Variational inequality for a Timoshenko plate contacting at the boundary with an inclined obstacle.

A class of variational inequalities describing the equilibrium of elastic Timoshenko plates whose boundary is in contact with the side surface of an inclined obstacle is considered. At the plate boundary, mixed conditions of Dirichlet type and a non-penetration condition of inequality type are imposed on displacements in the mid-plane. The novelty consists of modelling oblique interaction with the inclined obstacle which takes into account shear deformation and rotation of transverse cross-sections in the plate.

Forward and inverse problems for creep models in viscoelasticity.

This study examines a class of time-dependent constitutive equations used to describe viscoelastic materials under creep in solid mechanics. In nonlinear elasticity, the strain response to the applied stress is expressed via an implicit graph allowing multi-valued functions. For coercive and maximal monotone graphs, the existence of a solution to the quasi-static viscoelastic problem is proven by applying the Browder-Minty fixed point theorem.

The energy release rate for non-penetrating crack in poroelastic body by fluid-driven fracture.

A new class of constrained variational problems, which describe fluid-driven cracks (that are pressurized fractures created by pumping fracturing fluids), is considered within the nonlinear theory of coupled poroelastic models stated in the incremental form. The two-phase medium is constituted by solid particles and fluid-saturated pores; it contains a crack subjected to non-penetration condition between the opposite crack faces. The inequality-constrained optimization is expressed as a saddle-point problem with respect to the unknown solid phase displacement, pore pressure, and contact force.

Non-smooth variational problems and applications.

Mathematical methods based on the variational approach are successfully used in a broad range of applications, especially those fields that are oriented on partial differential equations. Our problem area addresses a wide class of nonlinear variational problems described by all kinds of static and evolution equations, inverse and ill-posed problems, non-smooth and non-convex optimization, and optimal control including shape and topology optimization. Within these directions, we focus but are not limited to singular and unilaterally constrained problems arising in mechanics and physics, which are governed by complex systems of generalized variational equations and inequalities.

Quasi-variational inequality for the nonlinear indentation problem: a power-law hardening model.

The Boussinesq problem, which describes quasi-static indentation of a rigid punch into a deformable body, is studied within the context of nonlinear constitutive equations. By this, the material response expresses the linearized strain in terms of the stress and cannot be inverted in general. A contact area between the punch and the body is unknown , whereas the total contact force is prescribed and yields a non-local integral condition.

On an Implicit Model Linear in Both Stress and Strain to Describe the Response of Porous Solids.

We study some mathematical properties of a novel implicit constitutive relation wherein the stress and the linearized strain appear linearly that has been recently put into place to describe elastic response of porous metals as well as materials such as rocks and concrete. In the corresponding mixed variational formulation the displacement, the deviatoric and spherical stress are three independent fields. To treat well-posedness of the quasi-linear elliptic problem, we rely on the one-parameter dependence, regularization of the linear-fractional singularity by thresholding, and applying the Browder-Minty existence theorem for the regularized problem.

On proportional deformation paths in hypoplasticity.

We investigate rate-independent stress paths under constant rate of strain within the hypoplasticity theory of Kolymbas type. For a particular simplified hypoplastic constitutive model, the exact solution of the corresponding system of nonlinear ordinary differential equations is obtained in analytical form. On its basis, the behaviour of stress paths is examined in dependence of the direction of the proportional strain paths and material parameters of the model.

Corrector estimates in homogenization of a nonlinear transmission problem for diffusion equations in connected domains.

This paper is devoted to the homogenization of a nonlinear transmission problem stated in a two-phase domain. We consider a system of linear diffusion equations defined in a periodic domain consisting of two disjoint phases that are both connected sets separated by a thin interface. Depending on the field variables, at the interface, nonlinear conditions are imposed to describe interface reactions.

On the states of stress and strain adjacent to a crack in a strain-limiting viscoelastic body.

The viscoelastic Kelvin-Voigt model is considered within the context of quasi-static deformations and generalized with respect to a nonlinear constitutive response within the framework of limiting small strain. We consider a solid possessing a crack subject to stress-free faces. The corresponding class of problems for strain-limiting nonlinear viscoelastic bodies with cracks is considered within a generalized formulation stated as variational equations and inequalities.

Nonlinear elasticity with limiting small strain for cracks subject to non-penetration.

A major drawback of the study of cracks within the context of the linearized theory of elasticity is the inconsistency that one obtains with regard to the strain at a crack tip, namely it becoming infinite. In this paper we consider the problem within the context of an elastic body that exhibits limiting small strain wherein we are not faced with such an inconsistency. We introduce the concept of a non-smooth viscosity solution which is described by generalized variational inequalities and coincides with the weak solution in the smooth case.

Unexpected Reactivity of Trifluoromethyl Diazomethane (CF3CHN2): Electrophilicity of the Terminal N-Atom.

After more than 70 years since its discovery, CF3CHN2 was found to possess a novel reactivity mode: N-terminal electrophile. With C-nucleophiles it gives hydrazones that are easily transformed into valuable CF3-heterocycles.

A discontinuous Poisson-Boltzmann equation with interfacial jump: homogenisation and residual error estimate.

A nonlinear Poisson-Boltzmann equation with inhomogeneous Robin type boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic multiphase medium with dilute solid particles. The key issue stems from interfacial jumps, which necessitate discontinuous solutions to the problem.

On the topological derivative due to kink of a crack with non-penetration. Anti-plane model.

A topological derivative is defined, which is caused by kinking of a crack, thus, representing the topological change. Using variational methods, the anti-plane model of a solid subject to a non-penetration condition imposed at the kinked crack is considered. The objective function of the potential energy is expanded with respect to the diminishing branch of the incipient crack.

[Additional phragmoplast corrects abnormal cytokinesis in wheat x rye hybrid pollen mother cells].

The phragmoplast dysfunction in wheat x rye hybrid F1 male meiosis has been described. The pollen mother cells (PMCs) show the phenotype where transition from central spindle fibers (forming a solid bundle) to a phragmoplast (hollow cylinder) is blocked. The blockade suppresses centrifugal movement of the phragmoplast and cell plate formation.

Radiation factors in space and a system for their monitoring.

The radiation environment is of special concern when the spaceship flies in deep space. The annual fluence of the galactic cosmic rays is approximately 10(8) cm-2 and the absorbed dose of the solar cosmic rays can reach 10 Gy per event behind the shielding thickness of 3-5 g cm-2 Al. For the radiation environment monitoring it is planned to place a measuring complex on the space probes "Mars" and "Spectr" flying outside the magnetosphere.