1,720,993 research outputs found
Finite-scale Microstructures and Metastability In One-dimensional Elasticity
No full textThis paper addresses the non-uniqueness pointed out by Ericksen in his classical analysis of the equilibrium of a one-dimensional elastic bar with non-convex energy [1]. Following some previous work in this area, we suitably regularize the problem in order to investigate this degenerancy. Our approach gives an explicit framework for the the study of the rich variety of finite-scale equilibrium microstructures for the bar in a hard loading device, and their stability properties. In this way we clarify the role of interfacial energy in creating finite-scale microstructures, by considering the combined effect of the oscillation-inducing and oscillation-inhibiting terms in the energy functional
Ericksen's bar revisited: Energy wiggles
No full textThis paper addresses the non-uniqueness pointed out by Ericksen in his classical analysis of the equilibrium of a one-dimensional elastic bar with non-convex energy. According to Ericksen, for the bar in a hard device, the piecewise constant functions delivering the global minimum of the energy can have an arbitrary number N of discontinuities in strain (phase-boundaries). Following some previous work in this area, we regularize the problem in order to resolve this degeneracy. We add two non-local terms to the energy density: one depends on the high (second) derivatives of the displacement, the other contains low (zero) derivatives. The low-derivative term (scaled with a constant beta) introduces a strong non-locality, and simulates a three-dimensional interaction with the loading device, forcing the formation of layered microstructures in the process of energy minimization. The high-derivative (strain-gradient) term (scaled with a different constant alpha), represents a surface energy contribution which penalizes the formation of phase interfaces and prevents the infinite refinement of microstructures. In our description we consider the positions of interfaces as variables. This singles out in a natural way an infinite number of finite-dimensional subspaces, where all the essential nonlinearity is concentrated. In this way we can calculate explicitly the local minimizers (metastable states) and their energy, which turns out to be a multi-valued function of the interface positions and the imposed overall strain d. Our approach thus gives an explicit framework for the study of the rich variety of finite-scale equilibrium microstructures for the bar and their stability properties, This allows for the study of a number of properties of phase transitions in solids; in particular their hysteretic behavior. Among our goals is the investigation of the phase diagram of the system, described by the function N(d, alpha, beta) giving the number of phase-boundaries in the absolute minimizer. We observe the somewhat counterintuitive effect that the energy at the global minimum, as a function of the overall strain, generically develops non-smooth oscillations (wiggles). Copyright (C) 1996 Elsevier Science Lt
Macro and micro cracking in one-dimensional elasticity
No full textIn classical fracture mechanics, the equilibrium configurations of an elastic body are obtained by minimizing an energy functional containing two contributions, bulk and surface. Usually, the bulk energy is convex and the surface energy is concave. While this type of minimization successfully describes macroscopic cracks, it fails to model micro-defects forming a so-called process zone. To describe this phenomenon, we consider, in this paper, a model with a non-concave, `bi-modal' surface energy, which allows the formation of both macro- and micro-cracks. Specifically, we consider the simplest one-dimensional problem for a bar in a hard device and show that if the surface energy is not subadditive, the solution exhibits a new mode of failure with a finite number of micro-cracks coexisting with one fully developed macro-crack. We present an explicit example of a `quantized' micro-cracking with a subsequent development into a single macro-crack
Elastic bars with cohesive energy
No full textMost quasi-static variational models of fracture are based on the splitting of the energy functional into the sum of two terms: bulk, depending on the displacement gradient, and surface, depending on the displacement discontinuities. In this paper we consider the simplest one dimensional problem of this type, a bar stretched by a given axial displacement, and systematically compare two alternative interpretations of the surface energy term. In the first interpretation (elastic model), the surface energy is viewed as a cohesive energy which is stored and can be recovered. In the second (inelastic model), it is irreversibly lost. We show that by assuming an evolution scheme based on local minimization and by varying the convexity-concavity properties of the surface energy the elastic model can reproduce a broad class of macroscopic material responses which have been traditionally treated as unrelated. These responses are associated with monotone loading and range from brittle fracture to rate independent plasticity. However, a realistic description for both loading and unloading is achieved only within the inelastic model
A one-dimensional model for localized and distributed failure
No full textFor an elastic body with limited strength, the equilibrium configurations can be obtained by minimization of an energy functional containing two contributions, bulk and cohesive : the bulk energy is a function of strain and the cohesive energy is a function of the relative displacement on a surface of discontinuity. In the present communication we consider the simplest one-dimensional problem for a bar with this type of energy in a hard device.
We assume that the bulk energy is convex, and we vary the concavity propertiess of the cohesive energy, obtaining thereby three distinct modes of failure. If the cohesive energy is concave for all admissible displacements, failure occurs with the formation of a single crack, and the opening of the crack may be either abrupt or gradual, depending on the length of the bar. If the cohesive energy is concave at large displacements but convex at the origin, the deformation may progress at constant stress (yielding), through formation of an infinite numer of infinitesimal cracks (structured deformation). Finally, when the cohesive energy is characterized by two domains of concavity, (in the vicinity, and far away from the origin), separated by a domain of convexity, fracture procedes through a successive formation of a finite number of cracks of small but finite size. We conjecture that the different modes of fracture, produced by this simple model, may be associated with various experimentally well-documented regimes of localized and distributed damage
Mechanics of reversible unzipping
No full textWe study the mechanics of a reversible decohesion (unzipping) of an elastic layer subjected to quasi-static end-point loading. At the micro level the system is simulated by an elastic chain of particles interacting with a rigid foundation through breakable springs. Such system can be viewed as prototypical for the description of a wide range of phenomena from peeling of polymeric tapes, to rolling of cells, working of Gecko's fibrillar structures and denaturation of DNA. We construct a rigorous continuum limit of the discrete model which captures both stable and metastable configurations and present a detailed parametric study of the interplay between elastic and cohesive interactions. We show that the model reproduces the experimentally observed abrupt transition from an incremental evolution of the adhesion front to a sudden complete decohesion of a macroscopic segment of the adhesion layer. As the microscopic parameters vary the macroscopic response changes from quasi-ductile to quasi-brittle, with corresponding decrease in the size of the adhesion hysteresis. At the micro-scale this corresponds to a transition from a 'localized' to a 'diffuse' structure of the decohesion front (domain wall). We obtain an explicit expression for the critical debonding threshold in the limit when the internal length scales are much smaller than the size of the system. The achieved parametric control of the microscopic mechanism can be used in the design of new biological inspired adhesion devices and machines
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Volume changes during active shape fluctuations in cells
Full text linkCells modify their volume in response to changes in osmotic pressure but it is usually assumed that other active shape variations do not involve significant volume fluctuations. Here we report experiments demonstrating that water transport in and out of the cell is needed for the formation of blebs, commonly observed protrusions in the plasma membrane driven by cortex contraction. We develop and simulate a model of fluid mediated membrane-cortex deformations and show that a permeable membrane is necessary for bleb formation which is otherwise impaired. Taken together our experimental and theoretical results emphasize the subtle balance between hydrodynamics and elasticity in actively driven cell morphological changes
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