Numerical simulation of rheological processes in hardening plastics under stress control

The paper concerns the simulation of rheological processes in hardening plastics (resins) under stress control. It is assumed that the resins work in the glassy state, under normal conditions, and the rheological processes are quasi-static and isothermal. The reduced stress levels do not exceed 30% of the instantaneous tensile strength. A resin is modelled as a homogeneous, isotropic, linearly viscoelastic material. The HWKK/H rheological model, developed recently by the author, is used. Short-term, medium-term, and long-term shear strain components are considered and described by one fractional and two normal exponential functions as the stress history (memory) functions. A novel algorithm for the numerical simulation of rheological processes in resins has been developed, which is unified for all stress history functions in the HWKK/H model. The algorithm employs the Boltzmann superposition principle, a virtual table for the classic creep process, and a high-rank Gaussian quadrature. The stress function is approximated with a stair case function. The constitutive equations governing the HWKK/H model are trans formed into an algebraic form suitable for algorithmization. The problem of quasi-exact calculation of the double-improper integral resulting from the fractional exponential function is solved effectively. The algorithm has been tested successfully on selected loading programs of unidirectional tension of epoxide. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 201–212, March–April, 2007.