The creep equations are integrated with an explicit Euler forward algorithm, which is efficient for problems having small amounts of contained creep strains. A modified total strain is computed:

(3–1)

This equation is analogous to Equation 4–18 for plasticity. The superscripts are described with Understanding Theory Reference Notation and subscripts refer to the time point n. An equivalent modified total strain is defined as:

(3–2)

Also an equivalent stress is defined by:

(3–3)

where:

The equivalent creep strain increment (Δε^cr) is computed as a scalar quantity from the relations given in Rate-Dependent Viscoplastic Materials and is normally positive. If C₁₁ = 1, a decaying creep rate is used rather than a rate that is constant over the time interval. This option is normally not recommended, as it can seriously underestimate the total creep strain where primary stresses dominate. The modified equivalent creep strain increment , which would be used in place of the equivalent creep strain increment (Δε^cr) if C₁₁ = 1, is computed as:

(3–4)

where:

Next, the creep ratio (a measure of the increment of creep strain) for this integration point (C_s) is computed as:

(3–5)

The largest value of C_s for all elements at all integration points for this iteration is called C_max and is output with the label "CREEP RATIO".

The creep strain increment is then converted to a full strain tensor. N_c is the number of strain components for a particular type of element. If N_c = 1,

(3–6)

Note that the term in brackets is either +1 or -1. If N_c = 4,

(3–7)

(3–8)

(3–9)

(3–10)

The first three components are the three normal strain components, and the fourth component is the shear component. If N_c = 6, components 1 through 4 are the same as above, and the two additional shear components are:

(3–11)

(3–12)

Next, the elastic strains and the total creep strains are calculated as follows, using the example of the x-component:

(3–13)

(3–14)

Stresses are based on . This gives the correct stresses for imposed force problems and the maximum stresses during the time step for imposed displacement problems.