Model or Experiment?

I was invited to deliver a seminar on composites modeling at a prominent aircraft company. My host, a very experienced engineer, introduced me with the comment: all models are wrong, some are useful.

There are some truths to this comment as it is impossible for a model to capture the complete reality, but it is possible for a model to predict something useful, particularly those of our interests. Interestingly enough, I encountered the same sentiment from another engineer almost the following week just before presenting the significance of predictive modeling for composites to a government review panel.

This sarcastic attitude towards modeling is unfortunately prevalent, particularly within the composites industry. It is disheartening that the following quote by astronomer Harlow Shapley (1885-1972) closely reflects the current state of modeling in the composites industry.

No one trusts a model except the man who wrote it; everyone trusts an observation, except the man who made it.

Experiment Measures What Model Defines

It is indeed puzzling how modeling and simulation have found themselves in such a challenging situation. While I do not fully align with the statement of Sir Arthur Eddington (1882-1944): Never trust an experimental result until it has been confirmed by theory, I wholeheartedly agree with Einstein (1879-1955) in his response to Heisenberg (1901-1976): It is the theory which decides what can be observed.

Experimentalists are often relying on models for making the specimens and interpreting the measurements, although some models are so rudimentary that we almost forget that they are models. Let us take the example of measuring Young's modulus E of a solid material using a simple tension test.

In order to accurately measure Young's modulus, we must ensure that the specimen is designed to experience a uniaxial stress state because the equation we use to obtain Young's modulus is valid only under such a stress state according to the theory of linear elasticity.

For this simple experiment, it is also imperative to make sure that the stress is uniformly distributed over the cross-section of the specimen. This assumption is necessary because we compute the stress using the applied axial force divided by the cross-sectional area. Additionally, we must ensure that the strain distribution over the cross-section and within the gauged length remains uniform because strain is computed as the elongation divided by the undeformed length. Thus, the simple tensile test relies on the simple model E=sigma/epsilon with three critical assumptions: uniaxial stress, uniform stress, and uniform strain, plus those assumptions already inherent in three-dimensional (3D) linear elasticity. Any deviation from these assumptions can result in measured results differing from the Young's modulus defined in 3D linear elasticity.

Experiment Validates Model

With this being said, I want to make it clear that I have no intention whatsoever to devalue the significance of experiments. In fact, I completely agree what has been said by Richard Feynman (1918-1988), It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with the experiment, it's wrong.

Both experiments and models hold equal importance in the pursuit of knowledge. Experiments serve as a means to validate models, while models provide guidance and direction for experiments. Moreover, data obtained from experiments can be used to refine and update existing models, as well as to inspire the development of new ones. It is worth noting that the complexities inherent in real systems often make it challenging to construct a comprehensive mathematical representation of such systems. In these cases, experiments play a crucial role in gathering data that complements our limited understanding and fills the gaps in our knowledge of the real system. Therefore, experiments and models are interdependent and should work hand in hand to advance our understanding of the world.

Model Summarizes, Abstracts, and Transcends Data

I also would like to clarify that I am not suggesting that observations cannot be made without models. Throughout human history, we have made numerous observations without prior theoretical knowledge. My intention is to underscore the crucial role of observations in generating data and emphasize the importance of identifying patterns or order within that data to acquire knowledge that can be shared with others. As Jacob Bronowski (1908-1974) aptly stated: The progress of science is the discovery at each step of a new order which gives unity to what had long seemed unlike. An exemplary case that exemplifies this process is the comprehensive and accurate planetary observations conducted by Tycho Brahe (1546-1601). However, the impact of Brahe's observations would have been limited if it were not for Johannes Kepler (1571-1630), who ingeniously devised three formulas known as Kepler's laws of planetary motion fitting Brahe's data. In contemporary terms, we can consider Kepler's laws as empirical models. Although Kepler's laws perfectly fit the observed data, he had no understanding of why they held true. The true epistemic knowledge came later with Sir Isaac Newton (1643-1727) and his publication of the laws of motion and universal gravitation in his Principia several decades later. Today, Brahe's data is largely unknown, fewer people are familiar with Kepler's laws, but any individual with a basic education knows Newton's laws of motion. Moreover, Newton's laws govern not only the motion of planets but also a myriad of other bodies. The widely employed Molecular Dynamics Simulation (MDS) in materials science and engineering revolves around solving assemblies of molecules governed by Newton's laws of motion.

Therefore, it is crucial to recognize that observations generate valuable data, but it is through the development of models that we can uncover underlying principles and achieve a deeper understanding of the physical world. In other words, models summarize, abstract, and transcend the data from experiments.

What Shall Modelers Do Now?

Instead of dwelling on the skepticism surrounding the value of modeling and passionately advocating for its importance, it is crucial for us as modelers to reflect on what we can do to improve the acceptance of modeling in industries, particularly those involving composites. Below are my two suggestions.

Firstly, engineers need simple models. This is evident from the fact that the rules of mixtures and classical lamination theory are among the most frequently used models in composites industries. Simplicity often translates to efficiency, which is essential for rapid turnaround times demanded by engineering design and analysis in a production environment.

Secondly, models must be reliable and possess sufficient predictive capabilities. Unfortunately, many models for composites, particularly those related to failure and damage analysis, often rely on sophisticated curve-fitting techniques applied to experimental data. By adjusting model parameters, these models can fit experimental data well. However, the agreement with experiments heavily relies on the data obtained from those experiments. These models can be likened to Keplerian models, limited in their ability to make predictions beyond the specific experimental conditions. In this sense, what these models provide is post-diction not pre-diction. It is thus understandable that skepticism persists among composite engineers regarding modeling, because the models we have developed lack robust predictive capabilities.

Thus, to win the trust of engineers and provide values to composites industry, we as modelers should strive for developing simple yet predictive models. These models should be easy and simple to use (i.e., not requiring a PhD degree to properly use them) and it should correlate with experiments. We don't have models meeting all challenges of composites right now. However, we can start now by identifying the main challenges and addressing them one by one.

Listen to an AI-generated podcast based on this article at https://open.spotify.com/episode/0XQFJt5XfEwfdCWxq5dy5M.