传统的晶体材料拓扑有序，空间上具有晶格周期结构。20世纪30年代，学界提出的晶体位错概念沿用至今，由位错主导的晶体塑性变形及断裂已经得到广泛的研究。并且     ，基于晶体缺陷的各种强韧化机制也层出不穷。晶体材料的结构-性能关联已逐渐明了。但是，对于不具备完整周期性的固体材料来说，没有明显的晶格和易于辨识的结构缺陷，这导致从结构角度理解其力学性能十分困难。低对称固体的结构动力学关联，对材料科学领域长期以来“结构决定性质”的研究范式提出挑战。如何合理描述广义上不具备拓扑有序结构的材料特征及建立结构-性能的关联成为固体力学和凝聚态物理悬而未决的问题之一。为此，本文针对拓扑无序非晶合金的原子尺度变形与断裂行为，以及准周期晶体（准晶）材料的结构、热力学、动力学和振动特性，开展了系统且深入的研究，并取得以下研究成果。

首先，针对非晶固体的原子尺度变形与断裂，本文基于大规模分子动力学模拟研究了多种非晶固态物质体系（例如CuZr、ZrCuAl、Si、FeP、Lenanrd-Jones等），具有不同特征尺寸下的塑性变形和断裂行为。研究发现表观断裂应变与非晶材料的直径-长度比（长径比）之间存在线性关系，非晶固体的变形、断裂模式转变等宏观力学行为强烈依赖于材料的临界长径比（～3:1）。同时，该研究建立了剪切局域化与颈缩变形的连续介质力学模型，给出了断裂模式转变的理性判据，定量确定了初始应变尺寸及其对最终断裂应变与断裂模式的影响，宏观力学理论预测结果与微观分子动力学模拟一致。最终，研究提出非晶固体原子理想应变及塑性参与度概念，通过连续介质理论将不同非晶体系断裂应变的尺寸依赖性得到统一，证明了非晶断裂行为及其尺寸效应的普适性。

其次，对于准晶材料的结构动力学行为，本文构建了全新的Lennard-Jones-Gaussian（LJG）势函数，成功制备出热力学稳定的二维十二重准晶模型。基于该模型和分子动力学模拟，本文系统研究了准晶形成体系随冷却的相变过程，观察到液相-六方晶相-准晶相的两次相转变。此外，本文对二维十二重准晶的动力学行为开展了系统研究，发现结构弛豫与扩散均表现出偏离Arrhenius关系的趋势，这源于准晶的动力学行为与温度的强相关性，具体表现为低温下的孤立空位跃迁主导的动力学行为，以及高温下的协同链状扩散运动。研究进一步基于最小能量路径搜索，计算了两类动力学时间的反应路径与激活能，给出了准晶的两相扩散行为的能量依据，并且揭示了空位跃迁行为和链状运动的结构诱导因子均为局部六边形缺陷。另外，本文发现Stokes-Einstein关系在二维十二重准晶中存在“解耦”关系，进一步证实作为“中间态”物质的准晶具有与非晶材料更为类似的动力学行为。

最后，学界对于准晶的振动特征存在长期广泛的争议，即准晶物质是否表现出低频的异常振动模式（相位子）。本文采用原子模拟计算了二维十二重准晶的振动模式及与结构动力学的关联，发现准晶的低频振动态密度遵循经典德拜模型，并没有表现出类似于玻色峰的短时振动特征，表明准晶与非晶材料的振动行为有所差异。并且，振动模式分析澄清了准晶材料领域争议最多的相位子模式，其并不能作为准晶材料的本征特性。此外，我们探索了二维十二重准晶中频段的主要振动模式及其微观结构起源，揭示了准晶振动特性与动力学行为之间的关联，阐明了共同的结构起源--局部缺陷。对色散关系的进一步分析刻画了准晶振动模式的演化过程。与非晶类似，准晶声子寿命并不完全遵循经典的Rayleigh关系，同时发现横波的Ioffe-Regel频率精准预测准晶独特动力学行为的频率，再次证实其振动特性与结构动力学之间的强关联性，研究丰富了对于准晶振动的认知。

