OS-V: 0830 Nonlinear Static Analysis with Chaboche Combined Hardening Material

Chaboche model, which is the extension of Frederick–Armstrong model, is commonly used in modeling uniaxial and multiaxial ratcheting.

The precise identification of material hardening parameters is essential for the prediction of ratcheting. Using the Chaboche hardening parameters, numerical simulations of ratcheting are performed in OptiStruct. Numerical results are then compared with experimental data obtained in a stress-controlled cyclic loading test.

Model Files

Before you begin, copy the file(s) used in this problem to your working directory.

Benchmark Model

The model consists of a CHEXA element with constraints and enforced displacement. In Figure 1, the node ID’s are constrained in their respective direction:
  1. In X-direction: Constrained at all 8 nodes.
  2. In Y-direction: Constrained at Node ID 1,2,5, & 6.
  3. In Z-direction: Constrained at Node ID 1,2,3, & 4.
The enforced displacement in the X-direction with a magnitude of 0.02 mm is provided normal to the X-direction at the node ID (2,3,6 & 7) as shown in Figure 1 (Right).
Figure 1. Model with Boundary Conditions. Left: Constraints, Right: Enforced Displacement

The cyclic plasticity concerns an elastoplastic stress–strain response of materials in closed and repeated loading paths. Among the cyclic plasticity phenomena, ratcheting can result in the additional damage of materials and the shortening of their fatigue life. Ratcheting is defined as a progressive strain accumulation in a material under stress-controlled cycling loading with nonzero mean stress. The specimen is constrained at the left end in the longitudinal direction, and an enforced displacement is applied to the right end of the specimen. A time-dependent enforced displacement is used (Figure 2).
Figure 2. Time-dependent Enforced Displacement


PA6 Aluminum and combined hardening material properties:

In the Chaboche model, three nonlinear terms, as well as the voce isotropic, are used to simulate the ratcheting for PA6 aluminum. Hardening parameters for the Chaboche model are determined based on the experimental stress-strain curves obtained in strain-controlled cyclic tension/compression tests.

Young's modulus (E)
71000 MPa
Poisson’s Ratio (u)
Identification of a MAT1 entry (MID)
Hardening Rule (HR)
Kinetic Hardening Properties
Data input for kinematic hardening.
Number of back stresses for kinematic hardening (NKIN)
Initial yield stress (SIGY0)
410.0 MPa
Parameter Ci of back stress components for NLKIN (PARAM) in MPa.
Parameter Gi of back stress components for NLKIN (PARAM).
Isotropic Hardening
Data input for isotropic hardening.
Initial yield stress (SIGY0)
Parameter Q for NLISO (Q)
150.0 MPa
Parameter B for NLISO (B)


The results compare experimental and numerical stress-strain curves for the Chaboche model after optimization by the least-square method.

Figure 3. Reference Result

The elemental stress versus strain graph OptiStruct result (Left) and the experimental stress-strain curve for PA6 aluminum (Right) are shown in Figure 4 .
Figure 4. OptiStruct Result

The results obtained in OptiStruct, using a combined hardening material model, are similar to the experimental result.

Figure 5. Superimpoased Reference and OptiStruct Result

Figure 5 shows the match between the OptiStruct results and the reference results. The OptiStruct result curves follow perfectly with reference result curves.

1 The application of Chaboche model in uniaxial ratcheting simulations, Advances in Manufacturing Science and Technology, Marta Wójcik and Andrzej Skrzat, DOI: 10.2478/amst-2019-0010 AMST 44(2) 202