publications
Ordered by most recent.
2024
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Laura Nunez-Alvarez, Joanna K. Ledwon, Sarah Applebaum, and 6 more authors -
Vahidullah Tac, Ellen Kuhl, and Adrian Buganza TepoleExtreme Mechanics Letters, Aug 2024@article{tacDatadrivenContinuumDamage2024a, title = {Data-Driven Continuum Damage Mechanics with Built-in Physics}, author = {Tac, Vahidullah and Kuhl, Ellen and Tepole, Adrian Buganza}, year = {2024}, month = aug, journal = {Extreme Mechanics Letters}, pages = {102220}, issn = {23524316}, doi = {10.1016/j.eml.2024.102220}, urldate = {2024-08-13}, langid = {english}, url = {https://www.sciencedirect.com/science/article/pii/S2352431624001007} } -
Vahidullah Taç, Manuel K. Rausch, Ilias Bilionis, and 2 more authorsEngineering with Computers, May 2024@article{tacGenerativeHyperelasticityPhysicsinformed2024, title = {Generative Hyperelasticity with Physics-Informed Probabilistic Diffusion Fields}, author = {Ta{\c c}, Vahidullah and Rausch, Manuel K. and Bilionis, Ilias and Sahli Costabal, Francisco and Tepole, Adrian Buganza}, year = {2024}, month = may, journal = {Engineering with Computers}, issn = {0177-0667, 1435-5663}, doi = {10.1007/s00366-024-01984-2}, urldate = {2024-05-20}, langid = {english}, url = {https://link.springer.com/article/10.1007/s00366-024-01984-2} } -
Vahidullah Tac, and Adrian B. TepoleIn Comprehensive Mechanics of Materials (First Edition), Jan 2024@incollection{tac18ModelerGuide2024, title = {A Modeler׳s Guide to Soft Tissue Mechanics}, booktitle = {Comprehensive Mechanics of Materials (First Edition)}, author = {Tac, Vahidullah and Tepole, Adrian B.}, editor = {Silberschmidt, Vadim}, year = {2024}, month = jan, pages = {432--451}, publisher = {Elsevier}, address = {Oxford}, doi = {10.1016/B978-0-323-90646-3.00053-8}, url = {https://www.sciencedirect.com/science/article/pii/B9780323906463000538?via%3Dihub} }
2023
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Vahidullah Taç, Manuel K. Rausch, Francisco Sahli Costabal, and 1 more authorComputer Methods in Applied Mechanics and Engineering, Jan 2023We 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 human brain tissue, blood clots, natural rubber and human myocardium and show that the data-driven method outperforms traditional, closed-form models of viscoelasticity.
@article{TAC2023116046, title = {Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {411}, pages = {116046}, year = {2023}, issn = {0045-7825}, doi = {https://doi.org/10.1016/j.cma.2023.116046}, url = {https://www.sciencedirect.com/science/article/pii/S0045782523001706}, author = {Taç, Vahidullah and Rausch, Manuel K. and {Sahli Costabal}, Francisco and Tepole, Adrian Buganza}, keywords = {Viscoelasticity, Neural ordinary differential equations, Data-driven mechanics, Tissue mechanics, Nonlinear mechanics, Physics-informed machine learning}, } -
Vahidullah Taç, Kevin Linka, Francisco Sahli-Costabal, and 2 more authorsComputational Mechanics, Jun 2023Data-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.
2022
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Vahidullah Tac, Francisco Sahli Costabal, and Adrian B TepoleComputer Methods in Applied Mechanics and Engineering, Jun 2022Data-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.