Typical crystal materials with periodic structure are topologically ordered along the spatial lattice. The concept of crystal dislocation defined in the 1930s has been used ever since. The plastic deformation and fracture of crystals dominated by dislocations have been extensively studied. And various strengthening and toughening mechanisms based on crystal defects have emerged one after another. The relationship between the structure and property of crystal materials has gradually become clear. However, for materials without complete periodicity, there are no obvious lattice and easily identifiable structural defects, which makes it very difficult to understand their mechanical properties from a structural perspective. The relationship between structure and dynamics in low-symmetry solids poses a challenge to the long-standing research paradigm of "structure determines properties" in the field of materials science. How to reasonably describe the structural characteristics of materials without topological order in a broad sense and establish the relationship between structure and property has become one of the unresolved issues in condensed matter physics. Therefore, this paper has carried out a series of studies on the atomic-level deformation and fracture behavior of topologically disordered amorphous alloys, as well as the structure, thermodynamics, dynamics, and vibration characteristics of quasi-periodic quasicrystalline materials, and achieved following research findings.

Firstly, regarding the atomic-level deformation and fracture of amorphous solids, large-scale molecular dynamics simulations were conducted to investigate the deformation and fracture behaviors of various amorphous materials systems (such as CuZr, ZrCuAl, Si, FeP, Lenanrd-Jones, etc.) under different sizes. It was found that there is a linear correlation between the superficial fracture strain and the diameter-to-length ratio of amorphous materials, and the deformation and fracture mode transitions strongly depend on the critical aspect ratio (~3:1) of amorphous materials. At the same time, the study established a continuous mechanical model of shear localization and necking, providing a rational judgment for the transition of fracture modes, and quantitatively determining the initial strain size and its influence on the final fracture strain and modes. The theoretical prediction results are consistent with the molecular dynamics simulation. Finally, based on the atomic-level ideal strain and plastic participation, the theory unified the size-dependent fracture strain of different amorphous systems, demonstrating the universality of amorphous fracture behavior and its size effect.

Then, for the structural dynamics behavior in quasicrystalline materials, we design a novel Lennard-Jones-Gaussian (LJG) potential. Thermodynamically stable two-dimensional dodecagonal quasicrystalline models were successfully prepared. Based on this model and molecular dynamics simulation, we systematically studied the phase transition process of the quasicrystal-forming system with cooling. Two phase transitions from liquid phase to hexatic and liquid phase to quasicrystal were observed. In addition, a systematic study was conducted on the dynamic behavior of two-dimensional dodecagonal quasicrystal. Both structural relaxation and diffusion exhibited a trend of deviation from the Arrhenius relationship, which stemmed from the strong correlation between the dynamic behavior of quasicrystals and temperature. This manifested as isolated vacancy jumps dominated dynamics at low temperatures and collective string-like motion diffusion at high temperatures. Based on the minimum energy path, the activation energies of the two types of dynamic behaviors were directly calculated, providing an energetic basis for the two-phase diffusion behavior of quasicrystals. It was also revealed that the structural inducing factor of both the vacancy jumps and string-like motions were local hexagonal defects. Furthermore, the decoupling relationship of the Stokes-Einstein relation was found in two-dimensional dodecagonal quasicrystals, further confirming that quasicrystals, as "intermediate" materials, exhibit dynamic behaviors more similar to amorphous materials.

Finally, there has been a long-standing and extensive international debate on the vibration characteristics of quasicrystals, specifically whether they exhibit low-frequency abnormal vibration modes (phasons). In this study, atomic simulation methods were employed to calculate the vibration modes and structural dynamics correlations of 2D dodecagonal quasicrystals. The low-frequency VDOS of quasicrystals follows the classical Debye model and does not exhibit short-time vibration characteristics similar to the Bose peak, indicating that the vibration behavior of quasicrystals differs from that of amorphous materials. Furthermore, analysis on vibrational modes demonstrates that the phason mode, which has been the most controversial in the field of quasicrystals, cannot be considered as an intrinsic property. Additionally, we explored the main vibration modes and their microscopic origins in the mid-frequency range of 2D dodecagonal quasicrystals, revealing the correlation between the vibration characteristics and dynamics of quasicrystals and clarifying their common structural origin—local defects. Furthermore, a thorough analysis of the dispersion relations characterized the evolution of the vibration modes in quasicrystals. Similar to amorphous materials, the phonon lifetime of quasicrystals does not fully follow the classical Rayleigh relationship. Meanwhile, the transverse Ioffe-Regel frequency accurately predicts the frequency of the unique dynamic behavior of quasicrystals, once again confirming the strong correlation between their vibration characteristics and structural dynamics. These studies have greatly enriched our understanding of quasicrystal vibrations.