The default transient scheme for the nonlinear system is the same as that used for linear elasticity: the Newmark Method. The semi-discretized equation of transient motion for the nonlinear system is given as:

(16–30)

Note that the internal load is dependent on the current displacement at time . The linearized form of the previous equation can be obtained by the Newton-Raphson method resulting in following equation:

(16–31)

and

(16–32)

(16–33)

The same logic is extended to the Backward Euler scheme when used in conjunction with the Nonlinear Elasticity model.