Numerical Manifold Method with Endochronic Theory for Elastoplasticity Analysis

Table 1

Description of the algorithm.

Step	Description
1	Assume the state at step 𝑛−1 is known, and step 𝑛 is the current step
2	The prediction solution is obtained by calculation with elastic constitutive. Update the incremental stress matrix
4	Initialize Δ𝜉
5	Use the Newton-Raphson technique to calculate ^𝑛Δ𝑧 by (8)
6	Substitute ^𝑛Δ𝑧 to (15) and calculate 𝐷^epand 𝑓^′
7	Solve (22) for Δ𝑑. Update the global displacements Δ𝑢 and the global incremental strain matrix Δ𝜀
8	Go to the next step.