About the stress-strain state of growing viscoelastic systems

A problem of calculation of the stress-strain state of viscoelastic heterogeneously ageing growing systems at the various moments of time is considered. The efficient numerical technique based on the Finite Element Method (FEM) is suggested. The constitutive equation between stresses and strains in the viscoelastic growing solid is corresponded with the Maslov-Arutyunyan theory. The general system of equations of the FEM-based technique is being formed for nodal displacement increments on the basis of variation of the total energy functional by components of the vector of nodal displacement increments. The numerical technique allows to take into account linear and nonlinear creep of the material, shrinkage (if it is necessary) and the instantly-elastic modulus time-dependence. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)