Fig. 2 – modeFRONTIER – LS-DYNA workflow
The set-up of the procedure firstly required the selection of a set of simple experimental tests to obtain proper data fitting, and also to integrate the finite element LS-DYNA models into the modeFRONTIER environment.
2.1 Selection of experimental tests
The experimental tests should describe in an accurate way the different material behaviors under different loading conditions, avoiding at the same time information redundancy. By using the same ASTM D 790 specimen geometry (rectangular cross section bar), the following four destructive tests have been selected and performed:
- 3 Points Bending Test (16mm width specimen);
- 3 Points Bending Test (25mm width specimen);
- 4 Points Bending Test;
- Charpy Pendulum Test.
The Global Stiffness and the Total Absorbed Energy quantities have been measured for 3 and 4-Points Bending tests, while Absorbed Energy and Local Failure Mode were selected for Charpy Pendulum. For these quantities, 9 objective functions to be minimized (nine relative errors) were considered in order to investigate the material behaviors.
2.2 Process Integration: modeFRONTIER – LS-DYNA workflow
As the LS-DYNA material model calibration process is characterized by a large number of goals (i.e. the 9 objective functions) and design parameters (MAT 58 – MAT_LAMINATED_COMPOSITE_FABRIC – selected as the most suitable to describe the composite sandwich which requires 23 input variables), it cannot be solved by using a simple trial-and-error procedure. The efficient method we propose here, instead, takes advantage of the modeFRONTIER Process Integration and Design Optimization capabilities.
The process integration of the numerical models related to the experimental tests can be implemented and described within modeFRONTIER by means of the workflow illustrated in Fig. 2.
From top to bottom, following the blue links, the so-called “Data Flow” can be seen. The green block at the top defines the input variables (the constitutive parameters) for which a suitable range of variations can be set. Each time a new combination of their values is proposed by the modeFRONTIER optimization strategy, the MAT 58 card file is updated (node “mat_inp”) and transferred to the four LS-DYNA models. These computations deliver outputs that are post-processed and finally provide numerical forecasts of the nine physical responses, whose values are re-arranged in the nine relative errors with the aim to minimize the discrepancy (red blocks).
From left to right, following the dotted link, the so-called “Logic Flow” is shown: it represents the sequence of operations that modeFRONTIER will automate, and the logic behind them. The “DOE” node, the first block on the left side, means “Design Of Experiments”. This node allows the user to design a suitable initial population (combinations of input variable values) in respect of an efficient exploration of the design phase. Looking at the performances provided by these configurations, the “Scheduler” node realizes how the investigated phenomenons behave and based on its internal search strategy, starts to generate completely new designs. The new configurations flow sequentially into the four LS-DYNA models, whose numerical simulation is run in batch modality by modeFRONTIER, so that eventually a new evaluation of the objective functions is performed.
In this way, the workflow describes in a graphical and a very intuitive way, how the whole process is carried out.
Fig. 3 - objectives’ Correlation Chart