## Mathematical Elasticity & Calculus of Variations

My work in this area
focuses on the long-standing question in mathematical hyperelasticity on how to
combine known convexity notions (quasiconvexity in particular) with
requirements on the injectivity and orientation-preservation of the admissible
deformations.

I currently approach this question only for planar deformations by trying to
combine conformal analysis and its generalizations with calculus of variations;
results include the first explicit characterizations of Young measures
generated by gradients of homeomorphisms.

I also work on questions concerning lower-semicontinuity of functionals in
general, for example when connected to quasiconvexity on the boundary

**Related publications and preprints:**

- [16] B. BENEŠOVÁ, M. KRUŽÍK, A. SCHLÖMERKEMPER:
*A note on locking materials and gradient polyconvexity*, accepted to M3AS. (Preprint at arXiv)
- [13] B. BENEŠOVÁ, M. KRUŽÍK:
*Weak lower semicontinuity of integral functionals and applications*, SIAM Review 59 (2017), 703-766. (Preprint at arXiv)
- [11] B. BENEŠOVÁ, M. KAMPSCHULTE:
*Gradient Young measures
generated by quasiconformal maps the plane*, SIAM J.Math. Anal. 47 (2015) 4404-4435. (Preprint at RWTH Aachen)
- [10] B. BENEŠOVÁ, S KRÖMER, M. KRUŽÍK:
*Boundary effects and weak* lower semicontinuity for signed integral functionals on BV*, ESAIM:COCV 21 (2015), 513-534. (Preprint at RWTH Aachen),
- [9] B. BENEŠOVÁ, M. KRUŽÍK:
*Characterization of gradient Young measures
generated by homeomorphisms in the plane*, ESAIM:COCV 22 (2016), 267-288. (Preprint at RWTH Aachen)
- [5] B. BENEŠOVÁ, M. KRUŽÍK, G. PATHÓ:
*Young measures supported on invertible
matrices.* Appl. Anal., 93 (2014), 105-123.(ArXiv Link)

## Microstructure Formation & Shape-memory Alloys

Convexity conditions in
calculus of variations are strongly linked to microstructure formation in
so-called “smart” solids like shape-memory alloys or ferromagnets. My research
concerns proposing suitable models for these materials on the single- and
polycrystalline scale and their mathematical analysis.

My results include thermomechanical extensions of established single-crystalline
models of SMA or polycrystalline models with a refined description of the
dissipation.

My ongoing projects in this area include modeling of modulated martensite in
NiMnGa.

**Related publications and preprints:**

- [12] B. BENEŠOVÁ, M. FROST, M. KAMPSCHULTE, C. MELCHER, P. SEDLÁK, H. SEINER:
*Incommensurateness in nanotwinning models of modulated martensites*, Phys. Rev. B (Rapid Commun.), 92, 180101(R) (2015) - Chosen as editor´s suggestion.
- [8] M. FROST, B. BENEŠOVÁ, P. SEDLÁK:
*A microscopically motivated constitutive model for shape memory alloys: formulation, analysis and computations*, Math. Mech. Solids, 21(3) (2016), 358-382. Preprint at RWTH Aachen
- [6] B. BENEŠOVÁ, M. KRUŽÍK, G. PATHÓ:
*A mesoscopic thermomechanically-coupled model for thin-film shape-memory alloys by dimension reduction and scale transition*, Cont. Mech.Thermodyn., 26(5) (2014):683–713. (Preprint at RWTH Aachen)
- [4] P. SEDLÁK, M. FROST, B.BENEŠOVÁ, T. BEN ZINEB, P. ŠITTNER:
*Thermomechanical model for NiTi-based shape memory alloys including R-phase
and material anisotropy under multi-axial loadings*, Int. J. Plasticity, 39 (2012), 132-151.
- [3] B. BENEŠOVÁ, T. ROUBÍČEK:
*Micro-to-meso scale limit for shape-memory-alloy models with thermal coupling*. Multiscale Model. Simul., 10 (2012), 1059–1089. (Preprint at the Nečas centre, Charles University in Prague)
- [2] B. BENEŠOVÁ, M. KRUŽÍK, T. ROUBÍČEK:
*Thermodynamically-consistent
mesoscopic model of the ferro/paramagnetic transition*. Zeit. angew. Math. Phys., 64 (2013), 1-28. (Preprint at ArXiv)

## Numerical Studies

I work on the design and
implementation of efficient as well as reliable numerical methods for solving
PDE’s describing microstructure formation. Results include improved algorithms
for dissipative, rate-independent systems and design of an unconditionally stable
implicit midpoint spectral scheme for the Cahn-Hilliard equation.

**Related publications and preprints:**

## Miscellaneous

During my collaborations with physicist or mathematicians, results were obtained that lie outside of my main research focus. Examples include analysis
of a simple model in magnetoelasticity (which is not focused on pattern formation) or uniqueness of a fitting procedure in ultrafast spectroscopy.

**Related publications and preprints:**

- [15] B. BENEŠOVÁ, J. FORSTER, C. LIU, A. SCHLÖMERKEMPER:
*Existence of weak solutions to an evolutionary model for magnetoelasticity*. SIAM J. Math. Anal., 50 (2018), 1200-1236.(Preprint at ArXiv)
- [14] J. DOSTÁL, B. BENEŠOVÁ, T. BRIXNER:
*Two-Dimensional Electronic Spectroscopy Can Fully Characterize the Population Transfer in Molecular Systems *, J. Chem. Phys., 145, 124312 (2016).