Introduction of Mechanics of Continua

Prager, William; Gerstle, Kurt H.

doi:10.1115/1.3640581

Cited by 65 publications

(95 citation statements)

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“…Bingham's equation for a viscoplastic material under uniaxial stress was generalized by Hohenemser and Prager (1932), Prager (1937Prager ( , 1961 and Oldroyd (1947) for a multiaxial state of stress. Our derivation follows that of Prager (1937) and standard treatments of plasticity (Hill, 1950).…”

Section: Constitutive Relationsmentioning

confidence: 99%

An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth

Dumais¹,

Shaw²,

Steele³

et al. 2006

Int. J. Dev. Biol.

185

206

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Plant cell morphogenesis depends critically on two processes: the deposition of new wall material at the cell surface and the mechanical deformation of this material by the stresses resulting from the cell's turgor pressure. We developed a model of plant cell morphogenesis that is a first attempt at integrating these two processes. The model is based on the theories of thin shells and anisotropic viscoplasticity. It includes three sets of equations that give the connection between wall stresses, wall strains and cell geometry. We present an algorithm to solve these equations numerically. Application of this simulation approach to the morphogenesis of tipgrowing cells illustrates how the viscoplastic properties of the cell wall affect the shape of the cell at steady state. The same simulation approach was also used to reproduce morphogenetic transients such as the initiation of tip growth and other non-steady changes in cell shape. Finally, we show that the mechanical anisotropy built into the model is required to account for observed patterns of wall expansion in plant cells.

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Section: Constitutive Relationsmentioning

confidence: 99%

An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth

Dumais¹,

Shaw²,

Steele³

et al. 2006

Int. J. Dev. Biol.

185

206

View full text Add to dashboard Cite

show abstract

“…Our purpose is to outline the basic structure of the theory and to use it as the basis of a natural rate-dependent extension, in the manner of the conventional extensions of classical rate-independent theory [22] to model viscoplastic behavior.…”

Section: Rate-independent Theory and A Natural Viscoplastic Extensionmentioning

confidence: 99%

A model for elastic–viscoplastic deformations of crystalline solids based on material symmetry: Theory and plane-strain simulations

Edmiston¹,

Steigmann²,

Johnson³

et al. 2013

International Journal of Engineering Science

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: A model for the elastic-viscoplastic response of metallic single crystals is developed on the basis of the modern finite-deformation theory of plasticity combined with considerations of material symmetry. This is proposed as an alternative to conventional crystal plasticity theory, based on a decomposition of the plastic deformation rate into a superposition of slips on active slip systems. A simple special case of the general theory, modeling evolving geometrically necessary dislocations and their effect on hardening, is developed and used as the basis of numerical experiments.

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“…Bingham ([104], p. 215) proposed a constitutive relation for a visco-plastic material in a simple shear flow where the relationship between the shear stress (or stress T in general), and the rate of shear (or the symmetric part of the velocity gradient D) is given by the following (see Prager [105], p. 137):…”

Section: Yield Stressmentioning

confidence: 99%

Slag Behavior in Gasifiers. Part II: Constitutive Modeling of Slag

Massoudi

Wang

2013

Energies

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Abstract:The viscosity of slag and the thermal conductivity of ash deposits are among two of the most important constitutive parameters that need to be studied. The accurate formulation or representations of the (transport) properties of coal present a special challenge of modeling efforts in computational fluid dynamics applications. Studies have indicated that slag viscosity must be within a certain range of temperatures for tapping and the membrane wall to be accessible, for example, between 1,300 °C and 1,500 °C, the viscosity is approximately 25 Pa·s. As the operating temperature decreases, the slag cools and solid crystals begin to form. Since slag behaves as a non-linear fluid, we discuss the constitutive modeling of slag and the important parameters that must be studied. We propose a new constitutive model, where the stress tensor not only has a yield stress part, but it also has a viscous part with a shear rate dependency of the viscosity, along with temperature and concentration dependency, while allowing for the possibility of the normal stress effects. In Part I, we reviewed, identify and discuss the key coal ash properties and the operating conditions impacting slag behavior.

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Introduction of Mechanics of Continua

Cited by 65 publications

References 0 publications

An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth

An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth

A model for elastic–viscoplastic deformations of crystalline solids based on material symmetry: Theory and plane-strain simulations

Slag Behavior in Gasifiers. Part II: Constitutive Modeling of Slag

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