颗粒材料在生活中处处可见，并且广泛应用于人类的生产和生活当中。由于独特的力学现象和丰富的力学行为，颗粒材料很早就引起了科学界的广泛关注和大量研究，但针对颗粒材料在颗粒尺度的研究在近几十年才逐渐兴起。颗粒系统的离散物理模型通常将颗粒视为相互接触的圆球、圆柱或椭球等理想形状，大量的理论、实验和数值计算研究通过理想颗粒系统探究了其物理性质背后的力学机制。然而由于实验与数值计算方面的成本较大，颗粒材料的研究尚不完善，尤其是在颗粒尺度的理论尚不清晰。

颗粒材料在冲击能量的吸收和耗散方面有着优秀的性能，但其具体的物理过程和力学机制尚不明确。许多研究专注于冲击物体本身动能的衰减情况，并建立了许多阻力与侵入深度关系的物理模型，然而鲜有研究关注能量由冲击物体传输到颗粒材料中之后如何被吸收与耗散的问题。与传统材料的区别在于，颗粒材料的能量吸收与耗散性能不依赖于颗粒的粘性或塑性变形。因此有必要建立一个基于颗粒间接触与摩擦的物理模型来研究颗粒材料的能量耗散机制。

许多研究表明力链是颗粒材料承担载荷和传递内力的重要形式。为研究被约束在颗粒系统中的力链对颗粒材料内部能量传播与耗散的影响，本文建立了一个两侧受到约束的有限长理想一维颗粒系统模型，探究了摩擦对颗粒材料耗能机制和力传播机制的影响。受到冲击的一维颗粒链中会产生一道主孤立波，主孤立波在远小于颗粒间最大接触力的摩擦力作用下仍然会产生显著的衰减，且外部环境施加的摩擦力越大该衰减行为越剧烈。本文采用离散元方法来研究该动力学过程中能量的耗散机理，模型中的颗粒之间、颗粒和约束之间的法向接触力采用非线性Hertz接触模型，切向接触力采用Mindlin剪切模型，通过分析主孤立波的幅值和波速以及颗粒间接触力的衰减规律来探究颗粒材料能量耗散机制。结果表明，当摩擦力显著小于颗粒间最大接触力时，系统中的动态能量会在有限深度内耗散，此耗散深度依赖于摩擦力的大小，与两侧约束施加在颗粒链上的库伦摩擦力呈现近似反比的关系。本文分析了能量在一维系统中的耗散规律，认为耗散过程可分为非线性接触主导过程、中间过程、摩擦和接触混合主导过程三个阶段。本文分别分析了每阶段相应的力学机制：在孤立波传播初期，摩擦力以滑动摩擦为主，可将其视为恒定且微小的力从而忽略其在动力学响应中的作用，系统中的力传播规律近似与无摩擦系统；随着孤立波衰减至临界值以下，摩擦力将转化为静摩擦力，且摩擦力对动力学响应的作用无法被忽略。我们发现，当考虑颗粒受到的法向接触力与切向静摩擦力耦合作用时，其力传递机制将会遵循一个新的，表达形式简易的规律，这将对深入理解颗粒系统的力学机制产生帮助。本研究能够为颗粒材料能量耗散物理机制的研究提供新的视野。

Granular materials are encountered in numerous industries and exhibit a wide range of unique behavior. There are few research on granular materials at the particle scale until last decades as it is usually randomly organized and complex. Although it has been studied and used for hundreds of years. The nonlinear contact and friction forces between particles is the key problem which results in diverse physical properties and acoustic responses. Some discrete methods in granular material research usually considers particles as ideal spheres, cylinders, or ellipsoids in contact with each other. Numerous theoretical, experimental, and numerical studies have explored the mechanical mechanisms at the particle scale. However, there are still many difficulties in experiments research and numerical calculations. Theoretical understandings of granular materials is still incomplete, especially the mechanical understanding at the particle scale.

Granular materials have excellent performance in absorbing and dissipating impact energy, but their specific physical processes and mechanical mechanisms are not yet clear. Many studies have focused on the attenuation of the kinetic energy of the impact striker or intruder, and have established many physical models between the resistance force and intrusion depth. However, few studies have focused on how energy is absorbed and dissipated after being transferred from the impact intruder into the granular material. Some studies have established continuum models for energy dissipation of granular materials, or focused on energy dissipation caused by breakage and viscosity of particles. But the difference between granular materials and traditional materials is that  they have excellent energy absorption and dissipation performance, which does not rely on the viscosity, failure or plastic deformation of particles, but is caused by friction between particles. Therefore, it is necessary to establish a physical model based on inter particle contact and friction forces to investigate the energy dissipation mechanism of granular materials.

Many studies indicate that force chains play an important role in granular materials, which transmits internal contact forces and monumen.Herein, a one-

dimensional particle system with finite length, which is constrained on both sides, is presented, and the influence of friction on energy reduction in granular materials is explored. A primary solitary wave can be produced when a striker collides with the second particle and dissipates remarkably in a chain, even though tangential frictional forces between particles and rigid boundary are very small. Normal contact forces acting between particles follow the nonlinear Hertz contact law, while the tangential shear forces acting between particles and plates follow the Mindlin shear force law. To simulate the wave propagation through a one-dimensional particle chain , a center difference method is applied, and the discrete element method kinetic equation is directly solved. Energy dissipation in granular materials can be deduced by comparing the amplitude and velocity of the main solitary wave and the maximum contact force between particles. The results show that the primary solitary wave will dissipate rapidly and eventually disappear within a finite distance in the one-dimensional chain, even though the frictional forces are much smaller than the average normal contact forces between particles. This finite distance depends on the frictional forces. As the wave propagates, three stages, including nonlinear collision collision stage, transition stage and friction-collision mixed stage, can be distinguished using the relation between wave speed and maximum contact force corresponding to different mechanisms.