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Matthias Fuchs - One of the best experts on this subject based on the ideXlab platform.
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first principles Constitutive Equation for suspension rheology
Physical Review E, 2012Co-Authors: Joseph M Brader, M E Cates, Matthias FuchsAbstract:The imposition of flow can drive a fluid far from equilibrium. Because of the occurrence of long relaxation times, this effect is ubiquitous in complex fluids (colloids, polymers, etc.) whose rheology is of significant technological interest, and also represents an important challenge in nonequilibrium statistical physics. Continuum approaches have provided important insights, using symmetry and other principles to construct or constrain phenomenological Constitutive relations. While the Constitutive Equations of Newtonian fluids and Hookian solids are derivable from fundamental starting points (the theory of linear response based on Onsager’s regression hypothesis), there has been less progress with their nonlinear generalizations for viscoelastic fluids, plastic solids and other strongly deforming soft materials. A central aim of theoretical rheology is thus to derive from the underlying microscopic interactions the Constitutive Equations that relate the stress tensor to the macroscopic deformation history of a material. For entangled polymer melts, the Constitutive Equation of Doi and Edwards [1] has enjoyed considerable success. An analogously general microscopic Constitutive Equation for colloidal dispersions remains conspicuously lacking [2]. Even the simplest hard-sphere colloids in concentrated suspension exhibit a broad range of viscoelastic behavior; alongside to flow-thinning [3] and thickening [4], slow structural relaxation leads to glasses showing a solidlike response, strain hardening or softening, and plastic flow [5]. But, while the linear viscoelastic spectra of colloidal suspensions are fairly well understood [6], only recently has progress been made in nonlinear flow predictions for simple shear [7,8]. Shear represents a relatively weak flow in which material lines grow linearly with time, while in elongational flows such growth is exponential, creating much more severe deformations of material elements. Thus, a description capable of handling arbitrary deformation histories is highly desirable. In the continuum approaches, invariance arguments strongly restrict the
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first principles Constitutive Equation for suspension rheology
Physical Review Letters, 2008Co-Authors: Joseph M Brader, M E Cates, Matthias FuchsAbstract:Using mode-coupling theory, we derive a Constitutive Equation for the nonlinear rheology of dense colloidal suspensions under arbitrary time-dependent homogeneous flow. Generalizing previous results for simple shear, this allows the full tensorial structure of the theory to be identified. Macroscopic deformation measures, such as the Cauchy-Green tensors, thereby emerge. So does a direct relation between the stress and the distorted microstructure, illuminating the interplay of slow structural relaxation and arbitrary imposed flow. We present flow curves for steady planar and uniaxial elongation and compare these to simple shear. The resulting nonlinear Trouton ratios point to a tensorially nontrivial dynamic yield condition for colloidal glasses.
W J Drugan - One of the best experts on this subject based on the ideXlab platform.
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micromechanics based variational estimates for a higher order nonlocal Constitutive Equation and optimal choice of effective moduli for elastic composites
Journal of The Mechanics and Physics of Solids, 2000Co-Authors: W J DruganAbstract:Abstract A generalization of the Hashin–Shtrikman variational formulation to random composites, due to J.R. Willis, is employed to derive micromechanics-based variational estimates for a higher-order nonlocal Constitutive Equation relating the ensemble averages of stress and strain, for a class of random linear elastic composite materials. We analyze two-phase composites with any isotropic and statistically uniform distribution of phases (which themselves may have arbitrary shape and anisotropy), within a formulation accounting for one- and two-point probabilities, and derive an explicit nonlocal Constitutive Equation that includes terms up through the fourth gradient of average strain. The analysis is carried out first for an arbitrary comparison medium. Then, a new approach is outlined and applied which employs the nonlocal correction to determine the optimal choice of comparison medium, and hence the optimal effective modulus tensor (as well as the optimal tensor coefficients of the nonlocal terms) for the amount of statistical information employed. The new higher order analysis provides a highly accurate nonlocal Constitutive Equation, valid down to quite small volume size scales and to rather strong variations of average strain with position. Among several applications illustrated, it permits accurate analytical assessment of the remarkably small predictions derived by Drugan and Willis (1996. Journal of the Mechanics and Physics of Solids 44, 497–524) of the minimum representative volume element (RVE) size needed for accuracy of the standard constant-effective-modulus macroscopic Constitutive Equation for elastic matrix-inclusion composites that have spherical inclusions/voids. It also affords an analytical assessment of the improved (i.e., reduced) minimum RVE size scale, compared to a standard constant-effective-modulus Constitutive Equation, to which the leading-order nonlocal Constitutive Equation derived by Drugan and Willis applies. This improvement is shown to be dramatic in some example cases.
