МATHEMATICAL MODELS AND NUMERICAL METHODS FOR THE STUDY OF TRANSPORT AND COUPLED PROCESSES RELATED TO MECHATRONICS AND SOME BIOMEDICAL APPLICATIONS
Miniaturization in the state-of-the-art devices in electronics, machine building and medicine and related manufacturing technologies require a study of the emerging mechanical processes, taking into account the specific phenomena, arising from the complex technological conditions and requirements. This has led to the need for new mathematical models, methods and approaches to be used in the design and for the proper operation of the products or devices.
Typical for a number of modern devices is the presence of conjugated fields: temperature, fluids (gas), electric and magnetic fields that interact with typical mechanical fields change the behavior of the elements of the structure. Typical such objects are the micro-electro-mechanical systems (MEMS), where heat transfer occurs between unbalanced gas currents and solids at micro-dimensional levels and thermal micro-gasses in complex geometric caverns and microchannel networks. The energy use systems, utilizing energy arising from the vibrations of piezoelectric, magneto-elastic and other elements, are increasingly used to power miniature devices such as sensors and micro-motors. Adaptive modeling of conjugated thermo-hydro-mechanical processes in porous media is gaining momentum in connection with the development of computational transport oncophysics and the increasingly active use of computer simulations in biomedicine (dental and orthodontic medicine, cardiology, orthopedics, etc.). Finding the numerical solution of the complex computational tasks, resulting from the modeling process, requires significant resources, including innovative methods, algorithms and software tools, and the most up-to-date infrastructure to deliver results in the foreseeable future.
1. Development and application of mathematical models and numerical methods for analysis of transport thermal phenomena in Micro-Electro-Mechanical Systems (MEMS)
New scheme of DSMC method for simulation of binary particle interactions in grid cells by using small number of simulators per cell will be analyzed and correspondingly, new modifications will be proposed for low variance simulations. Higher-order approximation schemes for convective terms of the continuum fluid model are in process of development. The new methods and the numerical algorithms will be used to study the interaction between the fluid and the microstructured surface.
The developed schemes with lower dispersion and diffusion for approximation of the convective terms will be implemented in the GPU algorithm of the SIMPLE-TS method. The DSMC method will be also implemented on GPU.
The particle Monte Carlo and continuum numerical methods will be applied to actual multiscale and heterogeneous problems, arising in the MEMS development and design, such as conjugated heat transfer between non-equilibrium gas flows and solid bodies at microscale levels and thermal micro-gas flow problems in complex geometry cavities and microchannel networks. An innovative approach will be developed for approximation of convective terms in convection-diffusion problems. The developed models and methods are aimed at using Fabless manufacturing of MEMS.
2. Mathematical modeling and advanced numerical tools for coupled phenomena in MEMS.
Mathematical models including high nonlinearities as: large deflections, coupled electro-mechanical, thermo-mechanical and thermo-electromechanical fields, “breathing cracks”, delamination, etc. for vibrating parts of MEMS will be developed. Methods for health monitoring and damage detection based on wireless sensors networks will be developed too.
The developed schemes and algorithms for the solution of the theoretically formulated coupled problems will be coded, parallelized and the codes will be run on high performance clusters. Stability analysis, study for multiple solutions, bifurcations and chaos will be performed.
This task includes study of conjugated heat transfer between non-equilibrium gas flows and deformable structures at micro-scale levels. The planned applications include computer simulations of the thermo-electro-elastic static deformation and vibration of structures (including composite and smart structures), applicable in MEMS, energy harvesting systems applicable for power supply of wireless sensors and smart materials. The 3D Digitization Lab will be used systematically for vibration analysis. “On-line” health-monitoring will be developed taking into account the influence of the temperature and environment conditions.
3. Application of computational mechanics and optimization strategies for adaptive simulation of coupled processes in porous media
Innovative applications of the gained in past experience in developing sophisticated approaches for analyzing the behavior of complex engineering systems (primarily in the fields of energy, materials, transportation) into/for understanding, predicting, and modulating the response of complicated biomedical processes. Adaptive modelling of coupled thermo-hydro-mechanical processes in porous media will be applied via hierarchical scale system of constitutive models.
This task includes the development of efficient strategies for model parameter sensitivity analysis (incl. parallelized algorithms, metamodeling of large scale non-linear models), scalability analysis, large scale finite element modelling, multiscale approach combined with advanced and robust homogenization technique.
Applications include modelling of tumor growth / modelling of the growth rate of the tumor mass as a function of the initial state, mechanical strain, cell geometry and nutrient concentration; dental medicine (optimization of orthodontic brackets made of memory shape alloys, assessment of the functionality of dentin to filler hybrid layer, etc.).
The advanced equipment of the 3D digitization lab will be actively used in this task, including the unique capabilities of the industrial CT scanner.