The peridynamic model of a solid is suitable for studying the dynamics of defects in materials. We use the bond-based peridynamic theory to propose a one-dimensional nonlocal continuum model to study a defect in equilibrium and in steady propagation. As the defect propagates, the material particles undergo a transition between two states. By using the Wiener–Hopf method, an explicit analytical solution of the problem is obtained. The relation between the applied force and the propagation speed of the defect is determined; our results show that the defect does not propagate if the applied force is less than a critical value, whereas propagation occurs when the force exceeds that value. The energy properties of the system are investigated.

固体的近场动力学模型适用于研究材料缺陷的动力学。我们使用基于键的近场动力学理论提出一维非局部连续介质模型来研究平衡和稳定传播中的缺陷。随着缺陷的传播，材料粒子会在两种状态之间发生转变。通过使用 Wiener-Hopf 方法，可以获得问题的显式解析解。确定所施加的力与缺陷的传播速度之间的关系；我们的结果表明，如果施加的力小于临界值，则缺陷不会传播，而当力超过该值时，就会发生传播。研究了系统的能量特性。