Material nonlinearities occur because of the nonlinear relationship between stress and strain; that is, the stress is a nonlinear function of the strain. The relationship is also path-dependent (except for the case of nonlinear elasticity and hyperelasticity), so that the stress depends on the strain history as well as the strain itself.
The program can account for many material nonlinearities, as follows:
Rate-independent plasticity is characterized by the irreversible instantaneous straining that occurs in a material.
Rate-dependent plasticity allows the plastic-strains to develop over a time interval. This is also termed viscoplasticity.
Creep is also an irreversible straining that occurs in a material and is rate-dependent so that the strains develop over time. The time frame for creep is usually much larger than that for rate-dependent plasticity.
Gasket material may be modelled using special relationships.
Nonlinear elasticity allows a nonlinear stress-strain relationship to be specified. All straining is reversible.
Hyperelasticity is defined by a strain-energy density potential that characterizes elastomeric and foam-type materials. All straining is reversible.
Viscoelasticity is a rate-dependent material characterization that includes a viscous contribution to the elastic straining.
Concrete materials include cracking and crushing capability.
Swelling allows materials to enlarge in the presence of neutron flux.
Llisted in this table are the number of stress and strain components involved. One component uses X (e.g., SX, EPELX, etc.), four components use X, Y, Z, XY, and six components use X, Y, Z, XY, YZ, XZ.
For the case of nonlinear materials, the definition of elastic strain given with Equation 2–1 has the form of:
 | (4–1) |
where:
| εel = elastic strain vector (output as EPEL) |
| ε = total strain vector |
| εth = thermal strain vector (output as EPTH) |
| εpl = plastic strain vector (output as EPPL) |
| εcr = creep strain vector (output as EPCR) |
| εsw = swelling strain vector (output as EPSW) |
In this case, {ε} is the strain measured by a strain gauge. Equation 4–1 is only intended to show the relationships between the terms. See subsequent sections for more detail).
In POST1, total strain is reported as:
 | (4–2) |
where:
| εtot = component total strain (output as EPTO) |
Comparing the last two equations,
 | (4–3) |
The difference between these two “total” strains stems from the different usages: {ε} can be used to compare strain gauge results and εtot can be used to plot nonlinear stress-strain curves.