Related papers: Geometric approach to mechanical design principles…
Adaptive structures are characterized by their ability to adjust their geometrical and other properties to changing loads or requirements during service. This contribution deals with a method for the design of quasi-static motions of…
The atomic theory of elasticity of amorphous solids, based on the nonaffine response formalism, is extended into the nonlinear stress-strain regime by coupling with the underlying irreversible many-body dynamics. The latter is implemented…
In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural)…
In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order…
Accretion and ablation, i.e. the addition and removal of mass at the surface, is important in a wide range of physical processes including solidification, growth of biological tissues, environmental processes, and additive manufacturing.…
We developed a physics-based analytical model to describe the nonlinear mechanical response of aspirated elastic shells. By representing the elastic energy through a stretching modulus, $K$, and a dimensionless ratio, $\delta$, capturing…
Motivated by results of the topological theory of glasses accounting for geometric frustration, we develop the simplest possible continuum mechanical model of defect dynamics in metallic glasses that accounts for topological, energetic, and…
Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the…
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
Microstructures, characterized by intricate structures at the microscopic scale, hold the promise of important disruptions in the field of mechanical engineering due to the superior mechanical properties they offer. One fundamental…
Mechanical metamaterials are those structures designed to convey force and motion in novel and desirable ways. Recently, Kane and Lubensky showed that lattices at the point of marginal mechanical stability (Maxwell lattices) possess a…
We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…
In the field of nonlinear mechanics, many challenging problems (e.g. plasticity, contact, masonry structures, nonlinear membranes) turn out to be expressible as conic programs. In general, such problems are non-smooth in nature (plasticity…
To go beyond the simple model for the fold as two flexible surfaces or faces linked by a crease that behaves as an elastic hinge, we carefully shape and anneal a crease within a polymer sheet and study its mechanical response. First, we…
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
Soft and biological matter come in a variety of shapes and geometries. When soft surfaces that do not fit into each other due to a mismatch in Gaussian curvatures form an interface, beautiful geometry-induced patterns emerge. In this paper,…
Instabilities in thin elastic sheets, such as wrinkles, are of broad interest both from a fundamental viewpoint and also because of their potential for engineering applications. Nematic liquid crystal elastomers offer a new form of control…
Surface growth, i.e., the addition or removal of mass from the boundary of a solid body, occurs in a wide range of processes, including the growth of biological tissues, solidification and melting, and additive manufacturing. To understand…
Geometric problems are usually formulated by means of (exterior) differential systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks for regular solutions. Here we adopt a dual…