Modeling of thermal-power deformation of concrete in a regime-hereditary formulation

Abstract

A method for using simple isothermal diagrams to study the crisis-strain state of concrete under regime-induced thermal-power loading and forced deformation is proposed. The methodological foundations of the study are built on a clear distinction between the concepts of strain additivity and loading non-commutativity, allowing for the adaptation of the classical traditional Boltzmann-Volterra principle to the nonlinear stage of material performance. It is demonstrated that nonlinear strain increments retain the property of physical additivity and can be correctly summed when the history and trajectory of thermal-power effects are taken into account step-by-step. The experimentally observed similarity in the geometric shape of the instantaneous, long-term, and high-temperature strain curves is substantiated in terms of the Unified Physical Law of Deformation of Concrete as a Viscoelastic Gravitationally Brittle Medium. An equation of state in the form of nonlinear Hooke's law is presented, observing the degree of structural damage based on a two-parameter Weibull statistical distribution. This allows for an analytical description of the complete concrete deformation diagram upon heating. A closed-loop algorithm for the transition between deformation and stress phenomena has been developed using intermediate point parameters according to N.I. Karpenko's methodology. It is effective for solving problems of both seasonal loading and seasonal relaxation of concrete.