PSI - Issue 35

4

Jarmil Vlach et al. / Procedia Structural Integrity 35 (2022) 132–140 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

135

Optimization of FE model Stiffness response

Optimization of FE model Strength response

Matrix and Fiber Elastic properties (p1, Fiber volume fraction )

Matrix and Fiber Strength properties (p2, Fiber tensile Strength )

ABAQUS/Standard model (MFH formulation)

ABAQUS/Explicit model (RVE formulation)

No

No

Yes

Yes

Extraction of optimal model parameters

Target function satisfied?

Target function satisfied?

Fig. 3. Schema of optimization.

For the determined volume concentration of fibres, a hexagonal elementary volume cell was generated with the help of ABAQUS RVE Plugin so that the control parameter for optimizing the strength of the composite was only the tensile strength of the fibres. The relationship between the deviations of the results of the RVE and MFH methods is reported by Pierard et al. (2004) and Abaqus (2017). The formulations are solved in the ABAQUS solver so that the methods give the results with the highest possible agreement. A generalized formulation for multi material stiffness optimization is given by Hvejsel et al. (2011). Since both optimization steps contain only one parameter, the numerical method Regula-Falsi, which is described in Rektorys (2003), was chosen as the most effective method. The target function was chosen as the smallest distance of the ABAQUS solver solution from the experiment with a maximum permissible error of 5 %. 4.3. Parameters of FE model The material stiffness parameters used in the impact simulations were obtained in the same way as reported by Ye and Wang (2017). The strength and failure parameters were obtained in the same way of loading the elementary material cell as in the case of elasticity, but up to failure. The overall approach is shown in Fig. 4.

Model of elementary cell (RVE formulation)

ABAQUS/Standard

Elasticity

ABAQUS/Explicit

Failure

ABAQUS/Explicit

Damage

Fig. 4. Schema of material parameters extraction.