Abstract The contact volume based energy-conserving contact model is presented in the current paper as a specialised version of the general energy-conserving contact model established in the first paper of this series (Feng, 2020). It is based on the assumption that the contact energy potential is taken to be a function of the contact volume between two contacting bodies with arbitrary (convex and concave) shapes in both 2D and 3D cases. By choosing such a contact energy function, the full normal contact features can be determined without the need to introduce any additional assumptions/parameters. By further exploiting the geometric properties of the contact surfaces concerned, more effective integration schemes are developed to reduce the evaluation costs involved. When a linear contact energy function of the contact volume is adopted, a linear contact model is derived in which only the intersection between two contact shapes is needed, thereby substantially improving both efficiency and applicability of the proposed contact model. A comparison of this linear energy-conserving contact model with some existing models for discs and spheres further reveals the nature of the proposed model, and provides insights into how to appropriately choose the stiffness parameter included in the energy function. For general non-spherical shapes, mesh representations are required. The corresponding computational aspects are described when shapes are discretised into volumetric meshes, while new developments are presented and recommended for shapes that are represented by surface triangular meshes. Owing to its additive property of the contact geometric features involved, the proposed contact model can be conducted locally in parallel using GPU or GPGPU computing without occurring much communication overhead for shapes represented as either a volumetric or surface triangular mesh. A set of examples considering the elastic impact of two shapes are presented to verify the energy-conserving property of the proposed model for a wide range of concave shapes and contact scenarios, followed by examples involving large numbers of arbitrarily shaped particles to demonstrate the robustness and applicability for more complex and realistic problems.

中文翻译：

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任意形状粒子离散元建模的能量守恒接触理论：基于接触体积的模型和计算问题

摘要 当前论文中提出了基于接触体积的节能接触模型，作为本系列第一篇论文 (Feng, 2020) 中建立的通用节能接触模型的专门版本。它基于以下假设：在 2D 和 3D 情况下，接触能势被视为具有任意（凸面和凹面）形状的两个接触体之间的接触体积的函数。通过选择这样的接触能量函数，可以确定完整的法向接触特征，而无需引入任何额外的假设/参数。通过进一步利用相关接触面的几何特性，开发出更有效的集成方案以降低所涉及的评估成本。当采用接触体积的线性接触能量函数时，推导出线性接触模型，其中只需要两个接触形状之间的交集，从而大大提高了所提出的接触模型的效率和适用性。这种线性节能接触模型与用于盘和球体的一些现有模型的这种线性节能接触模型进一步揭示了所提出的模型的性质，并为如何适当地选择能量函数中包括的刚度参数提供有识。对于一般的非球形形状，需要网格表示。当形状被离散化为体积网格时，描述了相应的计算方面，同时为由表面三角形网格表示的形状提出并推荐了新的发展。由于其所涉及的接触几何特征的可加性，所提出的接触模型可以使用 GPU 或 GPGPU 计算在本地并行进行，而不会对表示为体积或表面三角形网格的形状产生大量通信开销。提出了一组考虑两种形状的弹性影响的例子，以验证所提出的模型在各种凹面形状和接触情况下的能量守恒特性，然后是涉及大量任意形状粒子的例子，以证明其鲁棒性和适用于更复杂和更现实的问题。