Democratizing Engineering Analysis Through a Universal Material Subroutine

The Living Heart Project’s monthly webinar series is currently focusing on the democratization of engineering analysis through a universal material subroutine. The goal is to broaden access to simulation technologies and empower individuals with different backgrounds to participate in scientific discovery. By automating the process of model selection directly from data, finite element analysis can become more user-friendly, robust, and less vulnerable to human error. Hear from Dr. Ellen Kuhl from Stanford University and Dr. Mathias Peirlinck from Delft University of Technology, as they share their expertise on democratizing engineering analysis through a universal material subroutine.

By Katie Corey

Constitutive modeling is the cornerstone of continuum and structural mechanics. In a finite element analysis, the constitutive model is encoded in the material subroutine, providing the functional map between strains and stresses in the governing equations. This function is called within every finite element, at each integration point, within every time step, at each Newton iteration. Today’s finite element analysis packages offer large libraries of material models to choose from. However, the scientific criteria for appropriate model selection remain highly subjective and prone to user bias.

Here we show how to fully automate the process of model selection, autonomously discover the best model and parameters from experimental data, encode all possible discoverable models into a single material subroutine, and seamlessly integrate this universal material subroutine into finite element simulations. We have successfully prototyped this technology for various incompressible, isotropic, hyperelastic materials and, recently, further expanded it towards both compressible and anisotropic material behavior. We demonstrate how to collectively integrate these features into a single universal material subroutine that will be made available as a build-in material modeling feature in future Abaqus releases. Finite element simulations with this novel universal material subroutine show that it specializes well to traditional constitutive models, generalizes well to newly discovered models, and agrees excellently with both experimental data and previous simulations. Replacing dozens of individual material subroutines by a single universal material subroutine that is populated directly via automated model discovery, entirely without human interaction, will democratize engineering analysis and make finite element simulations more accessible to a more inclusive and diverse community to accelerate scientific innovation. 

Modeling Brain Tissue Behavior

The application of the universal material subroutine to brain tissue has shown promising results. The model was tested using data from tension, compression, and shear tests on human brain tissue samples. The results revealed significant variation in the behavior of different brain regions, indicating the complexity of brain tissue mechanics. The model was able to accurately capture this nonlinear and incompressible behavior, providing a more comprehensive representation of the brain tissue’s mechanical properties.

Comparing the performance of the model to traditional material models commonly used for brain tissue, the universal material subroutine outperformed the classical models, demonstrating a higher goodness of fit. The model’s ability to predict stress differences in different brain regions was particularly notable, showcasing its versatility and accuracy in capturing the complex behavior of brain tissue.

Furthermore, the model’s unique capability to generalize across different types of tissues was demonstrated by its successful application to skin tissue, where it exhibited consistent performance across multiple data sets, highlighting its potential for broad applicability and effectiveness in representing diverse material behaviors.

Exploring Further Applications and the Importance of Understanding Mechanical Properties

The universal material subroutine developed by the Living Heart Project has shown promising applications beyond the study of the human heart. The model has been successfully extended to analyze the mechanical behavior of other tissues such as skin and artificial meat. The ability to understand and predict the mechanical properties of various materials is of paramount importance in fields ranging from biomedicine to food science.

For instance, in the case of skin, the model has been used to explore the behavior of different layers and has provided insights into applications such as skin folding, wrinkling, and reconstructive surgeries. This demonstrates the versatility and wide-ranging implications of the developed model.

Moreover, the model’s application extends beyond research and practical use. It has also been integrated into teaching scenarios, offering students the opportunity to experiment with and understand the mechanical behavior of various materials. This includes a class that allows students to test different materials and analyze their mechanical properties. For example, in a class project, students tested artificial meat products and used the model to understand the relationship between material stiffness and the perception of taste.

Revolutionizing the Meat Industry with Artificial Meat Models

In this webinar, a groundbreaking model for artificial meat is introduced, marking a significant advancement in the field. The model is compared with classical models, demonstrating its remarkable accuracy and effectiveness. It is the first-ever constitutive model for artificial meat, showcasing the pioneering nature of this development. Furthermore, the class for teaching these methods is open for enrollment, providing an opportunity for individuals from various backgrounds, including corporate professionals, to participate and benefit from this innovative approach.

The potential impact of this model on the meat industry is immense, as it aims to replicate the taste and texture of real meat, enhancing the experience of consuming artificial meat. This model opens up new possibilities for the future of food technology and has the potential to revolutionize the way meat products are developed and consumed.

Revolutionizing Material Modeling with Neural Network Architecture

The potential of neural network architecture in material modeling is a game-changer. With the ability to replace thousands of models with a few functional building blocks, it paves the way for a unified material subroutine that can handle over 4000 models. This revolutionary approach allows for the creation of a single, unified material subroutine, streamlining the process of summarizing various material models. This capability opens up new possibilities for handling complex material behaviors and simulations, offering a more efficient and versatile approach to material modeling and analysis.

Implementation into Abaqus

The constitutive artificial neural network model has been integrated into Abaqus as a built-in subroutine with activation functions. This implementation corrects invariances to a zero-stress reference configuration, allowing for more accurate computational results. The neural network model has shown perfect matches between analytic and computational results, demonstrating its effectiveness in capturing complex material behaviors.

This integration allows for the use of the universal material subroutine, which enables the definition of material models with just a few parameters, making it comparable to traditional hyperelastic modeling. The implementation has been tested for materials exhibiting strong history dependence and has shown robust performance. Ongoing testing includes combining the approach with viscoelasticity and inelasticity, with promising results.

The open collaboration and availability of the model encourage researchers and engineers to explore its applications across various materials and simulations, contributing to advancements in biomedical stimulation and human health. The integration of the constitutive artificial neural network model into Abaqus marks a significant step towards enabling a wider audience to leverage its capabilities for diverse applications.

Advancements in Biomedical Simulations

The application of the constitutive artificial neural network model has shown promising results in biomedical simulations. It has been successfully applied in anisotropic cases, particularly in modeling brain tissue behavior, where it has demonstrated robustness and accuracy in capturing the complex nonlinear effects under stretch. Furthermore, the model has been tested for materials exhibiting strong history dependence, showing potential for broader applications in simulating time and rate-dependent behaviors.

The future integration of this model into Abaqus is a significant development that holds great prospects for the field of finite element analysis. Once integrated, it will enable engineers and researchers to utilize this advanced material model, potentially enhancing the accuracy and efficiency of simulations involving millions of elements. This integration is expected to provide a more interpretable and efficient definition of the material model, with just a few parameters needed to define the input file.

The collaborative nature of this work also opens doors for further advancements in biomedical simulations, including applications in modeling heart valves and different parts of the heart, as well as other materials relevant to the biomedical engineering community at large.

Listen to the full replay of this webinar, here