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Item type:Publication, Access status: with files , Inelastic Constitutive Kolmogorov–Arnold Networks: a generalized framework for automated discovery of interpretable inelastic material models(Elsevier, 2026-11-01); ; ; ; A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain history and stress. Machine learning has led to considerable advances in this field lately. Here we introduce inelastic Constitutive Kolmogorov–Arnold Networks (iCKANs). This novel artificial neural network architecture can discover in an automated manner symbolic constitutive laws describing both the elastic and inelastic behavior of materials. That is, it can translate data from material testing into corresponding free energy and dissipation potential functions in closed mathematical form. We demonstrate the advantages of iCKANs using both synthetic data and experimental data of the viscoelastic polymer materials VHB 4910 and VHB 4905. The results demonstrate that iCKANs accurately capture complex viscoelastic behavior while preserving physical interpretability. It is a particular strength of iCKANs that they can process not only mechanical data but also arbitrary additional information available about a material (e.g., about temperature-dependent behavior). This makes iCKANs a powerful tool to discover in the future also how specific processing or service conditions affect the properties of materials.Publicationtype: Journal Article20 7 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , A generalized dual potential for inelastic Constitutive Artificial Neural Networks: a JAX implementation at finite strainsWe present a methodology for designing a generalized dual potential, or pseudo potential, for inelastic Constitutive Artificial Neural Networks (iCANNs). This potential, expressed in terms of stress invariants, inherently satisfies thermodynamic consistency for large deformations. In comparison to our previous work, the new potential captures a broader spectrum of material behaviors, including pressure-sensitive inelasticity. To this end, we revisit the underlying thermodynamic framework of iCANNs for finite strain inelasticity and derive conditions for constructing a convex, zero-valued, and non-negative dual potential. To embed these principles in a neural network, we detail the architecture's design, ensuring a priori compliance with thermodynamics. To evaluate the proposed architecture, we study its performance and limitations discovering visco-elastic material behavior, though the method is not limited to visco-elasticity. In this context, we investigate different aspects in the strategy of discovering inelastic materials. Our results indicate that the novel architecture robustly discovers interpretable models and parameters, while autonomously revealing the degree of inelasticity. The iCANN framework, implemented in JAX, is publicly accessible at https://doi.org/10.5281/zenodo.14894687.Publicationtype: Journal Article22 20 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Automated model discovery for tensional homeostasis: Constitutive machine learning in growth and remodelingWe present a built-in physics neural network architecture, known as inelastic Constitutive Artificial Neural Network (iCANN), to discover the inelastic phenomenon of tensional homeostasis. In this course, identifying the optimal model and material parameters to accurately capture the macroscopic behavior of inelastic materials can only be accomplished with significant expertise, is often time-consuming, and prone to error, regardless of the specific inelastic phenomenon. To address this challenge, built-in physics machine learning algorithms offer significant potential. We introduce the incorporation of kinematic growth and homeostatic surfaces into the iCANN to discover the Helmholtz free energy and the pseudo potential. The latter describes the state of homeostasis in a smeared sense. To this end, we additionally propose a novel design of the corresponding feed-forward network in terms of principal stresses. We evaluate the ability of the proposed network to learn from experimentally obtained tissue equivalent data at the material point level, assess its predictive accuracy beyond the training regime, and discuss its current limitations when applied at the structural level. Our source code, data, examples, and an implementation of the corresponding material subroutine are made accessible to the public at https://doi.org/10.5281/zenodo.13946282.Publicationtype: Journal Article27 35 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , A comprehensive framework for computational modeling of growth and remodeling in tissue-engineered soft collagenous materials(Springer, 2025); ; ; ; Developing clinically viable tissue-engineered structural cardiovascular implants—such as vascular grafts and heart valves—remains a formidable challenge. Achieving reliable and durable outcomes requires a deeper understanding of the fundamental mechanisms driving tissue evolution during in vitro maturation. Although considerable progress has been made in modeling soft tissue growth and remodeling, studies focused on the early stages of tissue engineering remain limited. Here, we present a general, thermodynamically consistent model to predict tissue evolution and mechanical response throughout the in vitro maturation of passive, load-bearing soft collagenous constructs. The formulation utilizes a stress-driven homeostatic surface to capture volumetric growth, coupled with an energy-based approach to describe collagen densification via the strain energy of the fibers. We further employ a co-rotated intermediate configuration to ensure the model’s consistency and generality. The framework is demonstrated with two numerical examples: a uniaxially constrained tissue strip validated against experimental data and a cruciform-shaped biaxially constrained specimen subjected to load perturbation. These results highlight the potential of the proposed model to advance the design and optimization of tissue-engineered structural cardiovascular implants with clinically relevant performance.Publicationtype: Journal Article23 10