The work proposes a model for synthesising a ‘metallic matrix–reinforcing inclusions’ composite in a simplified reaction scheme. A suggested mathematical model takes into account the interdependence of thermal, chemical and mechanical phenomena. The problem includes kinetic equations for determining the composition of the synthesis products. The reactions are initiated by a thermal impulse from a surface. It was established that after some mathematical transformations and partial analytical solution, the model includes equivalent parameters of the reactions and equivalent thermophysical properties that depend on the mechanical modules. The model allowed us to study two variants of composite synthesis: in the quasi-stationary mode for a sample whose dimensions exceed the size of the heating and reaction zones, and in the unsteady mode for a finite-sized sample. It is shown that the consideration of the coupling of thermal, chemical and mechanical processes changes all the characteristics of conversion propagation and the values of stresses and strains in the reaction zone. The stresses in the reaction zone and in the products are affected by the parameters characterising the reaction itself. It is shown that there is a range of parameters at which a stable combustion wave is not formed.

这项工作提出了一种在简化反应方案中合成“金属基体增强夹杂物”复合材料的模型。建议的数学模型考虑了热、化学和机械现象的相互依赖性。该问题包括用于确定合成产物组成的动力学方程。反应由来自表面的热脉冲引发。经数学变换和部分解析解后，模型包括反应的等效参数和等效的热物理性质，取决于力学模块。该模型使我们能够研究复合合成的两种变体：对于尺寸超过加热区和反应区大小的样品的准稳态模式，并且对于有限大小的样本处于非稳态模式。结果表明，考虑热、化学和机械过程的耦合会改变转化传播的所有特性以及反应区的应力和应变值。反应区和产物中的应力受表征反应本身的参数的影响。结果表明，存在一定范围的参数，在该范围内没有形成稳定的燃烧波。