Rediscovering the Mullins Effect With Deep Symbolic Regression: Elastomer Softening Phenomenon Explored

Core Concepts

The author employs deep symbolic regression to generate accurate analytical models capturing the Mullins effect in elastomers, showcasing robustness and generalizability under sparse data conditions.

Abstract

In this study, a novel approach using deep symbolic regression is applied to model the Mullins effect in elastomers. The research focuses on accurately describing the softening behavior observed in rubber-like materials. Through benchmark tests and validation with experimental data, the proposed framework demonstrates efficiency and reliability in generating material models. The study highlights the importance of understanding complex phenomena like the Mullins effect for better material modeling and prediction.
The content delves into the history and significance of the Mullins effect, discussing various material models proposed in literature to capture this phenomenon accurately. It emphasizes the challenges associated with modeling such complex behaviors despite extensive research efforts.
Furthermore, it introduces a two-step framework involving strain energy function identification and damage function characterization to model primary loading and softening behavior under cyclic loading accurately. The study showcases how modern methods like deep symbolic regression can enhance constitutive modeling of rubber-like materials efficiently.
Through detailed analysis and benchmark tests with different material models, including Mooney-Rivlin and Ogden-Roxburgh models, the research validates the proposed framework's effectiveness in capturing complex material behaviors like softening phenomena.
Overall, this study provides valuable insights into utilizing deep symbolic regression for accurate material modeling of elastomers, specifically focusing on understanding and predicting the Mullins effect.

Stats

Highly specific damage models accurately representing complex characteristics of the Mullins effect are generated.
Validation of the framework with multiple data sets is demonstrated.
The proposed methodology is extensively validated on a temperature-dependent data set.
The strain energy function is determined based on stress-strain data of primary loading curves.
Stress-strain responses resulting from different temperature-dependent strain energy functions are shown.
Recovery rates for strain energies vary across different cases but maintain high 𝑅2 scores.

Quotes

"The efficiency of the proposed approach is demonstrated through benchmark tests using generalized Mooney-Rivlin and Ogden-Roxburgh models."
"The proposed method is extensively validated on a temperature-dependent data set, demonstrating its versatile performance."

Key Insights Distilled From

Rediscovering the Mullins Effect With Deep Symbolic Regression

by Rasul Abdusa... at arxiv.org 03-11-2024

https://arxiv.org/pdf/2403.05495.pdf

Deeper Inquiries

How can deep symbolic regression be applied to other types of materials beyond elastomers?

Deep symbolic regression can be applied to a wide range of materials beyond elastomers by adapting the framework to suit the specific characteristics and behaviors of different materials. For example, in metals, the strain energy functions may need to account for plasticity and hardening effects, while in composites, anisotropic behavior and fiber-matrix interactions could be incorporated into the models. By adjusting the input parameters and constraints in the deep symbolic regression process, material-specific features can be captured accurately.

What are potential limitations or biases that could arise from using machine learning methods for constitutive modeling?

One potential limitation is overfitting, where the model performs well on training data but fails to generalize to new data. This can lead to inaccuracies in predicting material behavior under different conditions. Biases may arise from human choices in setting up the machine learning algorithms or selecting input features, which could result in a skewed representation of the material's response. Additionally, complex models generated through machine learning methods may lack interpretability compared to traditional analytical models.

How does understanding phenomena like the Mullins effect contribute to advancements in material science beyond theoretical modeling?

Understanding phenomena like the Mullins effect provides insights into how materials behave under cyclic loading conditions and softening effects. This knowledge is crucial for designing more durable and resilient materials used in various applications such as automotive components, biomedical devices, and structural elements. By incorporating these complex behaviors into constitutive models through advanced techniques like deep symbolic regression, researchers can develop more accurate predictive tools for engineering applications. This contributes to advancements in material science by enabling tailored designs with improved performance characteristics based on a deeper understanding of material behavior under real-world conditions.