45 citations · 46 across the 14 of their papers we have counts for
16 papers
Extreme points and faces in the moment problem
Didier Henrion, Martin Kružík, Stephan Weis
The polyconvex envelope, used in the calculus of variations and elasticity theory, was expressed by Dacorogna pointwise as a linear program on finitely atomic measures on the space…
Semidefinite relaxations for nonlinear elasticity with energies convex in the Cauchy-Green strain tensor
Didier Henrion, Milan Korda, Martin Kružík +2
In nonlinear elasticity, finding the deformation of a material which minimizes a given stored energy density is a challenging calculus of variations problem which may fail to have…
Polyconvexity with Moments and Sums of Squares
Giovanni Fantuzzi, Didier Henrion, Martin Kru{ž}ík +2
A function of a matrix is polyconvex when it can be expressed as a convex function of the matrix minors. Polyconvexity is a regularity condition ensuring existence of minimizers in…
Sharp mean Hadamard inequalities and polyconvex integrands that give rise to convex functionals
Jonathan Bevan, Martin Kružík, Jan Valdman
We investigate several instances of the Hadamard inequality in the mean in two dimensions. As a consequence, we prove the uniqueness of minimizers of an integral functional with a…
On the passage from nonlinear to linearized viscoelastodynamics
Barbora Benešová, Malte Kampschulte, Martin Kružík
The equations of linearized viscoelastodynamics in Kelvin-Voigt rheology are rigorously derived from a nonlinear model that satisfies the time-dependent frame indifference in the s…
A decoupled, stable, and second-order integrator for the Landau--Lifshitz--Gilbert equation with magnetoelastic effects
Martin Kružík, Hywel Normington, Michele Ruggeri
We consider the numerical approximation of a nonlinear system of partial differential equations modeling magnetostriction in the small-strain regime consisting of the Landau--Lifsh…
Solving unbounded optimal control problems with the moment-SOS hierarchy *
Karolına Sehnalová, Didier Henrion, Milan Korda +1
The behaviour of the moment-sums-of-squares (moment-SOS) hierarchy for polynomial optimal control problems on compact sets has been explored to a large extent. Our contribution foc…
Positive temperature in nonlinear thermoviscoelasticity and the derivation of linearized models
Rufat Badal, Manuel Friedrich, Martin Kružík +1
According to the Nernst theorem or, equivalently, the third law of thermodynamics, the absolute zero temperature is not attainable. Starting with an initial positive temperature, w…
Measure structured deformations
stefan Krömer, Martin Kružík, Marco Morandotti +1
Measure structured deformations are introduced to present a unified theory of deformations of continua. The energy associated with a measure structured deformation is defined via r…
Non-interpenetration of rods derived by -limits
Barbora Benešová, Daniel Campbell, Stanislav Hencl +1
Ensuring non-interpenetration of matter is a fundamental prerequisite when modeling the deformation response of solid materials. In this contribution, we thoroughly examine how thi…
Hadamard's inequality in the mean
Jonathan Bevan, Martin Kružík, Jan Valdman
Let be a Lipschitz domain in and let . We investigate conditions under which the functional $$I_n(φ)=\int_Q |\nabla φ|^n+ f(x)\,\mathrm{det}…
Equilibrium of immersed hyperelastic solids
Manuel Friedrich, Martin Kružík, Ulisse Stefanelli
We discuss different equilibrium problems for hyperelastic solids immersed in a fluid at rest. In particular, solids are subjected to gravity and hydrostatic pressure on their imme…
Quasistatic evolution for dislocation-free finite plasticity
Martin Kružík, David Melching, Ulisse Stefanelli
We investigate quasistatic evolution in finite plasticity under the assumption that the plastic strain is compatible. This assumption is well-suited to describe the special case of…
Numerical approximation of von Kármán viscoelastic plates
Manuel Friedrich, Martin Kružík, Jan Valdman
We consider metric gradient flows and their discretizations in time and space. We prove an abstract convergence result for time-space discretizations and identify their limits as c…
Weak lower semicontinuity of integral functionals and applications
Barbora Benešová, Martin Kružík
Minimization is a reoccurring theme in many mathematical disciplines ranging from pure to applied ones. Of particular importance is the minimization of integral functionals that is…
Oscillations and concentrations up to the boundary
Stefan Krömer, Martin Kružík
Oscillations and concentrations in sequences of gradients , bounded in if and is a bounded domain with the extension pr…