ProductsAbaqus/ExplicitAbaqus/CAE Viscous shear behaviorThe resistance to flow of a viscous fluid is described by the following relationship between deviatoric stress and strain rate where is the deviatoric stress, is the deviatoric part of the strain rate, is the viscosity, and is the engineering shear strain rate. Newtonian fluids are characterized by a viscosity that only depends on temperature, . In the more general case of non-Newtonian fluids the viscosity is a function of the temperature and shear strain rate: where is the equivalent shear strain rate. In terms of the equivalent shear stress, , we have: Non-Newtonian fluids can be classified as shear-thinning (or pseudoplastic), when the apparent viscosity decreases with increasing shear rate, and shear-thickening (or dilatant), when the viscosity increases with strain rate. In addition to the Newtonian viscous fluid model, Abaqus/Explicit supports several models of nonlinear viscosity to describe non-Newtonian fluids: power law, Carreau-Yasuda, Cross, Herschel-Bulkley, Powell-Eyring, and Ellis-Meter. Other functional forms of the viscosity can also be specified in tabular format. In addition, in Abaqus/Explicit user subroutine VUVISCOSITY can be used. NewtonianThe Newtonian model is useful to model viscous laminar flow governed by the Navier-Poisson law of a Newtonian fluid, . Newtonian fluids are characterized by a viscosity that depends only on temperature, . You need to specify the viscosity as a tabular function of temperature when you define the Newtonian viscous deviatoric behavior. Input File Usage VISCOSITY, DEFINITION=NEWTONIAN (default) Abaqus/CAE Usage Property module: material editor: Power lawThe power law model is commonly used to describe the viscosity of non-Newtonian fluids. The viscosity is expressed as where is the flow consistency index and is the flow behavior index. When , the fluid is shear-thinning (or pseudoplastic): the apparent viscosity decreases with increasing shear rate. When , the fluid is shear-thickening (or dilatant); and when , the fluid is Newtonian. Optionally, you can place a lower limit, , and/or an upper limit, , on the value of the viscosity computed from the power law. Input File Usage VISCOSITY, DEFINITION=POWER LAW Abaqus/CAE Usage The power law model is not supported in Abaqus/CAE. Carreau-YasudaThe Carreau-Yasuda model describes the shear thinning behavior of polymers. This model often provides a better fit than the power law model for both high and low shear strain rates. The viscosity is expressed as where is the low shear rate Newtonian viscosity, is the infinite shear viscosity (at high shear strain rates), is the natural time constant of the fluid ( is the critical shear rate at which the fluid changes from Newtonian to power law behavior), and represents the flow behavior index in the power law regime. The coefficient is a material parameter. The original Carreau model is recovered when =2. Input File Usage VISCOSITY, DEFINITION=CARREAU-YASUDA Abaqus/CAE Usage The Carreau-Yasuda model is not supported in Abaqus/CAE. CrossThe Cross model is commonly used when it is necessary to describe the low-shear-rate behavior of the viscosity. The viscosity is expressed as where is the Newtonian viscosity, is the infinite shear viscosity (usually assumed to be zero for the Cross model), is the natural time constant of the fluid ( is the critical shear rate at which the fluid changes from Newtonian to power-law behavior), and is the flow behavior index in the power law regime. Input File Usage VISCOSITY, DEFINITION=CROSS Abaqus/CAE Usage The Cross model is not supported in Abaqus/CAE. Herschel-BulkleyThe Herschel-Bulkley model can be used to describe the behavior of viscoplastic fluids, such as Bingham plastics, that exhibit a yield response. The viscosity is expressed as Here is the “yield” stress and is a penalty viscosity to model the “rigid-like” behavior in the very low strain rate regime (), when the stress is below the yield stress, . With increasing strain rates, the viscosity transitions into a power law model once the yield threshold is reached, . The parameters and are the flow consistency and the flow behavior indexes in the power law regime, respectively. Bingham plastics correspond to the case =1. Input File Usage VISCOSITY, DEFINITION=HERSCHEL-BULKLEY Abaqus/CAE Usage The Herschel-Bulkley model is not supported in Abaqus/CAE. Powell-EyringThis model, which is derived from the theory of rate processes, is relevant primarily to molecular fluids but can be used in some cases to describe the viscous behavior of polymer solutions and viscoelastic suspensions over a wide range of shear rates. The viscosity is expressed as where is the Newtonian viscosity, is the infinite shear viscosity, and represents a characteristic time of the measured system. Input File Usage VISCOSITY, DEFINITION=POWELL-EYRING Abaqus/CAE Usage The Powell-Eyring model is not supported in Abaqus/CAE. Ellis-MeterThe Ellis-Meter model expresses the viscosity in terms of the effective shear stress, , as: where is the effective shear stress at which the viscosity is 50% between the Newtonian limit, , and the infinite shear viscosity, , and represents the flow index in the power law regime. Input File Usage VISCOSITY, DEFINITION=ELLIS-METER Abaqus/CAE Usage The Ellis-Meter model is not supported in Abaqus/CAE. TabularIn Abaqus/Explicit the viscosity can be specified directly as a tabular function of shear strain rate and temperature. Input File Usage VISCOSITY, DEFINITION=TABULAR Abaqus/CAE Usage Specifying the viscosity directly as a tabular function is not supported in Abaqus/CAE. User-defined (Abaqus/Explicit only)In Abaqus/Explicit you can specify a user-defined viscosity in user subroutine VUVISCOSITY (see VUVISCOSITY). Input File Usage VISCOSITY, DEFINITION=USER Abaqus/CAE Usage User-defined viscosity is not supported in Abaqus/CAE. Temperature dependence of viscosity (Abaqus/Explicit only)The temperature-dependence of the viscosity of many polymer materials of industrial interest obeys a time-temperature shift relationship in the form: where is the shift function and is the reference temperature at which the viscosity versus shear strain rate relationship is known. This concept for temperature dependence is usually referred to as thermo-rheologically simple (TRS) temperature dependence. In the Newtonian limit for low shear rates, when , we have Thus, the shift function is defined as the ratio of the Newtonian viscosity at the temperature of interest to that of the chosen reference state: . See Thermo-rheologically simple temperature effects for a description of the different forms of the shift function available in Abaqus. Input File Usage Use the following options to define a thermo-rheologically simple (TRS) temperature-dependent viscosity: VISCOSITY TRS Abaqus/CAE Usage Defining a thermo-rheologically simple temperature-dependent viscosity is not supported in Abaqus/CAE. Material optionsMaterial shear viscosity in Abaqus/Explicit must be used in combination with an equation of state to define the material's volumetric mechanical behavior (see Equation of state). ElementsMaterial shear viscosity can be used with any solid (continuum) elements in Abaqus/Explicit except plane stress elements. |