Prakash Thakolkaran

Prakash Thakolkaran, Akshay Joshi, Yiwen Zheng et al.

We propose a new approach for unsupervised learning of hyperelastic constitutive laws with physics-consistent deep neural networks. In contrast to supervised learning, which assumes the availability of stress-strain pairs, the approach only uses realistically measurable full-field displacement and global reaction force data, thus it lies within the scope of our recent framework for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID) and we denote it as NN-EUCLID. The absence of stress labels is compensated for by leveraging a physics-motivated loss function based on the conservation of linear momentum to guide the learning process. The constitutive model is based on input-convex neural networks, which are capable of learning a function that is convex with respect to its inputs. By employing a specially designed neural network architecture, multiple physical and thermodynamic constraints for hyperelastic constitutive laws, such as material frame indifference, (poly-)convexity, and stress-free reference configuration are automatically satisfied. We demonstrate the ability of the approach to accurately learn several hidden isotropic and anisotropic hyperelastic constitutive laws - including e.g., Mooney-Rivlin, Arruda-Boyce, Ogden, and Holzapfel models - without using stress data. For anisotropic hyperelasticity, the unknown anisotropic fiber directions are automatically discovered jointly with the constitutive model. The neural network-based constitutive models show good generalization capability beyond the strain states observed during training and are readily deployable in a general finite element framework for simulating complex mechanical boundary value problems with good accuracy.

Yiwen Zheng, Prakash Thakolkaran, Agni K. Biswal et al.

Vitrimer is a new, exciting class of sustainable polymers with the ability to heal due to their dynamic covalent adaptive network that can go through associative rearrangement reactions. However, a limited choice of constituent molecules restricts their property space, prohibiting full realization of their potential applications. To overcome this challenge, we couple molecular dynamics (MD) simulations and a novel graph variational autoencoder (VAE) machine learning model for inverse design of vitrimer chemistries with desired glass transition temperature (Tg) and synthesize a novel vitrimer polymer. We build the first vitrimer dataset of one million chemistries and calculate Tg on 8,424 of them by high-throughput MD simulations calibrated by a Gaussian process model. The proposed novel VAE employs dual graph encoders and a latent dimension overlapping scheme which allows for individual representation of multi-component vitrimers. By constructing a continuous latent space containing necessary information of vitrimers, we demonstrate high accuracy and efficiency of our framework in discovering novel vitrimers with desirable Tg beyond the training regime. To validate the effectiveness of our framework in experiments, we generate novel vitrimer chemistries with a target Tg = 323 K. By incorporating chemical intuition, we synthesize a vitrimer with Tg of 311-317 K, and experimentally demonstrate healability and flowability. The proposed framework offers an exciting tool for polymer chemists to design and synthesize novel, sustainable vitrimer polymers for a facet of applications.

Prakash Thakolkaran, Yaqi Guo, Shivam Saini et al.

Traditional constitutive models rely on hand-crafted parametric forms with limited expressivity and generalizability, while neural network-based models can capture complex material behavior but often lack interpretability. To balance these trade-offs, we present monotonic Input-Convex Kolmogorov-Arnold Networks (ICKANs) for learning polyconvex hyperelastic constitutive laws. ICKANs leverage the Kolmogorov-Arnold representation, decomposing the model into compositions of trainable univariate spline-based activation functions for rich expressivity. We introduce trainable monotonic input-convex splines within the KAN architecture, ensuring physically admissible polyconvex models for isotropic compressible hyperelasticity. The resulting models are both compact and interpretable, enabling explicit extraction of analytical constitutive relationships through a monotonic input-convex symbolic regression technique. Through unsupervised training on full-field strain data and limited global force measurements, ICKANs accurately capture nonlinear stress-strain behavior across diverse strain states. Finite element simulations of unseen geometries with trained ICKAN hyperelastic constitutive models confirm the framework's robustness and generalization capability.