Numerical study of a thermomechanical behavior of a crystallizing polymer medium with regard to finite deformations

The paper presents phenomenological constitutive relations for a crystallizing polymer medium, obtained in the framework of nonlinear solid mechanics. The relationships are based on the representation of the medium in the form of a composition of a molten and fully crystallized material, taking into account the history of a continuous nucleation and deformation of a new phase in the temperature range of phase transformations. A general formulation is carried out regarding the evolutionary boundary-value problem of the nonlinear mechanics of polymer materials under phase transitions with the use of the proposed constitutive relations. Algorithms are considered that are aimed at a numerical realization of the thermokinetic problem and determining the stress-strain state of the solidifying system for the case of a plane deformed state. A linearization procedure is developed - which is convenient for constructing numerical algorithms to solve the set evolutionary boundary value problems - using the assumption of the proximity of each intermediate configuration to the current one, which corresponds to the procedure for superimposing small deformations of crystallized particles on finite deformations of a crystallizing medium. The linearization procedure for the initial formulation of mechanics problem is realized taking into account temperature and structural deformations. A numerical algorithm aimed at solving a flat boundary value problem is developed and implemented with the aim of investigating the evolution of the stress-strain state in a polymer structure. A method is proposed and implemented to construct a discrete analogue of boundary value problems, based on the use of the Galerkin method with a selection basis functions with a compact support by the finite element method. In this case, the increments of the displacement functions at the current time step are taken as nodal unknowns. The regularities of a shell type defect’s formation in the crystallizing polymer cylinder are established.