Session: 13-19-01: Scientific Machine Learning (SciML) for Characterization, Modeling, and Design of Structures and Materials I

Paper Number: 167192

Physics-Informed Data-Driven Constitutive Modeling of Hyperelasticity and Damage in Soft Materials 

A physics-informed machine learning-based constitutive model is proposed to accurately capture the nonlinear stress-strain response of soft materials, including the effects of mechanical damage. The model is designed for a wide range of soft materials, such as elastomers, biological tissues, and hydrogels, which exhibit highly nonlinear mechanical behaviors. The proposed model represents the total stress as a multiplicative decomposition of two distinct components: (i) a hyperelastic stress component, which captures the response of the intact, undamaged material, and (ii) a damage component, which accounts for the gradual reduction in load-carrying capacity due to mechanical degradation. This approach ensures that the intact material's behavior is modeled adequately while simultaneously capturing the effects of progressive mechanical damage as the material undergoes large deformations. The hyperelastic stress component is further additively decomposed into volumetric and isochoric parts, ensuring a physically meaningful separation between bulk and shear responses. Separate ML-based surrogate models are developed for the elastic and the damage components, the sequential combination of which results in the overall data-driven constitutive model.

Using the Coleman–Noll procedure, we show that each elastic stress component can be written as a linear combination of the components of certain irreducible integrity bases. Two Gaussian process regression (GPR) surrogates are thus trained to discover the mapping between invariants of the right Cauchy-Green deformation tensor and the corresponding response coefficients of these integrity bases. It is shown that this type of model construction imposes several physical constraints: frame-indifference, material symmetry, stress-free reference state, and the second law of thermodynamics. A third GPR surrogate is trained between the response coefficients of the elastic stress (from the previous GPR surrogates) and a variable that captures the stress reduction due to mechanical damage. A constraint is imposed on this surrogate to ensure strict concavity of this variable with respect to the hyperelastic strain energy density, ensuring irreversible damage accumulation. This constraint is imposed during optimization of the marginal log-likelihood function of this surrogate.

Numerical tests are conducted by training the three GPR surrogates using artificially generated stress-strain data in a limited range of tensile deformation, and then predicting responses in shear. It is demonstrated that the data-driven constitutive model offers accurate fitting of the training data and makes physically reasonable predictions outside the training regime. Finally, the data-driven model is applied on experimentally obtained tensile damage response of agarose gel, a physically-crosslinked hydrogel. Both good fitting accuracy and prediction performance is observed.

Presenting Author: Kshitiz Upadhyay Louisiana State University

Presenting Author Biography: Kshitiz Upadhyay is an Assistant Professor in the Department of Mechanical and Industrial Engineering at Louisiana State University, where he directs the Soft Materials Mechanics Laboratory. His research focuses on the mechanics of soft polymers, with an emphasis on constitutive modeling, experimental solid mechanics, data-driven methods, and injury biomechanics. Dr. Upadhyay’s work is supported by the National Science Foundation (NSF), the Office of Naval Research (ONR), the National Aeronautics and Space Administration (NASA), and the Louisiana Board of Regents (LABoR). He received the 2022 Early Career Research Award from the World Council of Biomechanics for his research on the mechanics of the human brain. Before joining LSU, he was a postdoctoral fellow at the Hopkins Extreme Materials Institute at Johns Hopkins University (2020–2022). He earned his Ph.D. and M.S. in Mechanical Engineering from the University of Florida (2020, 2019) and a B.Tech. from the National Institute of Technology–Bhopal, India (2014).

Authors:

Kshitiz Upadhyay Louisiana State University