ABAQUS Analysis User's Manual  


10.3.1 Elastic behavior of porous materials

Products: ABAQUS/Standard  ABAQUS/CAE  

References

Overview

A porous elastic material model:

  • is valid for small elastic strains (normally less than 5%);

  • is a nonlinear, isotropic elasticity model in which the pressure stress varies as an exponential function of volumetric strain;

  • allows a zero or nonzero elastic tensile stress limit; and

  • can have properties that depend on temperature and other field variables.

Defining the volumetric behavior

Often, the elastic part of the volumetric behavior of porous materials is modeled accurately by assuming that the elastic part of the change in volume of the material is proportional to the logarithm of the pressure stress (Figure 10.3.1–1):

where is the “logarithmic bulk modulus”; is the initial void ratio; is the equivalent pressure stress, defined by

is the initial value of the equivalent pressure stress; is the elastic part of the volume ratio between the current and reference configurations; and is the “elastic tensile strength” of the material (in the sense that as ).

Input File Usage:           Use all three of the following options to define a porous elastic material:
 
*POROUS ELASTIC, SHEAR=G or POISSON to define  and  
*INITIAL CONDITIONS, TYPE=STRESS to define  
*INITIAL CONDITIONS, TYPE=RATIO to define

Figure 10.3.1–1 Porous elastic volumetric behavior.

ABAQUS/CAE Usage: 

Property module: material editor: MechanicalElasticityPorous Elastic

and are always zero; you cannot define initial values for the equivalent pressure stress or void ratio in ABAQUS/CAE.

Defining the shear behavior

The deviatoric elastic behavior of a porous material can be defined in either of two ways.

By defining the shear modulus

Give the shear modulus, . The deviatoric stress, , is then related to the deviatoric part of the total elastic strain, , by

In this case the shear behavior is not affected by compaction of the material.

Input File Usage:           
*POROUS ELASTIC, SHEAR=G

ABAQUS/CAE Usage: 

Property module: material editor: MechanicalElasticityPorous Elastic: Shear: G


By defining Poisson's ratio

Define Poisson's ratio, . The instantaneous shear modulus is then defined from the instantaneous bulk modulus and Poisson's ratio as

where is the logarithmic measure of the elastic volume change. In this case

Thus, the elastic shear stiffness increases as the material is compacted. This equation is integrated to give the total stress–total elastic strain relationship.

Input File Usage:           
*POROUS ELASTIC, SHEAR=POISSON

ABAQUS/CAE Usage: 

Property module: material editor: MechanicalElasticityPorous Elastic: Shear: Poisson


Material options

The porous elasticity model can be used by itself, or it can be combined with:

It is not possible to use porous elasticity with rate-dependent plasticity or viscoelasticity.

Porous elasticity cannot be used with the porous metal plasticity model (“Porous metal plasticity,” Section 11.2.9).

See “Combining material behaviors,” Section 9.1.3, for more details.

Elements

Porous elasticity cannot be used with hybrid elements or plane stress elements (including shells and membranes), but it can be used with any other pure stress/displacement element in ABAQUS/Standard.

If used with elements with hourglass control, ABAQUS/Standard cannot calculate a default value for the hourglass stiffness of the element if the shear behavior is defined through Poisson's ratio. Hence, you must specify the hourglass stiffness. See “Section controls,” Section 13.1.4, for details.

If fluid pore pressure is important (such as in undrained soils), stress/displacement elements that include pore pressure can be used.