An adaptive coupling of PD-CCM model involving a viscoelastic constitutive relation for quasi-brittle material dynamic failure

Abstract

A new viscoelastic bond-based peridynamic model (VBPD) is developed to describe the nonlinear deformation and dynamic failure of quasi-brittle materials under different loading rates. This model is established on the viscoelastic constitutive equation of classical continuum mechanics, which involves damage and strain rate effects. The model superbly generalizes the definition of strain rate in classical continuum mechanics phenomenally to the bond stretch rate in the bond-based peridynamics under one-dimensional strong impact loads. To describe the progressive damage of the peridynamic bond, The scalar value function related to bond stretch and bond stretch rate is introduced in the model to define the deformation of the peridynamic bond. Moreover, the model also considers the history of bond force under cyclic load. To improve the computational efficiency of simulation, the adaptive coupling of peridynamics and the classical continuum mechanics (PD-CCM) model established by the Morphing method is used to simulate the failure process of quasi-brittle materials. By combining the VBPD model and the PD-CCM model, the VBPD model is utilized to simulate the deformation and failure process of quasi-brittle materials under dynamic load with the least peridynamic subdomain. Finally, the validity of the proposed model is verified by three two-dimensional numerical examples.