Mechanics and Geometry in Soft and Living Matter
Soft mechanical meta materials
Mechanical metamaterials inherit their mechanical properties from structure rather than composition. Origami and Kirigami, the Japanese arts of cutting and folding paper, form a powerful means of manipulating the geometry and mechanics of thin elastic sheet via structural manipulations. The mathematical formulation of Kirigami introduces high level of complexity due to the multiple boundary conditions on the holes edges. In our group we study the mechanics of sliced and perforated sheets, and develop new analytical tools within a Riemannian formalism of image elastic charges. For example, our methods provide new tools for calculating Kirigami patterns designed to suit desired mechanical properties.
Nonlinear mechanics of thin frames Physical Review E 99 (1), 2019
Kirigami mechanics as stress relief by elastic charges Physical Review Letters 122 (4), 2019
Mathematical methods in theories of elasticity
The modern view on mechanics of solids is relied on deep geometric insights together with phenomenology based on recent experiments. Theories of elasticity has been amended accordingly, followed by an increasing complexity of the governing equation. With the rapid progress made in this field, new analytical methods are valuable, with applications ranges from equilibrium of geometrically frustrated elastic solid, to the nonlinear response of complex mechanical structures. In our group we develop new tools for solving mechanical problems in nonlinear elasticity, with applications to metamaterials, cracks, and more.
Elastic interactions between two-dimensional geometric defects Physical Review E (2015)
The plane stress state of residually stressed bodies: A stress function approach (2014)
Mechanics of living and inanimate cellular tissue
Classical solid mechanics describes inanimate matter whose degrees of freedom are microscopic positions of the constituting elements. In biological cellular tissue, where basic elements are biological cells, shape is another important degree of freedom, similar to foam and other complex materials. The importance of cell shapes for the mechanics of cellular tissue makes its analysis a daunting task, commonly attacked using numerical tools. In our group, motivated by experimental observations, we develop and study new continuum models describing the mechanics of cellular tissue via a Riemannian formulations of elasticity theory.
Geometric Frustration and Solid-Solid Transitions in 2D Tissue Physical Review Letters (2018)
Geometric charges in simple solids and thin sheets
Cracks, topological defects in crystalline solids, and forces applied by biological cells adhered to elastic substrate, are only few out of many physical realizations of singular sources of elastic fields. The concept of Geometric-Charges unifies all singular sources of elastic fields within a single Riemannian formalism of elasticity theory, and provides new tools for modeling and solving problems involving singular and distributed sources of stresses. In our group we work on physical problems related with the concept of geometric charges, with example including the mechanics and geometry of wrinkles pattern, mechanical metamaterials, cracks in thin sheets, and more.
Mechanics of non-euclidean plates
A frustrated non-euclidean plate is a thin elastic sheet whose preferred geometry cannot be realized in our 3D euclidean space. Consequently, the physical configuration commonly depends on system dimensions, with complex morphologies and shapes. Non-euclidean plates provides the basic understanding for many natural phenomena such as growth mechanics, self-assembly of macro-molecules, and shape design in man-made systems
Shape selection in chiral ribbons: from seed pods to supramolecular assemblies, Soft-Matter, (2014)
