Dr. Victor A. Kovtunenko
University of Graz
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Academic Career Length
33Years (1994-Present)
(Calculated once Scilit publication data is synced: current year − year of first publication + 1)
Representative Publications
View All Publications14 March 2016 in Mathematics and Mechanics of Solids
Journal Article
HIHiromichi Itou
Hiromichi ItouVictor A. KovtunenkoKRKumbakonam R Rajagopal
Kumbakonam R Rajagopal
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. The well-posedness is proved by the construction of an approximation problem using elliptic regularization and penalization techniques.
1 January 2016 in SIAM Journal on Control and Optimization
Journal Article
Victor A. KovtunenkoGLGünter Leugering
Günter Leugering
We consider the shape-topological control of a singularly perturbed variational inequality. The geometry-dependent state problem that we address in this paper concerns a heterogeneous medium with a...
1 October 2006 in IMA Journal of Applied Mathematics
Journal Article
Victor A. KovtunenkoBased on a level-set description of a crack moving with a given velocity, the problem of shape perturb‐ation of the crack is considered. Nonpenetration conditions are imposed between opposite crack surfaces which result in a constrained minimization problem describing equilibrium of a solid with the crack. We suggest a minimax formulation of the state problem thus allowing curvilinear (nonplanar) cracks for the consideration. Utilizing primal–dual methods of shape sensitivity analysis we obtain the general formula for a shape derivative of the potential energy, which describes an energy-release rate for the curvilinear cracks. The conditions sufficient to rewrite it in the form of a path-independent integral (J-integral) are derived.
1 April 2011 in SIAM Journal on Optimization
Journal Article
Motivated by an obstacle problem for a membrane subject to cohesion forces, constrained minimization problems involving a nonconvex and nondifferentiable objective functional representing the total potential energy are considered. The associated first-order optimality system leads to a hemivariational inequality, which can also be interpreted as a special complementarity problem in function space. Besides an analytical investigation of first-order optimality, a primal-dual active set solver is introduced. It is associated to a limit case of a semismooth Newton method for a regularized version of the underlying problem class. For the numerical algorithms studied in this paper, global as well as local convergence properties are derived and verified numerically.
30 May 2017 in Mathematics and Mechanics of Solids
Journal Article
HIHiromichi Itou
Hiromichi ItouVictor A. KovtunenkoKRKumbakonam R Rajagopal
Kumbakonam R Rajagopal
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. Its generalized solution, relying on the space of bounded measures, is proved rigorously with the help of an elliptic regularization and a fixed-point argument.
27 April 2009 in IMA Journal of Applied Mathematics
Journal Article
The mathematical model of a crack with non-penetration conditions is considered in the framework of 3D elasticity. The spatial crack problem is investigated with respect to its numerical realization in the context of constrained optimization. Specifically, for homogeneous isotropic solids with planar cracks, a Papkovich–Neuber-based representation is adopted. It allows to employ a primal–dual active set strategy with an unconditional global and monotone convergence property. The iterates turn out to be primally feasible. Illustrative numerical examples are presented.
About Me
Victor A. Kovtunenko was born in 1966 in Karaganda, USSR. In 1990, he graduated from the Faculty of Mathematics and Mechanics of the Novosibirsk State University, Russia, and defended his dissertation (Ph.D.) in 1994. Since 1990, he has been working at the Lavrentyev Institute of Hydrodynamics of the Siberian Division of the Russian Academy of Sciences (Leading Researcher). In 1998--2000, he was the recipient of the Alexander von Humboldt Fellowship at the Mathematical Institute A of Stuttgart University, Germany. In 2002, he was awarded the Lise Meitner Fellowship of the Austrian Science Foundation. He is currently working at the Institute for Mathematics and Scientific Computing of the University of Graz (Project Leader) and part-time at Graz University of Technology, Austria; see https://homepage.uni-graz.at/victor.kovtunenko/ accessed on 14 December 2023.