纯近场动力学模型相同的受拉裂纹板裂纹附近点的变形行为，计算成本较低，边界条件应用更容易。

原创性/价值

这项工作旨在克服基于能量的耦合方案中长期存在的鬼力问题。裂纹板问题的数值结果展示了对动态问题的有希望的扩展。