Multi-Scale Numerical Approach to the Polymer Filling Process in the Weld Line Region

Abstract

In this paper, a multi-scale coupling mathematical model is suggested for simulating the polymer filling process in the weld line region on a micro scale. The model considers two aspects: one is the coupling model based on stresses in the whole cavity region; the other is the multi-scale coupling model of continuum mechanics (CM) and the molecular dynamics (MD) in a weldline region. A weak variational formulation is constructed for the finite element method (FEM), which is coupled with the Verlet algorithm based on the domain decomposition technique. Meanwhile, an overlap region is designed so that the FEM and the MD simulations are consistent with each other. The molecular backbone orientation of the whole cavity is illustrated and the position of the weld line is determined by the characteristics of the molecular backbone orientation. Finally, the properties of the polymer chain in the weld line region are studied conformationally and dynamically. The conformational changes and movement process elucidate that the polymer chains undertake stretching, entangling and orientating. Moreover, the effect of the number of chains and melt temperature on the spatial properties of chain conformation are investigated.

Weld‐lines and its strength evaluation in injection molded parts: A review

“…d ij is zero energy distance and ϵ ij is minimal interaction energy, r is length and K r is stiffness, θ is bond angle and K θ represents angle stiffness; V i n (n = 1, 2, 3) are fitting parameters, and ;i is the improper dihedral angle. 33 The healing of weld-line is studied in refs. 34-36 where weld-line factor (F WL ) is used to define strength of the weld-line and it is defined as the ratio of strength weld-line material σ b to the strength of without weld-line material σ u as mentioned in Equation (8).…”

“…The theoretical approach to the polymer filling process at weld‐line area is defined by Wang and Saeed 33 . This method is based on a multiscale numerical approach for molecular filling based on atoms mass, the distance between atoms, intermolecular force, and energy at the weld‐line area as below in Equations (1) and (2).…”

Numerical analysis of the SIS infectious disease model with spatial heterogeneity

“…This part primarily examines the impact of host migration and spatial variation on disease dynamics. Mathematical software is used for numerical simulation based on the references (Zhenxiang and Linfei, 2022; Erdogan et al , 2019; Mesgarani et al , 2022; Li et al , 2022; Marom et al , 2023b).…”

An application to formable transform: Novel numerical approach to study the nonlinear oscillator

“…He et al 16 utilized the formulation of frequency amplitude which is Hamiltonian-based to the complex mechanical phenomenon for the quick determination of frequency of nonlinear oscillators. Li et al 17 considered the model of a weld line in polymer processing and the multi-scale numerical approach implemented to tackle the problem numerically. He 18 expounded the nano-electro-mechanical model comprised of the fractal space and its behavior by using the variational principle.…”