For research on granular materials, establishing a method to calculate continuum strain from particle displacements is necessary for understanding the material behaviour at macro‐level and developing continuum constitutive models. Existing methods are generally based on constructing a mesh or background grid to calculate strain from particle motions. These methods offer rigorous ways to measure strain for granular materials; however, they suffer from several problems such as mesh distortion and lacking grid‐to‐particle strain mapping procedure, which hinders their capability of calculating strain accumulation during large deformation processes of granular media. To address this issue, this study proposes a new strain calculation method for discrete element simulations of granular materials. This method describes a particle assembly as an equivalent continuum system of material points, each of which corresponds to a particle centre and represents a continuous region with its initial volume/area presumably equal to the volume/area of Voronoi cells generated in accordance with the particle assembly configuration. Smooth Particle Hydrodynamics (SPH) interpolation functions are then employed to calculate strain for these material points. This SPH‐based method does not require any mesh or background grid for computation, leading to advantages in calculating strain accumulation under large deformation. Simulations of granular materials in both uniform and heterogeneous gradations were carried out, and strain results obtained by the proposed method indicate good agreements with analytical and numerical solutions. This demonstrates its potential for strain calculations in discrete element simulations of granular materials involving large deformations and/or large displacements.

中文翻译：

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颗粒介质离散元模拟的大应变累积计算方法

对于颗粒材料的研究，建立一种从颗粒位移计算连续应变的方法对于理解宏观层面的材料行为并建立连续本构模型是必要的。现有方法通常基于构造网格或背景网格以根据粒子运动来计算应变。这些方法提供了测量颗粒材料应变的严格方法。但是，它们遭受了诸如网格变形和缺乏网格到粒子应变映射程序等问题的困扰，这阻碍了它们在颗粒介质大变形过程中计算应变累积的能力。为了解决这个问题，本研究提出了一种新的应变计算方法，用于颗粒材料的离散元模拟。此方法将粒子集合描述为等效的物质点连续系统，每个物质点对应于一个粒子中心，并表示一个连续区域，其初始体积/面积大概等于根据该粒子生成的Voronoi细胞的体积/面积。装配体配置。然后，使用平滑粒子流体动力学（SPH）插值函数来计算这些材料点的应变。这种基于SPH的方法不需要任何网格或背景网格即可进行计算，从而在计算大变形下的应变累积时具有优势。对粒状材料进行了均匀和非均质渐变的模拟，通过该方法获得的应变结果表明与解析解和数值解具有良好的一致性。