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In particular my interest is about existence and regularity of nonlinear PDE-Systems deriving from engineering applications and structural mechanics, as e.g., plasticity problems, extended continuum mechanics, shells and plates etc. Useful tools are newly derived coercive inequalities, like a generalized Korn‘s inequality or an inequality connecting the curl of a rotation to all partial derivatives. The precise amount of regularity of the (weak) solution is also a decisive information for subsequent FEM-implementations.
I am also interested in 3D-to-2D reduction of nonlinear elasticity theory to membrane-, plate- and shell theories. A main mathematical tool here is Gamma convergence, introduced by De Giorgi and developed notably by Dal Maso, Braides and coworkers. It provides a powerful and rigorous mathematical framework to pass from a finer-scale (or higher-dimensional) variational principle to a coarser-scale (or lower-dimensional) effective variational principle.
I am also interested in 3D-to-2D reduction of nonlinear elasticity theory to membrane-, plate- and shell theories. A main mathematical tool here is Gamma convergence, introduced by De Giorgi and developed notably by Dal Maso, Braides and coworkers. It provides a powerful and rigorous mathematical framework to pass from a finer-scale (or higher-dimensional) variational principle to a coarser-scale (or lower-dimensional) effective variational principle.
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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES (2024): 112661
Computer Methods in Applied Mechanics and Engineering (2024): 116944
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2024)
arXiv (Cornell University) (2024): 112700
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)
Computer Methods in Applied Mechanics and Engineering (2024): 116494-116494
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