Stress field around arbitrarily shaped cracks in two-dimensional elastic materials

The calculation of the stress field around an arbitrarily shaped crack in an infinite two-dimensional elastic medium is a mathematically daunting problem. With the exception of few exactly soluble crack shapes the available results are based on either perturbative approaches or on combinations of analytic and numerical techniques. We present here a general solution of this problem for any arbitrary crack. Along the way we develop a method to compute the conformal map from the exterior of a circle to the exterior of a line of arbitrary shape, offering it as a superior alternative to the classical Schwartz-Cristoffel transformation. Our calculation results in an accurate estimate of the full stress field and in particular of the stress intensity factors K_I and K_{II} and the T-stress which are essential in the theory of fracture.Comment: 7 pages, 4 figures, submitted for PR

Dynamics and Instabilities of Planar Tensile Cracks in Heterogeneous Media

The dynamics of tensile crack fronts restricted to advance in a plane are studied. In an ideal linear elastic medium, a propagating mode along the crack front with a velocity slightly less than the Rayleigh wave velocity, is found to exist. But the dependence of the effective fracture toughness $\Gamma(v)$ on the crack velocity is shown to destabilize the crack front if $(d\Gamma)/(dv)<0$. Short wavelength radiation due to weak random heterogeneities leads to this instability at low velocities. The implications of these results for the crack dynamics are discussed.Comment: 12 page

A complete parameterisation of the relative humidity and wavelength dependence of the refractive index of hygroscopic inorganic aerosol particles

Calculations of aerosol radiative forcing require knowledge of wavelength-dependent aerosol optical properties, such as single-scattering albedo. These aerosol optical properties can be calculated using Mie theory from knowledge of the key microphysical properties of particle size and refractive index, assuming that atmospheric particles are well-approximated to be spherical and homogeneous. We provide refractive index determinations for aqueous aerosol particles containing the key atmospherically relevant inorganic solutes of NaCl, NaNO3, (NH4)2SO4, NH4HSO4 and Na2SO4, reporting the refractive index variation with both wavelength (400–650 nm) and relative humidity (from 100 % to the efflorescence value of the salt). The accurate and precise retrieval of refractive index is performed using single-particle cavity ring-down spectroscopy. This approach involves probing a single aerosol particle confined in a Bessel laser beam optical trap through a combination of extinction measurements using cavity ring-down spectroscopy and elastic light-scattering measurements. Further, we assess the accuracy of these refractive index measurements, comparing our data with previously reported data sets from different measurement techniques but at a single wavelength. Finally, we provide a Cauchy dispersion model that parameterises refractive index measurements in terms of both wavelength and relative humidity. Our parameterisations should provide useful information to researchers requiring an accurate and comprehensive treatment of the wavelength and relative humidity dependence of refractive index for the inorganic component of atmospheric aerosol

Spiral cracks in drying precipitates

We investigate the formation of spiral crack patterns during the desiccation of thin layers of precipitates in contact with a substrate. This symmetry-breaking fracturing mode is found to arise naturally not from torsion forces, but from a propagating stress front induced by the fold-up of the fragments. We model their formation mechanism using a coarse-grain model for fragmentation and successfully reproduce the spiral cracks. Fittings of experimental and simulation data show that the spirals are logarithmic, corresponding to constant deviation from a circular crack path. Theoretical aspects of the logarithmic spirals are discussed. In particular we show that this occurs generally when the crack speed is proportional to the propagating speed of stress front.Comment: 4 pages, 5 figures, RevTe

Statistical Physics of Fracture Surfaces Morphology

Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich phenomenology of anomalous scaling. We argue that traditional models of fracture fail to reproduce this rich phenomenology and new ideas and concepts are called for. We present some recent models that introduce the effects of deviations from homogeneous linear elasticity theory on the morphology of fracture surfaces, succeeding to reproduce the multiscaling phenomenology at least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel methods of analysis based on projecting the data on the irreducible representations of the SO(2) symmetry group. It appears that this approach organizes effectively the rich scaling properties. We end up with the proposition of new experiments in which the rotational symmetry is not broken, such that the scaling properties should be particularly simple.Comment: A review paper submitted to J. Stat. Phy

Eigenfracture: An Eigendeformation Approach to Variational Fracture

We propose an approximation scheme for a variational theory of brittle fracture. In this scheme, the energy functional is approximated by a family of functionals depending on a small parameter and on two fields: the displacement field and an eigendeformation field that describes the fractures that occur in the body. Specifically, the eigendeformations allow the displacement field to develop jumps that cost no local elastic energy. However, this local relaxation requires the expenditure of a certain amount of fracture energy. We provide a construction, based on the consideration of ε-neighborhoods of the support of the eigendeformation field, for calculating the right amount of fracture energy associated with the eigendeformation field. We prove the Γ-convergence of the eigendeformation functional sequence, and of finite element approximations of the eigendeformation functionals, to the Griffith-type energy functional introduced in Francfort and Marigo [J. Mech. Phys. Solids, 46 (1998), pp. 1319–1342]. This type of convergence ensures the convergence of eigendeformation solutions, and of finite element approximations thereof, to brittle-fracture solutions. Numerical examples concerned with quasi-static mixed-mode crack propagation illustrate the versatility and robustness of the approach and its ability to predict crack-growth patterns in brittle solids

On the Path of a Quasi-static Crack in Mode III

A method for finding the path of a quasi-static crack growing in a brittle body is presented. The propagation process is modelled by a sequence of discrete steps optimizing the elastic energy released. An explicit relationship between the optimal growing direction and the parameters defining the local elastic field around the tip is obtained for an anti-plane field. This allows to describe a simple algorithm to compute the crack path

The pains of desistance

Desistance is generally presented in a positive light, with themes of ‘making good’ and generativity recurring in the literature. This article reports on two qualitative studies exploring the desistance journeys of two different groups of ex-offenders, drawing attention to the pains of this process. It examines the possible consequences of these ‘pains of desistance’ and how they are linked to three spheres of desistance: act-desistance; identity desistance; and relational desistance. The attempt to achieve act-desistance often led to the pain of isolation for our interviewees, while the clash between the need to achieve identity desistance and a lack of relational desistance (especially on the meso- and macro-levels) meant that they suffered the pain of goal failure. The pains of isolation and goal failure combined to lead to the further pain of hopelessness. Those interviewed were indeed ‘going straight’, but taking this path led many to a limited and often diminished life

Longitudinal associations between keeping a secret and psychosocial adjustment in adolescence

Increasing bodies of evidence suggest that keeping secrets may be detrimental to well-being and adjustment, whereas confiding secrets may alleviate the detriments of secrecy and benefit well-being and adjustment. However, few studies have addressed the consequences of keeping and confiding secrets simultaneously, and even fewer have done so longitudinally. This article reports on a two-wave longitudinal survey study among 278 adolescents (aged 13-18 years) that examined the associations of keeping and confiding a specific secret with psychosocial adjustment. Results confirmed a hypothesized longitudinal contribution of keeping a secret all to oneself to psychosocial problems, including depressive mood, low self-concept clarity, low self-control, loneliness, and poor relationship quality. Furthermore, confiding versus continuing to keep a secret all to oneself was associated with decreased psychosocial problems after six months, whereas starting to keep a secret versus not doing so was associated with increased psychosocial problems. These results suggest that the keeping or confiding of secrets may affect adolescents' psychosocial well-being and adjustment. © 2008 The International Society for the Study of Behavioural Development