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Equilibrium Response (equilibrium + response)
Selected AbstractsA robust algorithm for configurational-force-driven brittle crack propagation with R-adaptive mesh alignmentINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2007C. Miehe Abstract The paper considers a variational formulation of brittle fracture in elastic solids and proposes a numerical implementation by a finite element method. On the theoretical side, we outline a consistent thermodynamic framework for crack propagation in an elastic solid. It is shown that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global Clausius,Planck inequality in the sense of Coleman's method. Here, the canonical direction of the crack propagation associated with the classical Griffith criterion is the direction of the material configurational force which maximizes the local dissipation at the crack tip and minimizes the incremental energy release. On the numerical side, we exploit this variational structure in terms of crack-driving configurational forces. First, a standard finite element discretization in space yields a discrete formulation of the global dissipation in terms configurational nodal forces. As a consequence, the constitutive setting of crack propagation in the space-discretized finite element context is naturally related to discrete nodes of a typical finite element mesh. Next, consistent with the node-based setting, the discretization of the evolving crack discontinuity is performed by the doubling of critical nodes and interface segments of the mesh. Critical for the success of this procedure is its embedding into an r-adaptive crack-segment reorientation procedure with configurational-force-based directional indicator. Here, successive crack releases appear in discrete steps associated with the given space discretization. These are performed by a staggered loading,release algorithm of energy minimization at frozen crack state followed by the successive crack releases at frozen deformation. This constitutes a sequence of positive-definite discrete subproblems with successively decreasing overall stiffness, providing an extremely robust algorithmic setting in the postcritical range. We demonstrate the performance of the formulation by means of representative numerical simulations. Copyright © 2007 John Wiley & Sons, Ltd. [source] Facile synthesis, characterization, and potential applications of two kinds of polymeric pH indicators: Phenolphthalein formaldehyde and o -cresolphthalein formaldehydeJOURNAL OF POLYMER SCIENCE (IN TWO SECTIONS), Issue 5 2005Zhihong Liu Abstract Two kinds of applicable polymeric pH indicators were synthesized by the reaction of phenolphthalein and o -cresolphthalein with formaldehyde under alkaline conditions by a one-pot method. The synthesized products were fully characterized with Fourier transform infrared, 1H NMR, ultraviolet,visible spectroscopy, and gel permeation chromatography. The results indicated that the reaction was a typical phenol formaldehyde reaction. The dosage of formaldehyde and the reaction time were well controlled to obtain soluble polymers, instead of crosslinked products. The polymeric-pH-indicator-immobilized poly(vinyl alcohol) (PVA) membranes were easily fabricated and had good long-term stability under highly basic conditions and a fast equilibrium response. Moreover, the phenolphthalein formaldehyde immobilized PVA membrane had a linear response from pH 10.0 to 14.0, and so it has promise as a optical transducer for high pH value determinations. The o -cresolphthalein formaldehyde immobilized PVA membrane had a nonlinear response from pH 9.0 to 13.0. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1019,1027, 2005 [source] Diagnosis of climate models in terms of transient climate response and feedback response timeATMOSPHERIC SCIENCE LETTERS, Issue 1 2008David G. Andrews Abstract Climate models have traditionally been characterised by their climate sensitivity (equilibrium response to a doubling of CO2) and their ocean heat uptake. Together these determine a third property: the transient climate response to a linear increase in radiative forcing. A fourth property, the feedback response time is introduced here and shown to provide a complementary diagnostic of climate model behaviour. In particular, it demonstrates that the discrepancy between recent climate observations and the general circulation models in the ,IPCC ensemble' primarily arises because the models are undersampling the range of transient climate responses consistent with recent attributable greenhouse warming. Copyright © 2007 Royal Meteorological Society [source] Rheological characteristics of solid,fluid transition in dry granular dense flows: A thermodynamically consistent constitutive model with a pressure-ratio order parameterINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2010Chung Fang Abstract Dry granular flows are characterized as quasi-static, dense and collisional states by the interactions among the grains, which is indexed macroscopically by an internal variable, called the order parameter defined as the square root of the static pressure to the total pressure. The solid,fluid state transition is regarded as a second-order phase transition process, and is described by a kinematic evolution of the order parameter. The thermodynamic analysis, based on the Müller,Liu entropy principle, is employed to deduce the equilibrium responses of the constitutive equations, while the dynamic responses are postulated on the basis of a quasi-linear and the second-order Ginzburg,Landau phase transition theories. The obtained model is applied to study the rheological characteristics of a dry granular dense flow between two infinite parallel plates, of which the results are compared with those from DEM simulations to estimate the model validity. The present study provides a general framework for the theoretical justifications on the thermodynamic consistencies of order-parameter-based constitutive models, and can be extended to flows in quasi-static or collisional states. Copyright © 2009 John Wiley & Sons, Ltd. [source] | ||||||||||