蠕变模型

Coupled Creep and Drucker-Prager Plasticity Geomaterials may creep under certain conditions.When the loading rate is of the same order of magnitude as the creep time scale, the plasticity and creep equations must be solved using a coupled solution procedure.

ABAQUS has a creep model that can be used to augment the Drucker-Prager plasticity for such problems.

Basic Assumptions

ABAQUS always uses the coupled solution procedure when both Drucker-Prager plasticity and creep are active.

Using the Drucker-Prager creep model implies that the Drucker-Prager plasticity model uses isotropic linear elasticity, a hyperbolic plastic flow potential, and the linear Drucker-Prager yield surface with a circular yield surface in the deviatoric plane (K = 1).

The creep laws for the Drucker-Prager creep models are written in terms of an equivalent creep stress, , which is a measure of the creep ―intensity‖ of the state of stress at a material point.

The definition of depends upon the type of hardening (compression, tension, or shear) used with the linear Drucker-Prager plasticity model, but in all cases ()βσσ,,p q cr cr =:

()()()

ββσtan 3/11tan --=p q cr (compression) ()()()

ββtan 3/11tan +-=

p q (tension) ()βtan p q -=(shear)

The equivalent creep stress defines surfaces that are parallel to the yield surface in the meridional plane.

Points on the same surface have the same creep ―intensity.‖

There is a cone in the meridional plane in which no creep deformation will occur.

Creep Laws

The default creep laws provided are simple and are intended to model thesecondary creep of the material.

Time Hardening Creep Law Use this creep law when the stress in the material remains essentially constant:

()m n cr cr

t A σε=∙

Strain Hardening Creep Law Use this creep law when the stress in the material varies during the analysis:

()()[]111+∙⎪⎭

⎫ ⎝⎛+=m m cr n cr cr

m A εσε Singh-Mitchell Creep Law

Use this creep law when an exponential relationship between stress and creep strain rate is needed:

()m cr

t t Ae cr /1⎪⎭⎫ ⎝⎛∙=σαε

Creep Flow Potential

The Drucker-Prager creep model uses a hyperbolic creep flow potential that ensures the creep (deformation) flow direction is always defined uniquely: ()ψ-+ψ=tan tan 220p q G cr σε

The initial yield stress,

σ, is defined on the ∗DRUCKER PRAGER HARDENING

option.

Usage

The *DRUCKER PRAGER CREEP option must be used in conjunction with the

*DRUCKER PRAGER and DRUCKER PRAGER HARDENING options.

The *DRUCKER PRAGER CREEP option must be used with the linear

Drucker-Prager model with a von Mises (circular) section in the deviatoric stress plane (K=1 ; i.e., no third stress invariant effects are taken into account) and can be combined only with linear elasticity.

The material parameters in the default creep laws— A,n ,m ,t1 , and — can be defined as functions of temperature and/or field variables on the *DRUCKER PRAGER CREEP option.

–To avoid numerical problems with round-off, the values of should be larger than 27

10-.

The time in these creep laws is the total analysis time, so the duration of steps where creep is not considered (such as STATIC steps) should be relatively short.

More complex creep laws are defined with user subroutine CREEP.

The eccentricity of the creep potential, , is by default 0.1. Use the ECCENTRICITY parameter on the DRUCKER PRAGER option to

specify a different value.

–Using values much smaller than 0.1 can create convergence problems.

The creep flow potential uses the same dilation angle,ψ, as the Drucker-Prager plasticity model.

–Therefore, it is possible for the creep equations to be unsymmetric whenψ

β. In this case the *STEP, UNSYMM=YES option should be

≠

used.