Nonlinear lattice model of viscoelastic Mode III fracture

We study the effect of general nonlinear force laws in viscoelastic lattice models of fracture, focusing on the existence and stability of steady-state Mode III cracks. We show that the hysteretic behavior at small driving is very sensitive to the smoothness of the force law. At large driving, we find a Hopf bifurcation to a straight crack whose velocity is periodic in time. The frequency of the unstable bifurcating mode depends on the smoothness of the potential, but is very close to an exact period-doubling instability. Slightly above the onset of the instability, the system settles into a exactly period-doubled state, presumably connected to the aforementioned bifurcation structure. We explicitly solve for this new state and map out its velocity-driving relation

Fracture precursors in disordered systems

A two-dimensional lattice model with bond disorder is used to investigate the fracture behaviour under stress-controlled conditions. Although the cumulative energy of precursors does not diverge at the critical point, its derivative with respect to the control parameter (reduced stress) exhibits a singular behaviour. Our results are nevertheless compatible with previous experimental findings, if one restricts the comparison to the (limited) range accessible in the experiment. A power-law avalanche distribution is also found with an exponent close to the experimental values.Comment: 4 pages, 5 figures. Submitted to Europhysics Letter

Phase-Field Model of Mode III Dynamic Fracture

We introduce a phenomenological continuum model for mode III dynamic fracture that is based on the phase-field methodology used extensively to model interfacial pattern formation. We couple a scalar field, which distinguishes between ``broken'' and ``unbroken'' states of the system, to the displacement field in a way that consistently includes both macroscopic elasticity and a simple rotationally invariant short scale description of breaking. We report two-dimensional simulations that yield steady-state crack motion in a strip geometry above the Griffith threshold.Comment: submitted to PR

Dynamical stability of the crack front line

Dynamical stability of the crack front line that propagates between two plates is studied numerically using the simple two-dimensional mass-spring model. It is demonstrated that the straight front line is unstable for low speed while it becomes stable for high speed. For the uniform model, the roughness exponent in the slower speed region is fairly constant around 0.4 and there seems to be a rough-smooth transition at a certain speed. For the inhomogeneous case with quenched randomness, the transition is gradual.Comment: 14 pages, 7 figure

The Classification of Obsessive–Compulsive and Related Disorders in the ICD-11

Background To present the rationale for the new Obsessive–Compulsive and Related Disorders (OCRD) grouping in the Mental and Behavioural Disorders chapter of the Eleventh Revision of the World Health Organization’s International Classification of Diseases and Related Health Problems (ICD-11), including the conceptualization and essential features of disorders in this grouping. Methods Review of the recommendations of the ICD-11 Working Group on the Classification for OCRD. These sought to maximize clinical utility, global applicability, and scientific validity. Results The rationale for the grouping is based on common clinical features of included disorders including repetitive unwanted thoughts and associated behaviours, and is supported by emerging evidence from imaging, neurochemical, and genetic studies. The proposed grouping includes obsessive–compulsive disorder, body dysmorphic disorder, hypochondriasis, olfactory reference disorder, and hoarding disorder. Body-focused repetitive behaviour disorders, including trichotillomania and excoriation disorder are also included. Tourette disorder, a neurological disorder in ICD-11, and personality disorder with anankastic features, a personality disorder in ICD-11, are recommended for cross-referencing. Limitations Alternative nosological conceptualizations have been described in the literature and have some merit and empirical basis. Further work is needed to determine whether the proposed ICD-11 OCRD grouping and diagnostic guidelines are mostly likely to achieve the goals of maximizing clinical utility and global applicability. Conclusion It is anticipated that creation of an OCRD grouping will contribute to accurate identification and appropriate treatment of affected patients as well as research efforts aimed at improving our understanding of the prevalence, assessment, and management of its constituent disorders

Continuum field description of crack propagation

We develop continuum field model for crack propagation in brittle amorphous solids. The model is represented by equations for elastic displacements combined with the order parameter equation which accounts for the dynamics of defects. This model captures all important phenomenology of crack propagation: crack initiation, propagation, dynamic fracture instability, sound emission, crack branching and fragmentation.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett. Additional information can be obtained from http://gershwin.msd.anl.gov/theor

Evolution of avalanche conducting states in electrorheological liquids

Charge transport in electrorheological fluids is studied experimentally under strongly nonequlibrium conditions. By injecting an electrical current into a suspension of conducting nanoparticles we are able to initiate a process of self-organization which leads, in certain cases, to formation of a stable pattern which consists of continuous conducting chains of particles. The evolution of the dissipative state in such system is a complex process. It starts as an avalanche process characterized by nucleation, growth, and thermal destruction of such dissipative elements as continuous conducting chains of particles as well as electroconvective vortices. A power-law distribution of avalanche sizes and durations, observed at this stage of the evolution, indicates that the system is in a self-organized critical state. A sharp transition into an avalanche-free state with a stable pattern of conducting chains is observed when the power dissipated in the fluid reaches its maximum. We propose a simple evolution model which obeys the maximum power condition and also shows a power-law distribution of the avalanche sizes.Comment: 15 pages, 6 figure

Dynamics of Viscoplastic Deformation in Amorphous Solids

We propose a dynamical theory of low-temperature shear deformation in amorphous solids. Our analysis is based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. These numerical simulations reveal behavior typical of metallic glasses and other viscoplastic materials, specifically, reversible elastic deformation at small applied stresses, irreversible plastic deformation at larger stresses, a stress threshold above which unbounded plastic flow occurs, and a strong dependence of the state of the system on the history of past deformations. Microscopic observations suggest that a dynamically complete description of the macroscopic state of this deforming body requires specifying, in addition to stress and strain, certain average features of a population of two-state shear transformation zones. Our introduction of these new state variables into the constitutive equations for this system is an extension of earlier models of creep in metallic glasses. In the treatment presented here, we specialize to temperatures far below the glass transition, and postulate that irreversible motions are governed by local entropic fluctuations in the volumes of the transformation zones. In most respects, our theory is in good quantitative agreement with the rich variety of phenomena seen in the simulations.Comment: 16 pages, 9 figure

Nonequilibrium brittle fracture propagation: Steady state, oscillations and intermittency

A minimal model is constructed for two-dimensional fracture propagation. The heterogeneous process zone is presumed to suppress stress relaxation rate, leading to non-quasistatic behavior. Using the Yoffe solution, I construct and solve a dynamical equation for the tip stress. I discuss a generic tip velocity response to local stress and find that noise-free propagation is either at steady state or oscillatory, depending only on one material parameter. Noise gives rise to intermittency and quasi-periodicity. The theory explains the velocity oscillations and the complicated behavior seen in polymeric and amorphous brittle materials. I suggest experimental verifications and new connections between velocity measurements and material properties.Comment: To appear in Phys. Rev. Lett., 6 pages, self-contained TeX file, 3 postscript figures upon request from author at [email protected] or [email protected], http://cnls-www.lanl.gov/homepages/rafi/rafindex.htm

Pattern formation in 2-frequency forced parametric waves

We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with 2 commensurate frequencies. The spatio-temporal behavior of 4 qualitatively different types of superlattice patterns is described in detail. These states are generated via a number of different 3--wave resonant interactions. They occur either as symmetry--breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two primary unstable modes generated by the two forcing frequencies. A coherent picture of these states together with the phase space in which they appear is presented. In addition, we describe a number of new superlattice states generated by 4--wave interactions that arise when symmetry constraints rule out 3--wave resonances.Comment: The paper contains 34 pages and 53 figures and provides an extensive review of both the theoretical and experimental work peformed in this syste