Vahidullah Tac

All Publications

• Data-driven continuum damage mechanics with built-in physics EXTREME MECHANICS LETTERS Tac, V., Kuhl, E., Tepole, A. 2024; 71

  View details for DOI 10.1016/j.eml.2024.102220

  View details for Web of Science ID 001299288400001

• Generative hyperelasticity with physics-informed probabilistic diffusion fields ENGINEERING WITH COMPUTERS Tac, V., Rausch, M. K., Bilionis, I., Sahli Costabal, F., Tepole, A. 2024

  View details for DOI 10.1007/s00366-024-01984-2

  View details for Web of Science ID 001226809000001

• Benchmarking physics-informed frameworks for data-driven hyperelasticity. Computational mechanics Taç, V., Linka, K., Sahli-Costabal, F., Kuhl, E., Tepole, A. B. 2024; 73 (1): 49-65

  Abstract

  Data-driven methods have changed the way we understand and model materials. However, while providing unmatched flexibility, these methods have limitations such as reduced capacity to extrapolate, overfitting, and violation of physics constraints. Recently, frameworks that automatically satisfy these requirements have been proposed. Here we review, extend, and compare three promising data-driven methods: Constitutive Artificial Neural Networks (CANN), Input Convex Neural Networks (ICNN), and Neural Ordinary Differential Equations (NODE). Our formulation expands the strain energy potentials in terms of sums of convex non-decreasing functions of invariants and linear combinations of these. The expansion of the energy is shared across all three methods and guarantees the automatic satisfaction of objectivity, material symmetries, and polyconvexity, essential within the context of hyperelasticity. To benchmark the methods, we train them against rubber and skin stress-strain data. All three approaches capture the data almost perfectly, without overfitting, and have some capacity to extrapolate. This is in contrast to unconstrained neural networks which fail to make physically meaningful predictions outside the training range. Interestingly, the methods find different energy functions even though the prediction on the stress data is nearly identical. The most notable differences are observed in the second derivatives, which could impact performance of numerical solvers. On the rich data used in these benchmarks, the models show the anticipated trade-off between number of parameters and accuracy. Overall, CANN, ICNN and NODE retain the flexibility and accuracy of other data-driven methods without compromising on the physics. These methods are ideal options to model arbitrary hyperelastic material behavior.

  View details for DOI 10.1007/s00466-023-02355-2

  View details for PubMedID 38741577

  View details for PubMedCentralID PMC11090478

• Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations. Computer methods in applied mechanics and engineering Taç, V., Rausch, M., Costabal, F. S., Tepole, A. B. 2023; 411

  Abstract

  We develop a fully data-driven model of anisotropic finite viscoelasticity using neural ordinary differential equations as building blocks. We replace the Helmholtz free energy function and the dissipation potential with data-driven functions that a priori satisfy physics-based constraints such as objectivity and the second law of thermodynamics. Our approach enables modeling viscoelastic behavior of materials under arbitrary loads in three-dimensions even with large deformations and large deviations from the thermodynamic equilibrium. The data-driven nature of the governing potentials endows the model with much needed flexibility in modeling the viscoelastic behavior of a wide class of materials. We train the model using stress-strain data from biological and synthetic materials including humain brain tissue, blood clots, natural rubber and human myocardium and show that the data-driven method outperforms traditional, closed-form models of viscoelasticity.

  View details for DOI 10.1016/j.cma.2023.116046

  View details for PubMedID 37426992

  View details for PubMedCentralID PMC10327622

• Data-driven Modeling of the Mechanical Behavior of Anisotropic Soft Biological Tissue. Engineering with computers Tac, V., Sree, V. D., Rausch, M. K., Tepole, A. B. 2022; 38 (5): 4167-4182

  Abstract

  Closed-form constitutive models are the standard to describe soft tissue mechanical behavior. However, inherent pitfalls of an explicit functional form include poor fits to the data, non-uniqueness of fit, and sensitivity to parameters. Here we design deep neural networks (DNN) that satisfy desirable physics constraints in order to replace expert models of tissue mechanics. To guarantee stress-objectivity, the DNN takes strain (pseudo)-invariants as inputs, and outputs the strain energy and its derivatives. Polyconvexity of strain energy is enforced through the loss function. Direct prediction of both energy and derivative functions enables the computation of the elasticity tensor needed for a finite element implementation. We showcase the DNN ability to learn the anisotropic mechanical behavior of porcine and murine skin from biaxial test data. A multi-fidelity scheme that combines high fidelity experimental data with a low fidelity analytical approximation yields the best performance. Finite element simulations of tissue expansion with the DNN model illustrate the potential of this method to impact medical device design for skin therapeutics. We expect that the open data and software from this work will broaden the use of data-driven constitutive models of tissue mechanics.

  View details for DOI 10.1007/s00366-022-01733-3

  View details for PubMedID 38031587

  View details for PubMedCentralID PMC10686525

• Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations. Computer methods in applied mechanics and engineering Tac, V., Sahli Costabal, F., Tepole, A. B. 2022; 398

  Abstract

  Data-driven methods are becoming an essential part of computational mechanics due to their advantages over traditional material modeling. Deep neural networks are able to learn complex material response without the constraints of closed-form models. However, data-driven approaches do not a priori satisfy physics-based mathematical requirements such as polyconvexity, a condition needed for the existence of minimizers for boundary value problems in elasticity. In this study, we use a recent class of neural networks, neural ordinary differential equations (N-ODEs), to develop data-driven material models that automatically satisfy polyconvexity of the strain energy. We take advantage of the properties of ordinary differential equations to create monotonic functions that approximate the derivatives of the strain energy with respect to deformation invariants. The monotonicity of the derivatives guarantees the convexity of the energy. The N-ODE material model is able to capture synthetic data generated from closed-form material models, and it outperforms conventional models when tested against experimental data on skin, a highly nonlinear and anisotropic material. We also showcase the use of the N-ODE material model in finite element simulations of reconstructive surgery. The framework is general and can be used to model a large class of materials, especially biological soft tissues. We therefore expect our methodology to further enable data-driven methods in computational mechanics.

  View details for DOI 10.1016/j.cma.2022.115248

  View details for PubMedID 38045634

  View details for PubMedCentralID PMC10691864

• Predicting the mechanical properties of biopolymer gels using neural networks trained on discrete fiber network data COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Leng, Y., Tac, V., Calve, S., Tepole, A. B. 2021; 387

  View details for DOI 10.1016/j.cma.2021.114160

  View details for Web of Science ID 000708703300009

• Micromechanical modelling of carbon nanotube reinforced composite materials with a functionally graded interphase JOURNAL OF COMPOSITE MATERIALS Tac, V., Gurses, E. 2019; 53 (28-30): 4337-4348

  View details for DOI 10.1177/0021998319857126

  View details for Web of Science ID 000487078400032

• Dynamic Frictional Sliding Modes between Two Homogenous Interfaces Taj, W., Coker, D., Karamis, M. B., Nair, F., Savas, S., Gocer, A., Hamamci, M. IOP PUBLISHING LTD. 2018

  View details for DOI 10.1088/1757-899X/295/1/012001

  View details for Web of Science ID 000448617300001