Numerical methods for solving the problem of polymer crystallizing media deformation taking into account finite deformations
DOI:
https://doi.org/10.7242/1999-6691/2014.7.2.18Keywords:
numerical algorithm, finite element method, polymers, crystallization, finite deformations, nonlinear problem, linearizationAbstract
Methodology and numerical algorithm are developed for solving the boundary problems of elastic polymer crystallizing. A class of problems describing processes in polymer specimens in the course of their manufacturing is studied. Due to the significance of shrinking deformations, the problem is considered in the framework of the finite strain theory. Constitutive relations are derived using the Peng-Landel potential. A weak variational formulation based on Galerkin approach is considered. The proposed algorithm is based on linearization methodology when small deformations are applied to finite ones. The deformation process is represented as a sequence of transitions through intermediate configurations. This approach makes it possible to reduce the solution to a sequence of linearized problems for which effective numerical algorithms have been designed. A numerical technique is based on the finite element method. Displacement increments at the considered time step are taken to be nodal unknowns. The algorithm was applied to solve the problem of deformation of a polyethylene pipe during its manufacturing. The problem was considered in an axisymmetric formulation. The temperature dependence of material characteristics was taken into account. The solution of coupled temperature - conversional problem was obtained with finite difference methods. The linearized geometrical and constitutive relations were defined. Distributions of displacement, radial and circular stresses fields were obtained. The main advantages of the proposed algorithm are formulated.
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