In the framework of direction 1 - main results in the area "Mechanochemistry"
New approaches to thermodynamically motivated statements of related boundary problems "diffusion - chemistry - mechanics" are developed. A new theory for analyzing the kinetics and stability of propagating fronts of chemical reactions in conjunction with a stressed-deformed state. Experimental research motivated by theory and focused on engineering practice.
1. Chemical affinity tensor is a tool for investigating the effect of stresses on the kinetics of the chemical reaction front.
2. Mechanical stresses can accelerate, slow down, block, and trigger the propagation of the reaction front.
3. Concept of forbidden zones and their construction. Impact of stress-strain states.
4. Stability of the reaction front. Competition between the global kinetics of the front and the kinetics of rising disturbances. Loss of front stability generates stress concentrations - the cause of destruction.
5. Experimental studies: growth of intermetallics in solders and silicon lithization reactions in lithium-ion batteries.
Immediate plans: volumetric and localized reactions (general theory);
different modes (reactions controlled by diffusion or reaction rate), the relationship between crack growth and reaction front propagation; modeling of anodes; biomechanics of growth.
In the framework of direction 2 - main results in the area "Construction of mathematical models of elastic and piezoelastic structures containing thin-walled elements"
The basis for the construction of mathematical models is the use of asymptotic analysis methods adapted to the study of solutions to boundary problems with singular perturbations.
In recent years, the properties of a thin elastic plate reinforced with periodic families of hardening thin fibers have been described. Equations describing properties of elastic plate with piezoelastic inclusion were derived, asymptotic analysis of thin rods from piezoelastic material was carried out. A one-dimensional model of a thin elastic rod with rounded or sharpened ends was created, boundary layers arising near the ends of such rod were examined. Mathematical model of increased accuracy of joints of elastic rods is built.
It is proposed to use developed asymptotic methods to create mathematical models of deformation of corrugated plates and small grids from elastic elements.
The results can be used to create new materials based on small-mesh and box-shaped elements, as well as in engineering practice when studying the deformation of corrugated structural elements.