22.3.1 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 22.3.1–1):
is the “logarithmic bulk modulus”; 
is the initial void ratio; p 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 |
| Abaqus/CAE Usage: | Use all three of the following options to define a porous elastic material: |
Property module: material editor: Mechanical Load module: Create Predefined Field: Step: Initial: choose Mechanical for the Category and Stress for the Types for Selected Step Load module: Create Predefined Field: Step: Initial: choose Other for the Category and Void ratio for the Types for Selected Step |
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, G. The deviatoric stress, 
, is then related to the deviatoric part of the total elastic strain, 
, by
| Input File Usage: | *POROUS ELASTIC, SHEAR=G |
| Abaqus/CAE Usage: | Property module: material editor: Mechanical |
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
is the logarithmic measure of the elastic volume change. In this case 
| Input File Usage: | *POROUS ELASTIC, SHEAR=POISSON |
| Abaqus/CAE Usage: | Property module: material editor: Mechanical |
Material options
The porous elasticity model can be used by itself, or it can be combined with:
the “Critical state (clay) plasticity model,” Section 23.3.4; or
isotropic expansion to introduce thermal volume changes (“Thermal expansion,” Section 26.1.2).
Porous elasticity cannot be used with the porous metal plasticity model (“Porous metal plasticity,” Section 23.2.9).
See “Combining material behaviors,” Section 21.1.3, 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 reduced-integration elements with total-stiffness 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 27.1.4, for details.
If fluid pore pressure is important (such as in undrained soils), stress/displacement elements that include pore pressure can be used.