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ON AN APPROACH TO THE DERIVATION OF CONSTITUTIVE EQUATIONS OF PHOTOCHROMIC MATERIALS

The paper presents constitutive equations of deformed solids, the state parameters of which, apart from the displacement vector, include concentrations of photochromic compounds. Equilibrium equations are completed with chemical kinetic equations, which are a system of, in a general case, nonlinear ordinary differential equations or parabolic-type equations accounting for the diffusion of products of photochromic reactions. Coefficients of such equations (for example, quantum reaction yield, reaction rate) can be assumed to depend on the stressed state. Several versions of the dependence of coefficients of chemical kinetic equations on the stressed-strained state are introduced. Also, in the assumption of electrostatics, possible effects of electric fields are taken into account. In analogy with mechanics of semiconductors and conductors, related equations of state are proposed. 
The introduced model of a coupled photo-electro-mechanical effect is a strongly nonlinear boundary-value problem, the equations of which contain a large number of material constants that must be determined experimentally. For conducting potential mechanical experiments, a simplified one-dimensional model is proposed, which is analogous to problems of tension-compression and bending in mechanics of bars and beams. In the framework thereof, solutions of related one-dimensional problems are constructed, which make it principally possible to define dimensionless complexes containing unknown material constants.