14 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 +1
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…