On the contribution of grain boundary sliding type creep to firn densification – an assessment using an optimization approach

Simulation approaches to firn densification often rely on the assumption that grain boundary sliding is the leading process driving the first stage of densification. Alley (1987) first developed a process-based material model of firn that describes this process. However, often so-called semi-empirical models are favored over the physical description of grain boundary sliding owing to their simplicity and the uncertainties regarding model parameters. In this study, we assessed the applicability of the grain boundary sliding model of Alley (1987) to firn using a numeric firn densification model and an optimization approach, for which we formulated variants of the constitutive relation of Alley (1987). An efficient model implementation based on an updated Lagrangian numerical scheme enabled us to perform a large number of simulations to test different model parameters and identify the simulation results that best reproduced 159 firn density profiles from Greenland and Antarctica. For most of the investigated locations, the simulated and measured firn density profiles were in good agreement. This result implies that the constitutive relation of Alley (1987) characterizes the first stage of firn densification well when suitable model parameters are used. An analysis of the parameters that result in the best agreement revealed a dependence on the mean surface mass balance. This finding may indicate that the load is insufficiently described, as the lateral components of the stress tensor are usually neglected in one-dimensional models of the firn column.

A modified Zerilli–Armstrong constitutive model for simulating severe plastic deformation of a steel alloy

A modified Zerilli–Armstrong model has been proposed and validated in previous works for simulating distinct deformation mechanisms of continuous-shear and shear-localization during severe plastic deformation of a face centered cubic alloy. In this paper, the validity of the modified Zerilli–Armstrong model has been further tested by using it for modeling the severe plastic deformation of another face centered cubic material, a steel alloy. In particular, the modified Zerilli–Armstrong model is used as a constitutive relation for simulating behavior of AISI 1045 steel alloy while undergoing severe plastic deformation through orthogonal and plane-strain machining. Accordingly, the performance of the constitutive relation in predicting flow stress distribution along the primary shear zone is validated by comparing with forecasts made using the distributed primary zone deformation, the original Zerilli-Armstrong and Johnson-Cook models. Furthermore, finite element simulations of orthogonal cutting of this steel alloy were carried out, and good agreement was observed between the predicted chip morphology and attendant cutting forces with experimental values reported in literature for a range of cutting conditions. The force predictions also fared better compared to those predicted by using the Zerilli-Armstrong and Johnson-Cook models. These validations provide further corroboration of using the modified Zerilli–Armstrong model as a constitutive relation for simulating the behavior of face-centered cubic materials under conditions of high plastic strains and also high strain-rates.

A convenient formulation of Sadowsky's model for elastic ribbons

Elastic ribbons are elastic structures whose length-to-width and width-to-thickness aspect ratios are both large. Sadowsky proposed a one-dimensional model for ribbons featuring a nonlinear constitutive relation for bending and twisting: it brings in both rich behaviours and numerical difficulties. By discarding non-physical solutions to this constitutive relation, we show that it can be inverted; this simplifies the system of differential equations governing the equilibrium of ribbons. Based on the inverted form, we propose a natural regularization of the constitutive law that eases the treatment of singularities often encountered in ribbons. We illustrate the approach with the classical problem of the equilibrium of a Möbius ribbon, and compare our findings with the predictions of the Wunderlich model. Overall, our approach provides a simple method for simulating the statics and the dynamics of elastic ribbons.

ENTIRE-REGION CONSTITUTIVE RELATION FOR TRELOAR'S DATA

ABSTRACT Hyperelastic materials can experience a large deformation process. A constitutive relation suitable for an entire region from small, moderate, to large deformations is of great importance for practical applications such as fracture problems. Treloar's data are first investigated, and the tension curve is divided into three regimes: small-to-moderate regime, strain-hardening regime, and limiting-chain regime. Next, the modeling theory of hyperelastic materials is introduced, and the tensile behaviors of basic energy functions are analyzed for different deformation regimes. Finally, a successive procedure is suggested to establish an entire-region constitutive relation and then applied to Treloar's data. The present constitutive relation can maintain the initial shear modulus while the experimental data are satisfactorily predicted. The present procedure is simple and feasible and hence applicable to other hyperelastic materials when their entire-region constitutive relations are studied based on experimental data.

Is Indian sedition law colonial? J. F. Stephen and the jurisprudence on free speech

This article critically evaluates the characterisation of sedition law as colonial by analysing the arguments made by J. F. Stephen in opposing such a claim. While Stephen obfuscated the close links between the sedition law and the requirements of colonial governance, he made a persuasive case for how the sedition law was completely consistent with British ideas of liberty, utility, and the rule of law. Stephen’s arguments about legitimate limits to political liberties, particularly his critique of J. S. Mill in this regard, offer us an opportunity to question the presumed antithesis between colonial and metropolitan jurisprudence and trace their shared origins in British political thought. To that end, with Stephen as an interlocutor, this article critically analyses themes such as the defence of empire, colonialism, and the idea of improvement within a wider set of writings by British political philosophers, to arrive at an alternative understanding of British political liberalism. My article concludes that rather than ‘colonial difference’, the constitutive relation between sedition law and liberal jurisprudence better explains the prevalence of similar authoritarian laws within democratic regimes across the globe.

Analysis and extension of the quadratic constitutive relation for RANS methods

The quadratic constitutive relation was proposed as an extension of minimal complexity to linear eddy-viscosity models in order to improve mean flow predictions by better estimating turbulent stress distributions. However, the successes of this modification have been relatively modest and are limited to improved calculations of flow along streamwise corners, which are influenced by weak secondary vortices. This paper revisits the quadratic constitutive relation in an attempt to explain its capabilities and deficiencies. The success in streamwise corner flows cannot be entirely explained by significant improvements in turbulent stress estimates in general, but is instead due to better prediction of the particular turbulent stress combinations which appear in the mean streamwise vorticity equation. As a consequence of this investigation, a new formulation of turbulent stress modification is proposed, which appears to better predict the turbulent stress distributions for a variety of flows: channel flow, equilibrium boundary layers, pipe flow, separated boundary layers and square duct flow.