Current Research Projects

1. Dynamic mechanical behavior and damage mechanism of B4C/Al composites. Supported by RFBR, grant #19-51-53006 (Joint project RFBR-NSF—). (RFBR - Russian Fund for Basic Research).

Key words: Dispersed composites, metal matrix, high-speed loading, two-level modeling, asymptotic averaging, 3D micro structure, numerical simulation, boron-aluminum composite (B4C/Al), X-ray micro tomography.

Composites based on metal matrix have excellent properties, such as light weight, high specific rigidity and hardness. The microstructure (structure at the level of inclusions) of such composites is complicated because of the strong inhomogeneity and random spatial arrangement of the inclusions. Models constructed from an idealized repeating cell were often used for modeling composites of this type. The novelty of this study is that a real 3D microstructure of the material will be used. Obtaining the real micro structure is now possible by non-destructive X-ray micro tomography, which provides 3D structure of the composite. It is supposed to use Shanghai Synchrotron Radiation Complex of the third generation. Modeling deformation and fracture at the macro level will be based on numerical simulation at the level of the material structure (at the micro level). 3D images and experimental data will be obtained by the Chinese team and will be used to develop and verify two-level simulation of the static and dynamic deformational response of the composite with a non-periodic structure. This is the task of the Russian team. The mechanical properties and damage mechanisms of this type composites under static and dynamic loading are associated not only with the properties of each component, but also with microscopic features. The project is aimed to reveal the mechanisms of communication between the mechanical properties of components, the damage development from one hand and the microstructure of dispersed composites from the another hand. It is supposed to calculate the macro response of the material to deformation, as well as the distribution of stresses at the structure level. The latter will also be used to analyze processes of deformation and the evolution of destruction. The advantage of the proposed joint research is in combining the experimental results of the Chinese group with the capability of the Russian group in the field of composite numerical simulation. The developed simulation is supposed to use for new dispersed composites design.

2. Mechanical Properties of Artificial Materials with Periodic Structure. Supported by RFBR, grant #19-51-53008 (Joint project RFBR-NSF—).

Key words: Artificial materials, negative Poisson's ratio, auxetics, couple theory of elasticity, mutual influence of bending and torsion on normal and shear strains, two-level asymptotic model of deformation, 3D microstructure, numerical simulation

Nowadays attention is attracted to increasing the performance characteristics of materials with artificial structure (meta materials) by implementing micro structures that lead to anomalous deformation properties. The mechanical properties of artificial materials under static and dynamic loading are caused by not only the properties of each component, but also complex structure. This results in such properties as anisotropy, the appearance of rotational degrees of freedom, etc. Due to unusual physical and mechanical properties, meta materials demonstrate the possibility of application in aerospace, transport and biomedical engineering. Therefore, they attract interest of the mechanicians and materials scientists throughout the world. Therefore, the proposed study is relevant. The project is aimed at developing an asymptotic method for studying the stress/strain state of artificial materials (composites) with a periodic structure. This is the fundamental task of the project. The matter is that such materials, generally speaking, demonstrate coupling of the stresses and moment stresses with strains, bending and torsion. In other words, these materials are described by the moment theory of elasticity. The asymptotic approach was used to derive coupled (in the sense of forces and moments) equations for plates and shells. In this project it is proposed to obtain the coupled 3D equations of the moment elasticity theory describing the properties of the meta materials. This is the novelty of the proposed study. It is proposed to investigate the effect of the negative Poisson's ratio on the transmission coefficients of pore pressure and thermal stresses. It is also proposed to study the influence of the coupling constitutive law at the macrolevel and the heterogeneity of the structure at the microlevel on the meta material dynamic characteristics. Finally, it is proposed to develop an algorithm for optimizing the structure of a periodic cell in order to increase/decrease any property of the material. For example, decreasing the Poisson's ratio or increasing the stresses coupling with torsion or bending.

Projects archive

(in work)

1. INTAS project #95_525 (participant).

Pneumatic tire 3D numerical simulation was developed for evaluation of stress/strain in the tire contacting a rigid road. The transient and steady rollings are applicable. The simulation developed is based on geometrically non-linear Elasticity, incremental approach for equations linearisation and iterations at each time step (implicit Euler method).

2. INTAS project #96-2306 (team leader).

Main objective of the project was modeling reinforced concrete structures subjected to loading caused by "soft impact". The aim was homogenization of the reinforced concrete plate and deriving the model of laminated plate in elastic/plastic strain range.

3. RFBR project, #96-01-00372 (team leader).

4. RFBR project, #98-01-00488 (team leader) "The combined iterative method for solution of boundary-value problems of Mechanics of Solids for highly anisotropic materials".

The Finite-Element Method applied results in badly conditioned linear systems in the case of materials with contrast anisotropic moduli. Therefore, it is desirable to develop iterative schemes most adapted for such systems. Obviously, effective preconditioner is required for reaching this purpose. Firstly, the multigrid method was tested as the preconditioner. Such a preconditioner was compared with the preconditioner based on the finite-element approximation of Laplace operator a the model domain. Secondly, the comparison of two-term and three-term Chebyshev iterative methods was carried out. Three-term method revealed to be a little bit more stable. Nevertheless, computations conducted for representative class of 2D boundary-value problems of Elasticity did not revealed any significant advantage of three-term method. Also the efficiency of the preconditioning was studied in comparison with the Domain Decomposition.

5. RFBR project, #02-01-00240 (team leader). The project title: Composites 3D Simulation on Parallel Computers.

1) The two-scale asymptotic homogenization developed for inhomogeneous in-plane periodic plates was applied for corrugated plate and reinforced concrete plate. 2) The transient rolling modeling was implemented as self-made code. 3) Numerical tests evaluating a number of parallel iterative solvers were conducted on a cluster computer system at Lomonosov Moscow State University.