粘弹性分析

models and the Ogden model

for the Arruda-Boyce and Van der Waals functions

and for the Marlow function

If long-term elastic moduli are defined, the instantaneous moduli are determined from

while the instantaneous bulk compliance moduli are obtained from

for the Marlow functions we have

Elastomeric foams

For elastomeric foam material behavior the instantaneous shear and bulk relaxation coefficients are assumed to be equal and are applied to the material constants in the energy function:

If only the shear relaxation coefficients are specified, the bulk relaxation coefficients are set equal to the shear relaxation coefficients and vice versa. If both shear and bulk relaxation

coefficients are specified and they are unequal, ABAQUS issues an error message.

If long-term elastic moduli are defined, the instantaneous moduli are determined from

Material response in different analysis procedures

The time-domain viscoelastic material model is active during the following procedures:

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transient static analysis (“Quasi-static analysis,” Section 6.2.5),

transient implicit dynamic analysis (“Implicit dynamic analysis using direct integration,” Section 6.3.2),

explicit dynamic analysis (“Explicit dynamic analysis,” Section 6.3.3),

steady-state transport analysis (“Steady-state transport analysis,” Section 6.4.1),

fully coupled temperature-displacement analysis (“Fully coupled thermal-stress analysis,” Section 6.5.4), and

transient (consolidation) coupled pore fluid diffusion and stress analysis (“Coupled pore fluid diffusion and stress analysis,” Section 6.7.1).

Viscoelastic material response is always ignored in a static analysis. It can also be ignored in a coupled temperature-displacement analysis or in a soils consolidation analysis by specifying that no creep or viscoelastic response is occurring during the step even if creep or viscoelastic material properties are defined (see “Fully coupled

thermal-stress analysis,” Section 6.5.4, or “Coupled pore fluid diffusion and stress analysis,” Section 6.7.1). In these cases it is assumed that

the loading is applied instantaneously, so that the resulting response corresponds to an elastic solution based on instantaneous elastic moduli. ABAQUS/Standard also provides the option to obtain the fully relaxed long-term elastic solution directly in a static or steady-state transport analysis without having to perform a transient analysis. The long-term value is used for this purpose. The viscous damping stresses (the internal stresses associated with each of the Prony-series terms) are increased gradually from their values at the beginning of the step to their long-term values at the end of the step if the long-term value is specified.

Material options

The viscoelastic material model must be combined with an elastic material model. It is used with the isotropic linear elasticity model (“Linear elastic behavior,” Section 17.2.1) to define classical, linear, small-strain, viscoelastic behavior or with the hyperelastic

(“Hyperelastic behavior of rubberlike materials,” Section 17.5.1) or hyperfoam (“Hyperelastic behavior in elastomeric foams,” Section 17.5.2) models to define large-deformation, nonlinear, viscoelastic behavior. The elastic properties defined for these models can be temperature dependent.

Viscoelasticity cannot be combined with any of the plasticity models or with the Mullins effect material model. See “Combining material behaviors,” Section 16.1.3, for more details.

Elements

The time domain viscoelastic material model can be used with any stress/displacement or coupled temperature-displacement element in ABAQUS.

Output

In addition to the standard output identifiers available in ABAQUS (“ABAQUS/Standard output variable identifiers,” Section 4.2.1, and “ABAQUS/Explicit output variable identifiers,” Section 4.2.2), the

following variables have special meaning in ABAQUS/Standard if viscoelasticity is defined:

EE CE

These strain measures are used to approximate the strain energy, SENER, and the viscous dissipation, CENER. These approximations may lead to underestimation of the strain energy and overestimation of the viscous dissipation since the effects of internal stresses on these energy quantities are neglected. This can be particularly noticeable in the case of non-monotonic loading.

For the case of large-strain viscoelasticity, ABAQUS/Explicit does not perform the computation of the viscous dissipation for performance reasons. Instead, the contribution of viscous dissipation is included in the strain energy output, SENER; and CENER is output as zero. Consequently, special care must be exercised when interpreting strain energy results of large-strain viscoelastic materials in ABAQUS/Explicit since they include viscous dissipation effects.

Elastic strain corresponding to the stress state at time t and the instantaneous elastic material properties. Equivalent creep strain defined as the difference between the total strain and the elastic strain.