Modeling of Non-Isothermal Viscoelastic-Viscoplastic Deformation of Bending Reinforced Plates

A model of non-isothermal viscoelastic-viscoplastic deformation of multidirectionally reinforced flexible plates has been developed. The viscoplastic deformation of isotropic materials of the composition is described by the relations of the flow theory with isotropic hardening, which take into account the dependences of the loading functions on temperature and strain rate intensity. The viscoelastic behavior of the composition components is described by the equations of the Maxwell-Boltzmann model. The weakened resistance of reinforced plates to transverse shifts is modeled by the Ambartsumian bending theory relations, and the geometric nonlinearity is modeled in the Karman approximation. The connection between the thermophysical and mechanical components of the problem of inelastic dynamic deformation of reinforced plates is taken into account. The temperature over the thickness of structures is approximated by a 7th order polynomial. The numerical solution of the formulated nonlinear two-dimensional problem is constructed using an explicit scheme of time steps. The viscoelastic-viscoplastic dynamic behavior of a relatively thin glass-plastic plate is studied with and without allowance for the thermal response in it. The structure is loaded transversely with an air blast wave. It is shown that the failure to take into account the thermal response in a fiberglass plate can significantly distort the calculated fields of residual deformations of the components of its composition, despite the fact that the maximum heating of such a structure does not exceed 10 degrees C. Viscoelastic-plastic calculations, when the sensitivity of the composite materials to the rate of their deformation can be neglected, can reasonably be carried out without taking into account the thermal response of the composite plate, if there are no external heat sources of non-mechanical origin.