A key problem in solid mechanics is the identification of the constitutive law of a material, which defines the relationship between strain history and stress. Recent advances in machine learning have significantly impacted this field. We introduce inelastic Constitutive Kolmogorov-Arnold Networks (iCKANs), a novel artificial neural network architecture capable of automatically discovering symbolic constitutive laws that describe both the elastic and inelastic behavior of materials. This network translates data from material testing into corresponding elastic and inelastic potential functions in closed mathematical form.
We demonstrate the advantages of iCKANs using both synthetic and experimental data from viscoelastic polymer materials VHB 4910 and VHB 4905. The results show that iCKANs accurately capture complex viscoelastic behavior while preserving physical interpretability. A particular strength of iCKANs is their ability to process not only mechanical data but also any additional information available about a material, such as temperature-dependent behavior. This positions iCKANs as a powerful tool for future discoveries on how specific processing or service conditions affect material properties.
Blogger's Review: The introduction of iCKANs offers a fresh perspective in material science, leveraging machine learning for the automated discovery of constitutive models. This not only increases efficiency but also enhances interpretability, showcasing vast potential for practical applications.