非晶态固体不存在位错运动等传统晶体塑性机制，而是以原子团簇在介尺度的“剪切转变”诱导塑性变形。由于时空尺度限制，研究剪切转变在动态载荷作用下的动力学过程十分困难，而联系微观动力学和宏观力学响应的介尺度模拟显示出独特的优势。然而，传统的介尺度模型假设剪切转变事件是瞬时完成的平衡过程，不符合动态加载情形。为了克服这一挑战，本文建立了一个非晶态固体变形的动态介尺度模型。该模型被用于求解两类问题：（1）不同应变率下的平面应变压缩问题，目的是考察惯性效应对变形的影响；（2）不同冲击速度和样品尺寸的一维应变冲击问题，目的是考察非晶态固体冲击波响应的机制。本论文的主要研究内容如下：

（1）建立了非晶态固体变形的介尺度模型。在本构模型中，引入了自由体积作为状态变量，用以描述变形过程中微观结构的演化。非晶态固体被离散为许多介尺度区域，每个区域的尺寸与塑性事件的典型尺寸相当。通过引入剪切转变激活时间作为时间步长，该模型可以实现这些介尺度区域根据各自概率发生剪切转变激活、扩散重排和弹性变形三种动力学过程，并可以捕捉单个剪切转变诱导的应力波及其与加载应力的相互作用。

（2）求解了不同应变率下的平面应变压缩问题。通过定义两个无量纲数：应变步和内禀德博拉数，给出了描述惯性对非晶态固体变形影响的相图。两者较小时，响应处在惯性效应对变形影响可以忽略的第一相。随着它们的增大，显著的惯性效应促进了剪切转变的激活和相互作用，导致塑性屈服较早，稳态流动应力较低，响应进入第二相。随着它们的进一步增大，响应进入第三相，冲击波可以直接驱动远低于全局屈服的剪切转换的激活。这些行为与不考虑剪切转变的惯性效应的准静态处理中的行为完全不同，从而加深了对非晶态固体动态变形的理解。

（3）系统模拟了在一维应变冲击下的弹塑性响应。结果表明，随着冲击速度的提高，自由面速度曲线逐渐偏离纯弹性而呈现弹塑性双波结构，并且塑性波上升沿斜率逐渐增加。分析表明，高速冲击下剪切转变及其应力波与加载波存在时空重叠，从而导致加载波传播发生显著衰减。随着冲击波传播距离变长，弹性极限和塑性应变率均呈指数衰减。本文还研究了塑性冲击前沿的幂律关系，发现该幂律指数与剪切转变激活的非线性增殖密切相关。

Amorphous solids, devoid of traditional crystalline plastic mechanisms such as dislocation movements, rely on the "shear transformation (ST)" of atomic clusters at the mesoscale to induce plastic deformation. Due to the limitations of spatiotemporal scales, investigating the dynamic process of ST under dynamic loading is exceedingly challenging. Meanwhile, mesoscale simulations that bridge the gap between microscopic dynamics and macroscopic mechanical responses exhibit unique advantages. However, conventional mesoscale models postulate that STs occur instantaneously as equilibrium processes, which is incompatible with dynamic loading scenarios. To overcome this challenge, this paper establishes a dynamic mesoscale model for the deformation of amorphous solids. This model is applied to solve two types of problems: (1) plane strain compression problems under various strain rates, aimed at investigating the inertia effect on deformation; (2) shock loading problems with different impact velocities and sample sizes, aimed at exploring the mechanisms of shock wave response in amorphous solids. The primary research contents of this thesis are outlined as follows:

(1) We develop a mesoscale model that describes the deformation behavior of amorphous solids. Free volume as a state variable is introduced in the constitutive model to characterize microstructural evolution during deformation. The solid is split into mesoscale blocks, featuring the typical size for plastic events. By introducing the ST activation time as the time step, these mesoscale regions can undergo three processes: ST activation, diffusive rearrangement, and elastic deformation, according to their respective probabilities. Additionally, the model captures the stress waves induced by individual STs and their interactions with applied stresses.

(2) We have solved the plane strain compression problems under different strain rates. By defining two dimensionless numbers: the strain step and the intrinsic Deborah number, a phase diagram is presented to characterize the influence of inertia on the deformation of amorphous solids. When both numbers are relatively small, the response falls into the first phase where the inertial effects have negligible impacts on deformation. As they increase, pronounced inertial effects facilitate the activation and interaction of STs, leading to an earlier plastic yield, a lower steady-state flow stress, which means that the response enters the second phase. With further increments in these numbers, the response enters the third phase, where shock waves can directly drive the activation of STs well below the global yield. These behaviors are fundamentally distinct from those observed in quasi-static treatments that neglect the inertial effects on STs, thereby enhancing the understanding of dynamic deformation in amorphous solids.