Estimation of composite material properties using an inverse approach with Quanscient Allsolve

Technical author

Dr. Abhishek Deshmukh
Application Engineer, Team Lead

Introduction

Mechanical characterization forms an integral part of packaging integrated circuits on PCBs, as different materials can influence the operation significantly. Engineers traditionally rely on experimental testing, which often requires extensive time and resources. These tests can involve multiple iterations, requiring physical prototypes and precise measurement setups. Computational approaches offer a viable alternative, reducing dependency on physical testing while still achieving reliable results. However, determining accurate material properties is crucial for reliable simulations, especially in complex material systems like PCBs. 

Finite Element Analysis (FEA) is a widely used numerical tool, but obtaining accurate material properties often demands iterative refinement. Inverse problems provide a powerful way to estimate unknown material properties by comparing simulated results with experimental data. Instead of directly measuring the properties, this method involves adjusting material parameters in a simulation until the model’s response aligns with experimental observations. 

This study explores how Quanscient Allsolve, in combination with an API-based optimization approach, streamlines material property extraction through inverse problem-solving. This method not only enhances efficiency but also ensures greater accuracy in defining material characteristics.

Impact of Quanscient Allsolve on material property optimization

Quanscient Allsolve introduces several advantages that make material property optimization more effective:

• Automated material property optimization: The API-driven workflow enables automation, reducing manual intervention and increasing repeatability.
• Cloud-based scalability: Simulations run in parallel on cloud-based infrastructure, significantly cutting down computational time.
• Integration with external optimization libraries: Standard Python library, SciPy, to facilitate the solution of inverse problems, allowing flexible algorithm selection.
• Efficient handling of complex material models: The system supports anisotropic properties, which are essential for accurately modeling composite and layered materials.

These features allow engineers to efficiently refine material parameters without the limitations of traditional experimental methods, making it a robust solution for real-world applications.

Case example: Equivalent material properties of a packaged PCB

A practical application of this approach was demonstrated with a JEDEC-standard drop test board measuring 132×77×1 mm³. This board featured a 3×5 full array of 13×13 mm packages. The objective was to determine the equivalent material properties using an inverse problem approach combined with modal analysis.

Fig.1: CAD model of the standard packaged PCB.

Simulation objective

The study aimed to:

• Estimate the unknown material properties of the PCB and its mounted packages. 
  • Minimizing the difference between simulated and experimental eigenfrequencies.
  • Optimizing material parameters through iterative numerical analysis using gradient-based methods.

The model

The simulation setup included:

• FEA configuration: The PCB was modeled as an anisotropic material with three independent elastic constants, while the packages were treated as isotropic.
• API-based workflow:
  • Define initial material properties.
  • Perform eigenmode analysis in Quanscient Allsolve.
  • Compare simulated eigenfrequencies with experimental data.
  • Compute the residual (difference) and update material properties using an optimization algorithm.
  • Repeat the process until the residual is minimized.

This structured approach allowed an efficient refinement of the material properties, ensuring that the final simulation results closely matched real-world measurements.

Fig. 2: API optimization workflow.

Key results

Fig. 3: Iterations of the material properties.

Table 1: Comparison between initial and optimized material properties.

Fig. 4: Comparison of predicted eigenfrequencies with experimental measurements.

Fig. 5: Error relative to experimental values of eigenfrequencies.

Mode shapes from Quanscient Allsolve were consistent with both experimental measurements and FEA results from the referred paper [2].

Fig. 6: Comparison of selected modes with experimental modal analysis and finite element analysis from Lee et al. [2]. The deviations in mode shapes are attributed to neglecting accelerometer mass and use of simple gradient-based optimization, leading to a local optimum rather than a global one.

Fig. 7 : Mode 17 animated in harmonic motion.

Key benefits demonstrated

This case study highlights several advantages of using Quanscient Allsolve for material property optimization:

• The inverse problem approach provided a reliable estimation of material properties, improving the precision of simulations.
• The API-driven setup significantly reduced manual effort, ensuring a streamlined and repeatable process

Other benefits of Quanscient Allsolve for material property optimization

Beyond the direct application to material property optimization, Quanscient Allsolve offers additional advantages for related simulation tasks:

• Cloud-native parallel computing reduces simulation time by distributing tasks across multiple processors.
• Domain decomposition method (DDM) enables faster large-scale simulations by dividing the computational workload into smaller, manageable sections.
• Multivariate parametric sweep capabilities allows for broader exploration of design spaces, helping engineers test multiple configurations efficiently.

These features make Quanscient Allsolve a versatile tool not only for material property estimation but also for a wide range of simulation-driven engineering applications.

Conclusion

Quanscient Allsolve provides an efficient and accurate method for material property optimization using API-driven inverse problem-solving. By automating FEA-based material characterization, engineers can achieve:

• Higher accuracy in defining material properties.
• Faster design iterations with an automated workflow.
• Reduced computational costs through cloud-based parallel processing.

This approach proves especially valuable for estimating material properties of composite systems where experimental characterization alone is not sufficient. By integrating computational techniques with experimental validation, engineers can achieve better results in less time, ultimately leading to improved product performance and reliability.

References

[1] Vauhkonen, M., Tarvainen, T., Lähivaara, T., “Inverse Problems,” In: Pohjolainen, S. (eds) Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-27836-0_12.

[2] Y.-C. Lee, B.-T. Wang, Y.-S. Lai, C.-L. Yeh, R.-S. Chen, “Finite element model verification for packaged printed circuit board by experimental modal analysis,” Microelectron. Reliab., 48, 11–12, 2008, pp. 1837-1846.

[3] R. Nagaraja, A. Deshmukh, B. Khouya, J. Lohi, M. Lyly, J. Ruuskanen, A. Halbach, “Accelerate and optimize your packaging using large-scale multiphysics simulations in your browser,”  Commercial White Paper - NordPac 2024, 2024.

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