Gradient polyconvexity and its application to problems of mathematical elasticity and plasticity

• Thesis title in Czech: Aplikace gradientní polykonvexity na problémy matematické pružnosti a plasticity
• Thesis title in English: Gradient polyconvexity and its application to problems of mathematical elasticity and plasticity
• Key words: slabá konvergence, Sobolevovy prostory, konvexita
• English key words: weak convergence, Sobolev spaces, convexity
• Academic year of topic announcement: 2017/2018
• Thesis type: diploma thesis
• Thesis language: angličtina
• Department: Mathematical Institute of Charles University (32-MUUK)
• Supervisor: prof. RNDr. Martin Kružík, Ph.D., DSc.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 25.01.2018
• Date of assignment: 25.01.2018
• Confirmed by Study dept. on: 29.03.2019
• Date and time of defence: 10.06.2019 10:30
• Date of electronic submission: 10.05.2019
• Date of submission of printed version: 10.05.2019
• Date of proceeded defence: 10.06.2019
• Opponents: prof. doc. Ing. Jan Zeman, Ph.D.

Guidelines

Student se seznámí se základními výsledky v matematické teorii pružnosti ve velkých deformacích. Cílem práce pak bude rozšířit model pružného materiálu popsaného pomocí gradientní polykonvexity na model elastoplastického tělesa.

References

Ball, J.M.: Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63
(1977), 337–403.


Ball, J.M.: Some open problems in elasticity. In Geometry, Mechanics, and Dynamics, pp. 3–59, Springer, New
York, 2002.

Benešová, B., Kružík, M.: Weak lower semicontinuity of integral functionals and applications. To appear in
SIAM Review 59 (2017), 703-766

Benešová, B., Kružík, M., Schlömerkemper, A.: A note on locking materials and gradient polyconvexity. Preprint arXiv:1706.04055

Ciarlet, P.G.: Mathematical Elasticity Vol. I: Three-dimensional Elasticity, North-Holland, Amsterdam, 1988