A peridynamic method for creep and stress relaxation incorporating a novel fractional viscoelastic model

Abstract

A fractional viscoelastic kernel function is proposed to describe the modulus evolution during the creep and stress relaxation behavior of quasi-brittle materials. A unified fractional viscoelastic model for creep and stress relaxation is further developed, which has the advantages of few parameters and high accuracy. The model can be degenerated into the basic viscoelastic models under different values of fractional order. The relationship between the force state in non-ordinary state-based peridynamics and the stress tensor in the continuum mechanics constitutive model is established. The developed fractional viscoelastic model is then integrated into the peridynamic framework to create a unified creep and stress relaxation peridynamic method. The calibration method of the model parameters is also determined through the equivalence of the peridynamics and the continuum mechanics, and the influence rules of parameters on the viscoelastic behavior of materials are discussed. The effectiveness of the proposed peridynamic method is verified by numerical simulations of a plate, bar, slate, and beam. The proposed method can accurately describe the deformation process from continuous to discontinuous in creep and stress relaxation. This study provides a valuable numerical tool for simulating structural damage caused by creep and stress relaxation in engineering structures during long-term operation.