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a micromechanics based nonlocal Constitutive Equation and estimates of representative volume element size for elastic composites
Journal of The Mechanics and Physics of Solids, 1996Co-Authors: W J Drugan, J R WillisAbstract:A variational formulation is employed to derive a micromechanics-based, explicit nonlocal Constitutive Equation relating the ensemble averages of stress and strain for a class of random linear elastic composite materials. For two-phase composites with any isotropic and statistically uniform distribution of phases (which themselves may have arbitrary shape and anisotropy), we show that the leading-order correction to a macroscopically homogeneous Constitutive Equation involves a term proportional to the second gradient of the ensemble average of strain. This nonlocal Constitutive Equation is derived in explicit closed form for isotropic material in the one case in which there exists a well-founded physical and mathematical basis for describing the material's statistics: a matrix reinforced (or weakened) by a random dispersion of nonoverlapping identical spheres. By assessing, when the applied loading is spatially-varying, the magnitude of the nonlocal term in this Constitutive Equation compared to the portion of the Equation that relates ensemble average stresses and strains through a constant “overall” modulus tensor, we derive quantitative estimates for the minimum representative volume element (RVE) size, defined here as that over which the usual macroscopically homogeneous “effective modulus” Constitutive models for composites can be expected to apply. Remarkably, for a maximum error of 5% of the constant “overall” modulus term, we show that the minimum RVE size is at most twice the reinforcement diameter for any reinforcement concentration level, for several sets of matrix and reinforcement moduli characterizing large classes of important structural materials. Such estimates seem essential for determining the minimum structural component size that can be treated by macroscopically homogeneous composite material Constitutive representations, and also for the development of a fundamentally-based macroscopic fracture mechanics theory for composites. Finally, we relate our nonlocal Constitutive Equation explicitly to the ensemble average strain energy, and show how it is consistent with the stationary energy principle.
Koichi Hashiguchi - One of the best experts on this subject based on the ideXlab platform.
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Constitutive Equation for Friction
Elastoplasticity Theory, 2020Co-Authors: Koichi HashiguchiAbstract:All bodies in the natural world are exposed to friction phenomena, contacting with other bodies, except for bodies floating in a vacuum. Therefore, it is indispensable to analyze friction phenomena rigorously in addition to the deformation behavior of bodies themselves in analyses of boundary value problems. The friction phenomenon can be formulated as a Constitutive relation in a similar form to that of the elastoplastic Constitutive Equation of materials. A Constitutive Equation for friction with the transition from the static to the kinetic friction and vice versa and the orthotropic and rotational anisotropy is described in this chapter.
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Constitutive Equation for Friction: Subloading-Friction Model
2020Co-Authors: Koichi HashiguchiAbstract:All bodies in the natural world are exposed to friction phenomena, contacting with other bodies, except for bodies floating in a vacuum. Therefore, it is indispensable to analyze friction phenomena rigorously in addition to the deformation behavior of bodies themselves in analyses of boundary value problems. The friction phenomenon can be formulated as a Constitutive relation in a similar form to the elastoplastic Constitutive Equation of materials. A Constitutive Equation for friction with the transition from the static to the kinetic friction and vice versa and the orthotropic and rotational anisotropy is described in this chapter. The stick-slip phenomenon, which is an unstable and intermittent motion caused by the friction, is of importance for the prediction of earthquake and influences on the performance of machinery. It will be also delineated as the application of Constitutive Equation for friction.
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rate dependent inelastic Constitutive Equation the extension of elastoplasticity
International Journal of Plasticity, 2005Co-Authors: Koichi Hashiguchi, Takashi Okayasu, Koshiro SaitohAbstract:A rate-dependent inelastic Constitutive Equation is formulated by extending the elastoplastic Constitutive Equation so as to retain the latter's mathematical structure and thus reduce to the latter Equation at an infinitesimal rate of deformation. That structure differs substantially from that of the over-stress model, the best-known rate-dependent inelastic Constitutive model. The proposed Constitutive model is a type of superposition model, which is premised on the additive decomposition of the inelastic strain rate into the plastic and creep strain rates. The plastic strain rate is formulated so as to become suppressed as the rate of deformation increases but is induced even at the infinite rate of deformation. This is the distinguishing features of this model from the existing superposition models. The present model can describe realistically the rate-dependent inelastic deformation for a wide range of strain rates. On the other hand, the over-stress model cannot predict appropriately the difference of mechanical response due to the rate of deformation, especially being inapplicable to the description of deformation at high rate of deformation as known from the unrealistic prediction of the infinite strength at an infinite rate of deformation. The proposed model is applied to various metals, and its adequacy is verified through comparisons with various test data under a wide variety of strain rates and temperatures.
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Elastoplastic Constitutive Equation with tangential stress rate effect
International Journal of Plasticity, 2001Co-Authors: Koichi HashiguchiAbstract:Abstract In traditional elastoplastic Constitutive Equation with a single smooth plastic potential surface, the plastic stretching is independent of the tangential stress rate , i.e. the component of stress rate which is tangential to the yield surface. This traditional model predicts an unrealistically stiff response when a loading path deviates significantly from the proportional loading. In order to overcome this defect various Constitutive models have been proposed. However, a pertinent model applicable to the description of the deformation behavior in a general loading process has not been proposed up to the present. In this article, an elastoplastic Constitutive Equation with the inelastic stretching induced by the deviatoric stress rate component tangential to the subloading surface is formulated by extending the subloading surface model with a smooth elastic–plastic transition. This model is applicable to the analysis of deformation in a general loading process of materials with an arbitrary yield surface. Based on this Equation, a Constitutive Equation of metals with isotropic-kinematic hardening is formulated and its basic characteristics are examined in detail.
