Related papers: On the Microscopic Foundations of Elasticity
Stressed dislocation pattern formation in crystal plasticity at finite deformation is demonstrated for the first time. Size effects are also demonstrated within the same mathematical model. The model involves two extra material parameters…
We investigate by exact optimization method properties of two- and three-dimensional systems of elastic lines in presence of splayed columnar disorder. The ground state of many lines is separable both in 2d and 3d leading to a random walk…
Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An…
In comparative and developmental neuroanatomy one encounters questions regarding the deformation of neural tissue under stress. The motivation of this note is an observation (Barbas {\it et al}) that at cortical folds or gyri, the layers of…
The generalized elastic model encompasses several physical systems such as polymers, membranes, single file systems, fluctuating surfaces and rough interfaces. We consider the case of an applied localized potential, namely an external force…
The linear response of two-dimensional amorphous elastic bodies to an external delta force is determined in analogy with recent experiments on granular aggregates. For the generated forces, stress and displacement fields, we find strong…
Stress-stress correlations in crystalline solids with long-range order can be straightforwardly derived using elasticity theory. In contrast, the `emergent elasticity' of amorphous solids, rigid materials characterized by an underlying…
The goal of quantitative elastography is to identify biomechanical parameters from interior displacement data, which are provided by other modalities, such as ultrasound or magnetic resonance imaging. In this paper, we analyze the stability…
Soft solids with tunable mechanical response are at the core of new material technologies, but a crucial limit for applications is their progressive aging over time, which dramatically affects their functionalities. The generally accepted…
Predicting when rupture occurs or cracks progress is a major challenge in numerous elds of industrial, societal and geophysical importance. It remains largely unsolved: Stress enhancement at cracks and defects, indeed, makes the macroscale…
An extremal model for the plasticity of amorphous materials is studied in a simple two-dimensional anti-plane geometry. The steady-state is analyzed through numerical simulations. Long-range spatial and temporal correlations in local slip…
It is shown that the dynamics of a two-dimensional crystal with a finite concentration of dislocations, as well as vacancy and interstitial defects, is governed by the hydrodynamic equations of a viscoelastic medium. At the longest length…
This paper presents an analytical study about the behavior of arbitrary shaped and sized non-cohesive two-dimensional granular materials. Several mechanical properties and relations are unraveled by connecting micro and macro scales in an…
A partially-wetting liquid can deform the underlying elastic substrate upon which it rests. This situation requires the development of theoretical models to describe the wetting forces imparted by the drop onto the solid substrate,…
Granular elasticity, an elasticity theory useful for calculating static stress distribution in granular media, is generalized to the dynamic case by including the plastic contribution of the strain. A complete hydrodynamic theory is derived…
We propose an extended kinematics of nominally elastic continuum solids allowing one to describe their mechanical interaction with micro-scale loading devices. The main new ingredient is the concept of a micro-displacement tensor which…
Unlike macroscopic multistable mechanical systems such as snap bracelets or elastic shells that must be physically manipulated into various conformations, microscopic systems can undergo spontaneous conformation switching between…
Most theories and applications of elasticity rely on an energy function that depends on the strains from which the stresses can be derived. This is the traditional setting of Green elasticity, also known as hyper-elasticity. However, in its…
We formulate a phenomenological elasto-plastic theory to describe a solid undergoing a structural transition from a square (p4mm) to an oblique (p2) lattice in two dimensions. Within our theory, the components of the strain may be…
We consider the topic of linearization of finite elasticity for pure traction problems. We characterize the variational limit for the approximating sequence of rescaled nonlinear elastic energies. We show that the limiting minimal value can…