On the initial boundary value problem for the propagating chemical reaction front in an elastic solid. (English) Zbl 07884709
Summary: The paper is concerned with the study of a chemical reaction between diffusing and solid constituents. The reaction is localized at a propagating reaction front and is accompanied by a transformation strain, which generates stresses affecting the reaction rate. The effect of mechanical stresses on the velocity of the reaction front is taken into account basing on the concept of a chemical affinity tensor. The initial boundary value problem of the propagation of the chemical reaction front is discussed by the example of an axisymmetric problem for a reaction in a cylinder in the case of linear elastic solid constituents. The stage of initial accumulation of the diffusing constituent and the stage of the propagation of the reaction front after its separation from the outer boundary of a body are distinguished. The time preceding the start of the reaction is determined. Conditions at the propagating chemical reaction front for the diffusion problem are discussed. A comparative analysis of the solutions obtained in the quasi-stationary and nonstationary formulations of the diffusion problem is carried out, taking into account and without taking into account the influence of the initially accumulated diffusing constituent on the reaction front velocity, as well as for the case of the absence of diffusion in the untransformed material.
MSC:
| 74E40 | Chemical structure in solid mechanics |
| 74B05 | Classical linear elasticity |
| 74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |
| 92E20 | Classical flows, reactions, etc. in chemistry |
Keywords:
chemical affinity tensor; circular cylinder; transformation strain; diffusion problem; series solution; linear elasticityReferences:
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