Simulation of the Deformation Diagram of a Viscoelastic Material Based on a Structural Model

A serious problem in computer simulation of a stress state of polymer structures is to validate the mathematical description of the mechanical properties of materials. The structural model of a viscoelastic material has a number of advantages in describing both the rheology of a material and strain curves of it. In this model, a material is described as a structure consisting of several elements with relatively simple rheological properties. Reproduction of a complex behavior of a material under alternating non-isothermal loading is provided through the interaction of these simple elements. A technique developed in this work for modeling a viscoelastic material is intended for strength calculations of structures made of materials operating under conditions of a long-term repetitive thermomechanical impact using the finite element method. The application of the developed procedure to a polymeric material, polymethyl methacrylate (PMMA), is considered. The results of testing this material under uniaxial compression at a constant temperature are presented. The methodology and results of identification of the developed structural model using a specialized software code are described. Formulas are obtained for the approximation of the deformation characteristics of the material at a constant strain rate and for the time dependence of the deformation of the material during its holding at a constant stress level. Approximation is an important stage in the validation of the material model, which facilitates the systematization of the initial experimental data and their further mathematical processing. The best approximation of the deformation characteristics of a viscoelastic material is provided by a hyperbolic tangent function, whereas a logarithmic function provides the best results for the deformation upon holding. Further construction of the structural model was performed by selecting sequential parameters of bilinear rheological functions of the separate elements of the model and by iterative refinement of these parameters. The simulation results are compared with the experiments performed at different strain rates and with holding at different stress levels. In this work, the results of the initial stage of the performed experimental and theoretical studies are presented.