The peridynamic model of viscoelastic creep and recovery

Abstract

Purpose – The purpose of this paper is to establish a peridynamic method in predicting viscoelastic creep behaviour with recovery stage and to find the suitable numerical parameters of peridynamic method. Design/methodology/approach – A rheological viscoelastic creep constitutive equation including recovery and an elastic peridynamic equation (with integral basis) are examined and used. The elasticity equation within the peridynamic equation is replaced by the viscoelastic equation. A new peridynamic method with two time parameters, i.e. numerical time and viscoelastic real time is designed. The two parameters of peridynamic method, horizon radius and number of nodes per unit volume are studied to get their optimal values. In validating this peridynamic method, comparisons are made between numerical and analytical result and between numerical and experimental data. Findings – The new peridynamic method for viscoelastic creep behaviour is approved by the good matching in numerical-analytical data comparison with difference of < 0.1 per cent and in numerical-experimental data comparison with difference of 4-6 per cent. It can be used for further creep test which may include non-linear viscoelastic behaviour and creep rupture. From this paper, the variation of constants in Burger’s viscoelastic model is also studied and groups of constants values that can simulate solid, fluid and solid-fluid viscoelastic behaviours were obtained. In addition, the numerical peridynamic parameters were also manipulated and examined to achieve the optimal values of the parameters. Research limitations/implications – The peridynamic model of viscoelastic creep behaviour preferably should have only one time parameter. This can only be done by solving the unstable fluctuation of dynamic results, which is not discussed in this paper. Another limitation is the tertiary region and creep rupture are not included in this paper. Practical implications – The viscoelastic peridynamic model in this paper can serve as an alternative for conventional numerical simulations in viscoelastic area. This model also is the initial step of developing peridynamic model of viscoelastic creep rupture properties (crack initiation, crack propagation, crack branching, etc.), where this future model has high potential in predicting failure behaviours of any components, tools or structures, and hence increase safety and reduce loss. Originality/value – The application of viscoelastic creep constitutive model on peridynamic formulation, effect of peridynamic parameters manipulation on numerical result, and optimization of constants of viscoelastic model in simulating three types of viscoelastic creep behaviours.

Peridynamic model for nonlinear viscoelastic creep and creep rupture of Polypropylene

“…Matrixes of X , X and X are introduced as matrix of position, velocity and acceleration of all nodes respectively. Matrix X includes acceleration, 22 t  u as in Equation. (27) of all nodes.…”

“…An averaging method from previous study is used to calculate the static value from the dynamic data [22]. The static value of particle position is calculated by adding all position values of all time points in the selected period, ta as shown in Figure 5(a) and the sum is divided with the number of time step in the period.…”

“…The averaging process is repeated in every real time cycle ( 1 2 3 , , , ... , A previous research is referred in determining the values of peridynamic parameters i.e. the number of nodes per volume and the radius of horizon to obtain accurate numerical calculation [22]. The number of nodes per volume parameter can be denoted by node intensity parameter, a which defined as minimum number of particle at sides of a model.…”

“…Peridynamic method application on linear and nonlinear viscoelastic creep behaviours allows improved fracture prediction in viscoelastic creep fracture simulation. Peridynamic method application on linear viscoelastic creep behaviour without fracture has been done in previous research [22]. Beside creep test, an impact test on viscoelastic material by using peridynamic method has been accomplished by other researchers [23].…”

Crack growth modeling and simulation of a peridynamic fatigue model based on numerical and analytical solution approaches

“…Bang and Madenci [31] derived PD hyperelastic strain energy density functions for three types of equibiaxial, planar, and uniaxial loadings. Besides, by using the PD theory, the PD viscoelasticity model [32][33][34][35] and the PD viscoplasticity model [36][37] have been developed.…”