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fundamentals in Constitutive Equation continuity and smoothness conditions and loading criterion
Soils and Foundations, 2000Co-Authors: Koichi HashiguchiAbstract:The continuity and smoothness conditions and the loading criterion are the most fundamental elements in Constitutive Equations for reversible/irreversible deformation, which have been defined and formulated by the author (Hashiguchi, 1993a, b, 1994). In this article the continuity and smoothness conditions are reviewed in detail. Further, the loading criterion for plastic stretching in the Constitutive Equation with the plastic potential surface is derived from the requirement that the proportionality factor in the plastic potential flow rule is positive ; this would generally be applicable even to Constitutive Equations for the description of time-dependent elastoplastic deformation. In addition, the defects caused by the violation of continuity and smoothness conditions are verified illustrating unrealistic deformation behaviors predicted by the conventional and well-known cyclic plasticity models.
Joseph M Brader - One of the best experts on this subject based on the ideXlab platform.
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first principles Constitutive Equation for suspension rheology
Physical Review E, 2012Co-Authors: Joseph M Brader, M E Cates, Matthias FuchsAbstract:The imposition of flow can drive a fluid far from equilibrium. Because of the occurrence of long relaxation times, this effect is ubiquitous in complex fluids (colloids, polymers, etc.) whose rheology is of significant technological interest, and also represents an important challenge in nonequilibrium statistical physics. Continuum approaches have provided important insights, using symmetry and other principles to construct or constrain phenomenological Constitutive relations. While the Constitutive Equations of Newtonian fluids and Hookian solids are derivable from fundamental starting points (the theory of linear response based on Onsager’s regression hypothesis), there has been less progress with their nonlinear generalizations for viscoelastic fluids, plastic solids and other strongly deforming soft materials. A central aim of theoretical rheology is thus to derive from the underlying microscopic interactions the Constitutive Equations that relate the stress tensor to the macroscopic deformation history of a material. For entangled polymer melts, the Constitutive Equation of Doi and Edwards [1] has enjoyed considerable success. An analogously general microscopic Constitutive Equation for colloidal dispersions remains conspicuously lacking [2]. Even the simplest hard-sphere colloids in concentrated suspension exhibit a broad range of viscoelastic behavior; alongside to flow-thinning [3] and thickening [4], slow structural relaxation leads to glasses showing a solidlike response, strain hardening or softening, and plastic flow [5]. But, while the linear viscoelastic spectra of colloidal suspensions are fairly well understood [6], only recently has progress been made in nonlinear flow predictions for simple shear [7,8]. Shear represents a relatively weak flow in which material lines grow linearly with time, while in elongational flows such growth is exponential, creating much more severe deformations of material elements. Thus, a description capable of handling arbitrary deformation histories is highly desirable. In the continuum approaches, invariance arguments strongly restrict the
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first principles Constitutive Equation for suspension rheology
Physical Review Letters, 2008Co-Authors: Joseph M Brader, M E Cates, Matthias FuchsAbstract:Using mode-coupling theory, we derive a Constitutive Equation for the nonlinear rheology of dense colloidal suspensions under arbitrary time-dependent homogeneous flow. Generalizing previous results for simple shear, this allows the full tensorial structure of the theory to be identified. Macroscopic deformation measures, such as the Cauchy-Green tensors, thereby emerge. So does a direct relation between the stress and the distorted microstructure, illuminating the interplay of slow structural relaxation and arbitrary imposed flow. We present flow curves for steady planar and uniaxial elongation and compare these to simple shear. The resulting nonlinear Trouton ratios point to a tensorially nontrivial dynamic yield condition for colloidal glasses.
Gillo Giuliano - One of the best experts on this subject based on the ideXlab platform.
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Constitutive Equation for superplastic ti 6al 4v alloy
Materials & Design, 2008Co-Authors: Gillo GiulianoAbstract:Abstract Superplasticity is the capability of some materials to exhibit large plastic deformations prior to failure. Structural superplasticity is observed in fine-grained alloys (the average grain size does not exceed 10 μm) under proper conditions of: • high temperature (greater than about one-half the absolute melting point); • a controlled strain-rate (within the strain-rate range 10 −4 to 10 −2 s −1 ). Commercial applications of superplastic forming are restricted to aluminium and titanium alloys. In the aircraft and automotive industries, superplastic forming shows promise as a main approach for producing light, complex-shaped parts. This paper describes a method to determine the material constants of superplastic alloys from a free forming test at constant pressure. In the finite element simulation the Constitutive Equation based on power law with hardening variables containing significant physical elements is chosen to fit the true stress, true strain and true strain-rate obtained from experimental data for Ti–6Al–4V at 1200 K. The finite element simulation of the free forming process is used to examine the validity of the suggested method.