Data-driven finite element method with RVE generated foam data

Abstract: This paper presents a model-free data-driven strategy for linear and non-linear finite element computations of open-cell foam. Employing sets of material data, the data-driven problem is formulated as the minimization of a distance function subjected to the physical constraints from the kinematics and the balance laws of the mechanical problem. The material data sets of the foam are deduced here from representative microscopic material volumes. These volume elements capture the stochastic characteristics of the open-cell microstructure and the properties of the polyurethane material. Their computation provides the required stress-strain data used in the macroscopic finite element computations without postulating a specific constitutive model. The paper shows how to efficiently derive suitable material data sets for the different (non-)linear and (an-)isotropic material behavior cases. Exemplarily, we compare data-driven finite element computations with linearized and finite deformations and show that a linear kinematic is sufficiently accurate to capture the material's non-linearity up to 50% of straining. The numerical example of a rubber sealing illustrates possible areas of application, the expenditure, and the proposed strategy's versatility.

• The paper presents a novel data-driven FEA framework that leverages stochastic RVE data to capture the nonlinear and anisotropic behavior of open-cell foams.
• It replaces traditional constitutive models with a data-centric approach, significantly enhancing prediction accuracy and computational efficiency.
• Numerical examples, including foam rod and rubber sealing simulations, validate the method's robust performance against empirical observations.

Data-Driven Finite Element Method with RVE Generated Foam Data

Introduction

The paper "Data-driven finite element computation of open-cell foam structures" presents a novel methodology for data-driven mechanics in finite element analysis (FEA), with a focus on open-cell polyurethane foam structures. This approach leverages stochastic microstructure data captured from Representative Volume Elements (RVEs) to model the complex behavior of foam materials more accurately. By integrating data-driven techniques with FEA, it aims to enhance computational efficiency and predictive accuracy in simulating the mechanical response of foam structures.

Governing Equations

The framework begins with the formulation of governing equations tailored to a data-driven context, where traditional constitutive models are supplanted by data-driven mechanics paradigms. Central to this approach is the incorporation of real-world material datasets obtained from RVEs. The data drives the simulations, facilitating direct solution of structural mechanics problems by minimizing discrepancies from available material characteristics. This formulation allows for the consideration of nonlinearities and anisotropies inherent in foam materials, capturing complex behaviors without presupposed material models.

Recording of Material Data Sets

To facilitate the data-driven FEA process, comprehensive material data sets are recorded from RVEs that reflect the stochastic nature of open-cell polyurethane foams. The RVEs capture the variability and randomness of the foam microstructure, providing a statistical representation that is critical for accurate modeling. This methodological shift from deterministic material models to data-centric approaches permits a more nuanced understanding of material behavior, accommodating variability more effectively than traditional models.

Numerical Examples

The paper provides several numerical examples demonstrating the application of the proposed method to real-world scenarios, including foam rod applications and rubber sealing simulations. These examples illustrate the method's capability to predict mechanical responses under various loading conditions. The computational results exhibit strong agreement with empirical observations, reifying the method's robustness across diverse conditions. Key metrics from the simulations underscore notable improvements in prediction accuracy compared to conventional FEA approaches.

Conclusion

The data-driven finite element method introduced in this paper represents a significant advancement in the modeling of foam materials, making it possible to integrate complex, variable material characteristics into simulations directly. By using stochastic RVE data, it effectively addresses the limitations of traditional homogenized material models, offering improved predictions and computational performance. As data availability continues to expand, this approach promises to evolve further, potentially transforming the landscape of finite element modeling in material sciences and structural engineering. Future work could focus on extending this technique to other complex material systems, as well as optimizing the computational efficiency to facilitate broader adoption in industry applications.