Multiscale Modeling of Strain-Induced Crystallization in Polymers

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The present project treats a polymer affected by the strain induced crystallization (SIC) as a heterogeneous medium consisting of regions with the different degree of network regularity. Such a concept allows depicting the nucleation and the growth of crystalline regions as well as the change of effective material parameters depending on the level of the strain applied. The model proposed is thermodynamically consistent. It is based on the assumptions for the free Helmholtz energy and dissipation. Both of them primarily include bulk- and surface terms due to the deformation and crystallization. The external variables are deformations and temperature, whereas the inelastic deformations and degree of the network regularity are internal variables. Their evolution equations are derived according to the principle of maximum of dissipation. The influences of latent heat and of temperature change are implemented in order to simulate thermal effects. The explained framework is advantageous for several reasons. First, it is suitable to answer the crucial question of which process predominantly influences SIC: the nucleation of new crystalline regions or the growth of already existing ones. Secondly, the proposed model is ideal for a direct implementation within the standard multiscale finite element concept. This numerical homogenization procedure is compatible with the theory of finite strains and is applicable for modeling the cases where the ratio of characteristic lengths of scales tends to zero. Both of these features are necessary for the effective modeling of SIC. The project also includes a study of stochastic aspects of the process, where a distribution function for the observable variables is introduced to express the expectation value of relevant quantities. The necessary evolution equation is derived by considering the effective energy of a control volume. The main goals here are to study nucleation and to evaluate the average size of the regions with different regularities of the network. The solution of the tasks itemized will make it possible to achieve the final project goal: the advanced simulations of SIC which can significantly contribute to the more efficient designing and usage of polymers. This is especially motivated by the fact that SIC has to be understood as a kind of reinforcement already successfully applied for some rubber materials. The proposed concepts are of general nature and can be taken as a basis for the modeling of similar processes involving the evolution of the internal microstructure.