Phase field approach with anisotropic interface energy and interface stresses: Large strain formulation

A thermodynamically consistent, large-strain, multi-phase field approach (with consequent interface stresses) is generalized for the case with anisotropic interface (gradient) energy (e.g. an energy density that depends both on the magnitude and direction of the gradients in the phase fields). Such a generalization, if done in the “usual” manner, yields a theory that can be shown to be manifestly unphysical. These theories consider the gradient energy as anisotropic in the deformed configuration, and, due to this supposition, several fundamental contradictions arise. First, the Cauchy stress tensor is non-symmetric and, consequently, violates the moment of momentum principle, in essence the Herring (thermodynamic) torque is imparting an unphysical angular momentum to the system. In addition, this non-symmetric stress implies a violation of the principle of material objectivity. These problems in the formulation can be resolved by insisting that the gradient energy is an isotropic function of the gradient of the order parameters in the deformed configuration, but depends on the direction of the gradient of the order parameters (is anisotropic) in the undeformed configuration. We find that for a propagating nonequilibrium interface, the structural part of the interfacial Cauchy stress is symmetric and reduces to a biaxial tension with the magnitude equal to the temperature- and orientation-dependent interface energy. Ginzburg–Landau equations for the evolution of the order parameters and temperature evolution equation, as well as the boundary conditions for the order parameters are derived. Small strain simplifications are presented. Remarkably, this anisotropy yields a first order correction in the Ginzburg–Landau equation for small strains, which has been neglected in prior works. The next strain-related term is third order. For concreteness, specific orientation dependencies of the gradient energy coefficients are examined, using published molecular dynamics studies of cubic crystals. In order to consider a fully specified system, a typical sixth order polynomial phase field model is considered. Analytical solutions for the propagating interface and critical nucleus are found, accounting for the influence of the anisotropic gradient energy and elucidating the distribution of components of interface stresses. The orientation-dependence of the nonequilibrium interface energy is first suitably defined and explicitly determined analytically, and the associated width is also found. The developed formalism is applicable to melting/solidification and crystal-amorphous transformation and can be generalized for martensitic and diffusive phase transformations, twinning, fracture, and grain growth, for which interface energy depends on interface orientation of crystals from either side

Mind the gap? The persistence of pathological discourses in urban regeneration policy

Urban regeneration policy has historically framed policy problems using a discourse that pathologises areas and spatial communities. Since 2001 in England, and 2002 in Scotland a structural change in policy has occurred where citywide partnerships are now meant overcome structural spatial inequalities, countering pathological explanations. This paper uses historical and discourse analysis to evaluate one of the major community regeneration strategies developed by the Scottish Executive in 2002: Better Communities in Scotland: Closing the Gap. It seeks to ask whether structural change in policy was paralleled by discursive change; what discursive path dependence is evidenced? The text is placed in the historic context of UK urban renewal policies dating back to the launch of the Urban Programme in 1968 and particularly the policy discourse created by the influential Conservative government policy of 1988 New Life for Urban Scotland and the wider discourses of poverty and neighbourhood renewal policy created by Labour governments since 1997. The close textual analysis of the text shows that Better Communities in Scotland continues to pathologise spatial communities. Although this suggests a degree of historical path dependency, the historic breadth of the analysis also problematises simple historical determinism

Lattice Instability during Solid-Solid Structural Transformations under a General Applied Stress Tensor: Example of Si I → Si II with Metallization

The density functional theory was employed to study the stress-strain behavior and elastic instabilities during the solid-solid phase transformation (PT) when subjected to a general stress tensor, as exemplified for semiconducting Si I and metallic Si II, where metallization precedes the PT, so stressed Si I can be a metal. The hydrostatic PT occurs at 76 GPa, while under uniaxial loading it is 11 GPa (3.7 GPa mean pressure), 21 times lower. The Si I → Si II PT is described by a critical value of the phase-field’s modified transformation work, and the PT criterion has only two parameters given six independent stress elements. Our findings reveal novel, more practical synthesis routes for new or known high-pressure phases under predictable nonhydrostatic loading, where competition of instabilities can serve for phase selection rather than free energy minima used for equilibrium processing

Strain-induced phase transformations under compression, unloading, and reloading in a diamond anvil cell

Strain-induced phase transformations (PTs) in a sample under compression, unloading, and reloading in a diamond anvil cell are investigated in detail, by applying finite element method. In contrast to previous studies, the kinetic equation includes the pressure range in which both direct and reverse PTs occur simultaneously. Results are compared to the case when “no transformation” region in the pressure range exists instead, for various values of the kinetic parameters and ratios of the yield strengths of low and high pressure phases. Under unloading (which has never been studied before), surprising plastic flow and reverse PT are found, which were neglected in experiments and change interpretation of experimental results. They are caused both by heterogeneous stress redistribution and transformation-induced plasticity. After reloading, the reverse PT continues followed by intense direct PT. However, PT is less pronounced than after initial compression and geometry of transformed zone changes. In particular, a localized transformed band of a weaker high pressure phase does not reappear in comparison with the initial compression. A number of experimental phenomena are reproduced and interpreted

Social inclusion and valued roles : a supportive framework

The aim of this paper is to examine the concepts of social exclusion, social inclusion and their relevance to health, well-being and valued social roles. The article presents a framework, based on Social Role Valorization (SRV), which was developed initially to support and sustain socially valued roles for those who are, or are at risk of, being devalued within our society. The framework incorporates these principles and can be used by health professionals across a range of practice, as a legitimate starting point from which to support the acquisition of socially valued roles which are integral to inclusio