基于混凝土黏弹性变形机制的近场动力学方法

Peridynamics Method Based on Viscoelastic Deformation Mechanism of Concrete

摘要:

原始近场动力学的控制方程由保守力做功的能量方程得到，从而无法合理反映材料的黏弹性变形行为和系统能量耗散。针对这一问题，提出一种考虑非保守力做功的近场动力学方法，其理论框架包括两部分：①材料点的黏弹性相互作用及其运动方程；②键的率相关断裂准则。在描述材料点运动方面，基于对混凝土变形机制的认识，提出了材料点之间的黏弹性相互作用模型，采用考虑能量耗散的哈密尔顿原理建立了黏弹性运动方程，利用黏弹性近场动力学方法与连续介质力学的能量密度等效的方法提出了弹性参数和黏性参数确定方法；在描述键的断裂和材料强度方面，利用混凝土动态单轴S强度准则发展了键的率相关断裂准则。通过数值实验，探讨了黏弹性近场动力学方法的功能和优越性。结果表明，发展的近场动力方法能够合理反映加载速率对混凝土变形、强度和开裂行为的影响。

Abstract:

The governing equation of the original peridynamics is derived from the energy equation of work done by conservative forces， which cannot reasonably reflect the viscoelastic deformation behavior of materials and the energy dissipation of the system. To solve this problem， a peridynamics method considering the work done by non-conservative forces is proposed. The theoretical framework includes two parts： viscoelastic interaction of material points and its motion equation， and rate dependent fracture criterion of bond. In describing the movement of material points， based on the understanding of the deformation mechanism of concrete， the viscoelastic interaction model between material points is proposed. The viscoelastic motion equation is established by using the Hamilton’s principle considering energy dissipation. Using the viscoelastic peridynamics method and the energy density equivalent method of continuum mechanics， the determination methods of elastic parameters and viscous parameters are proposed. In terms of describing bond fracture and material strength， the rate dependent fracture criterion of bond is developed by using the dynamic uniaxial S criterion of concrete. Numerical experiments are conducted to investigate the functions and advantages of the viscoelastic peridynamics method proposed. The results show that the peridynamics method proposed can reasonably reflect the influence of loading rate on the deformation， strength， and cracking behavior of concrete.