17 citations · 40 across the 14 of their papers we have counts for
18 papers
Convergence of Discontinuous Galerkin Methods for Quasiconvex and Relaxed Variational Problems
Georgios Grekas, Konstantinos Koumatos, Charalambos Makridakis +1
In this work, we establish that discontinuous Galerkin methods are capable of producing reliable approximations for a broad class of nonlinear variational problems. In particular,…
A class of Discontinuous Galerkin methods for nonlinear variational problems
Georgios Grekas, Konstantinos Koumatos, Charalambos Makridakis +1
In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming f…
Weak-strong uniqueness for measure-valued solutions to the equations of quasiconvex adiabatic thermoelasticity
Myrto Galanopoulou, Konstantinos Koumatos, Andreas Vikelis
This article studies the equations of adiabatic thermoelasticity endowed with an internal energy satisfying an appropriate quasiconvexity assumption which is associated to the symm…
Existence and uniqueness for a viscoelastic Kelvin-Voigt model with nonconvex stored energy
Konstantinos Koumatos, Corrado Lattanzio, Stefano Spirito +1
We consider nonlinear viscoelastic materials of Kelvin-Voigt type with stored energies satisfying an Andrews-Ball condition, allowing for non convexity in a compact set. Existence…
On the uniqueness of solutions to hyperbolic systems of conservation laws
Shyam Sundar Ghoshal, Animesh Jana, Konstantinos Koumatos
For general hyperbolic systems of conservation laws we show that dissipative weak solutions belonging to an appropriate Besov space and satisfying a one-sided boun…
-quasiconvexity, Gårding inequalities and applications in PDE constrained problems in dynamics and statics
Konstantinos Koumatos, Andreas Vikelis
A Gårding-type inequality is proved for a quadratic form associated to -quasiconvex functions. This quadratic form appears as the relative entropy in the theory of con…
Approximations of energy minimization in cell-induced phase transitions of fibrous biomaterials: -convergence analysis
Georgios Grekas, Konstantinos Koumatos, Charalambos Makridakis +1
We consider a model of energy minimization arising in the study of the mechanical behavior caused by cell contraction within a fibrous biological medium. The macroscopic model is b…
Quasiconvex elastodynamics: weak-strong uniqueness for measure-valued solutions
Konstantinos Koumatos, Stefano Spirito
A weak-strong uniqueness result is proved for measure-valued solutions to the system of conservation laws arising in elastodynamics. The main novelty brought forward by the present…
Shape programming for narrow ribbons of nematic elastomers
Virginia Agostiniani, Antonio DeSimone, Konstantinos Koumatos
Using the theory of -convergence, we derive from three-dimensional elasticity new one-dimensional models for non-Euclidean elastic ribbons, i.e. ribbons exhibiting spontaneous c…
Necessary and sufficient conditions for the strong local minimality of extremals on a class of non-smooth domains
Judith Campos Cordero, Konstantinos Koumatos
Motivated by applications in materials science, a set of quasiconvexity at the boundary conditions is introduced for domains that are locally diffeomorphic to cones. These conditio…
Optimality of General Lattice Transformations with Applications to the Bain Strain in Steel
Konstantinos Koumatos, Anton Muehlemann
This article provides a rigorous proof of a conjecture by E.C. Bain in 1924 on the optimality of the so-called "Bain strain" based on a criterion of least atomic movement. A genera…
The morphology of lath martensite: a new perspective
Anton Muehlemann, Konstantinos Koumatos
A mathematical framework is proposed to predict the features of the (5 5 7) lath transformation in low-carbon steels based on energy minimisation. This theory generates a one-param…
Quasiconvexity at the boundary and the nucleation of austenite
John Ball, Konstantinos Koumatos
Motivated by experimental observations of H. Seiner et al., we study the nucleation of austenite in a single crystal of a CuAlNi shape-memory alloy stabilized as a single variant o…
Differential inclusions and Young measures involving prescribed Jacobian
Konstantinos Koumatos, Filip Rindler, Emil Wiedemann
This work presents a general principle, in the spirit of convex integration, leading to a method for the characterization of Young measures generated by gradients of maps in $W^{1,…
Nucleation of austenite in mechanically stabilized martensite by localized heating
John M. Ball, Konstantinos Koumatos, Hanus Seiner
The nucleation of bcc austenite in a single crystal of a mechanically stabilized 2H-martensite of Cu-Al-Ni shape-memory alloy is studied. The nucleation process is induced by local…
An investigation of non-planar austenite-martensite interfaces
John M. Ball, Konstantinos Koumatos
Motivated by experimental observations on CuAlNi single crystals, we present a theoretical investigation of non-planar austenite-martensite interfaces. Our analysis is based on the…
From nonlinear to linearized elasticity via Gamma-convergence: the case of multiwell energies satisfying weak coercivity conditions
Virginia Agostiniani, Timothy Blass, Konstantinos Koumatos
Linearized elasticity models are derived, via Gamma-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and sa…
Orientation-preserving Young measures
Konstantinos Koumatos, Filip Rindler, Emil Wiedemann
We prove a characterization result in the spirit of the Kinderlehrer-Pedregal Theorem for Young measures generated by gradients of Sobolev maps satisfying the orientation-preservin…