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Soft yet tough materials are ubiquitous in nature and everyday life. The ratio between fracture toughness and intrinsic fracture energy of a soft material defines its toughness enhancement. Soft materials' toughness enhancement has been…
Experimental testing on dry woven fabrics exhibits a complex set of evidences that are difficult to be completely described using classical continuum models. The aim of this paper is to show how the introduction of energy terms related to…
Stress-strain curves, or more generally, stress functions, are an extremely important characterization of a material's mechanical properties. However, stress functions are often difficult to derive and are narrowly tailored to a specific…
Symbolic regression (SR) aims to discover concise closed-form mathematical equations from data, a task fundamental to scientific discovery. However, the problem is highly challenging because closed-form equations lie in a complex…
Hardness is a materials' property with implications in several industrial fields, including oil and gas, manufacturing, and others. However, the relationship between this macroscale property and atomic (i.e., microscale) properties is…
Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and…
We propose symbolic regression as a powerful tool for studying Beyond the Standard Model physics. As a benchmark model, we consider the so-called Constrained Minimal Supersymmetric Standard Model, which has a four-dimensional parameter…
We analyze plane strain cold rolling processes, at large strains but slow strain rates, by finite element modeling. At low temperatures, slow strain rates, and moderate thickness reductions during rolling (at which Bauschinger effect can be…
Hyperelastic material characterization is crucial for understanding the behavior of soft materials -- such as tissues, rubbers, hydrogels, and polymers -- under quasi-static loading before failure. Traditional methods typically rely on…
In computational materials science, predicting the yield strain of crosslinked polymers remains a challenging task. A common approach is to identify yield as the first critical point of stress-strain curves simulated by molecular dynamics…
We propose a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Our work is aligned with the popular DSR framework which focuses on learning a…
Symbolic regression discovers explicit, interpretable equations without assuming a functional form in advance. A Bayesian approach strengthens this through probability distributions over candidate expressions, thus quantifying uncertainty…
Process-structure-property relationships are fundamental in materials science and engineering and are key to the development of new and improved materials. Symbolic regression serves as a powerful tool for uncovering mathematical models…
The Deep Material Network (DMN) has emerged as a powerful framework for multiscale materials modeling, enabling efficient and accurate prediction of material behavior across different length scales. Unlike conventional data-driven…
Mathematical formulas are the crystallization of human wisdom in exploring the laws of nature for thousands of years. Describing the complex laws of nature with a concise mathematical formula is a constant pursuit of scientists and a great…
Microstructural heterogeneity affects the macro-scale behavior of materials. Conversely, load distribution at the macro-scale changes the microstructural response. These up-scaling and down-scaling relations are often modeled using…
Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased…
We investigate the cyclic mechanical behavior in uniaxial tension of three different commercial thermoplastic polyurethane elastomers (TPU) often considered as a sustainable replacement for common filled elastomers. All TPU have similar…
A new semi-analytic model of the metal rolling process is introduced, which, for the first time, is able to predict the through-thickness stress and strain oscillations present in long thin roll-gaps. The model is based on multiple-scales…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…