@article{tacDatadrivenTissueMechanics2022, title = {Data-Driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations}, author = {Tac, Vahidullah and Costabal, Francisco Sahli and Tepole, Adrian B}, year = {2022}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {398}, pages = {18}, doi = {10.1016/j.cma.2022.115248}, langid = {english}, url = {https://www.sciencedirect.com/science/article/pii/S0045782522003838} } -
Vahidullah Tac, Vivek D. Sree, Manuel K. Rausch, and 1 more authorEngineering with Computers, Sep 2022Closed-form constitutive models are currently the standard approach for describing soft tissues’ mechanical behavior. However, there are inherent pitfalls to this approach. For example, explicit functional forms can lead to poor fits, non-uniqueness of those fits, and exaggerated sensitivity to parameters. Here we overcome some of these problems by designing deep neural networks (DNN) to replace such explicit expert models. One challenge of using DNNs in this context is the enforcement of stress-objectivity. We meet this challenge by training our DNN to predict the strain energy and its derivatives from (pseudo)-invariants. Thereby, we can also enforce polyconvexity through physics-informed constraints on the strain-energy and its derivatives in the loss function. Direct prediction of both energy and derivative functions also enables the computation of the elasticity tensor needed for a finite element implementation. Then, we showcase the DNN’s ability by learning the anisotropic mechanical behavior of porcine and murine skin from biaxial test data. Through this example, we find that a multi-fidelity scheme that combines high fidelity experimental data with a low fidelity analytical approximation yields the best performance. Finally, we conduct finite element simulations of tissue expansion using our DNN model to illustrate the potential of data-driven approaches such as ours in medical device design. Also, we expect that the open data and software stemming from this work will broaden the use of data-driven constitutive models in soft tissue mechanics.
@article{tacDatadrivenModelingMechanical2022, title = {Data-Driven Modeling of the Mechanical Behavior of Anisotropic Soft Biological Tissue}, author = {Tac, Vahidullah and Sree, Vivek D. and Rausch, Manuel K. and Tepole, Adrian B.}, year = {2022}, month = sep, journal = {Engineering with Computers}, volume = {38}, number = {5}, pages = {4167--4182}, issn = {0177-0667, 1435-5663}, doi = {10.1007/s00366-022-01733-3}, langid = {english}, url = {https://link.springer.com/article/10.1007/s00366-022-01733-3} }
2021
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Yue Leng, Vahidullah Tac, Sarah Calve, and 1 more authorComputer Methods in Applied Mechanics and Engineering, Dec 2021Biopolymer gels, such as those made out of fibrin or collagen, are widely used in tissue engineering applications and biomedical research. Moreover, fibrin naturally assembles into gels in vivo during wound healing and thrombus formation. The macroscale properties of fibrin and other biopolymer gels are dictated by the response of a microscale fiber network. Hence, accurate description of biopolymer gels can be achieved using representative volume elements (RVE) that explicitly model the discrete fiber networks of the microscale. These RVE models, however, cannot be efficiently used to model the macroscale due to the challenges and computational demands of multiscale coupling. Here, we propose the use of an artificial, fully connected neural network (FCNN) to efficiently capture the behavior of the RVE models. The FCNN was trained on 1100 fiber networks subjected to 121 biaxial deformations. The stress data from the RVE, together with the total energy on the fibers and the condition of incompressibility of the surrounding matrix, were used to determine the derivatives of an unknown strain energy function with respect to the deformation invariants. During training, the loss function was modified to ensure convexity of the strain energy function and symmetry of its Hessian. A general FCNN model was coded into a user material subroutine (UMAT) in the software Abaqus. The UMAT implementation takes in the structure and parameters of an arbitrary FCNN as material parameters from the input file. The inputs to the FCNN include the first two isochoric invariants of the deformation. The FCNN outputs the derivatives of the strain energy with respect to the isochoric invariants. In this work, the FCNN trained on the discrete fiber network data was used in finite element simulations of biopolymer gels using our UMAT. We anticipate that this work will enable further integration of machine learning tools with computational mechanics. It will also improve computational modeling of biological materials characterized by a multiscale structure.
@article{lengPredictingMechanicalProperties2021, title = {Predicting the Mechanical Properties of Biopolymer Gels Using Neural Networks Trained on Discrete Fiber Network Data}, author = {Leng, Yue and Tac, Vahidullah and Calve, Sarah and Tepole, Adrian B.}, year = {2021}, month = dec, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {387}, pages = {114160}, issn = {00457825}, doi = {10.1016/j.cma.2021.114160}, langid = {english}, keywords = {Data-driven,NN}, url = {https://linkinghub.elsevier.com/retrieve/pii/S0045782521004916} }
2019
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Vahidullah Taç, and Ercan GürsesJournal of Composite Materials, Dec 2019This paper introduces a new method of determining the mechanical properties of carbon nanotube-polymer composites using a multi-inclusion micromechanical model with functionally graded phases. The nanocomposite was divided into four regions of distinct mechanical properties; the carbon nanotube, the interface, the interphase and bulk polymer. The carbon nanotube and the interface were later combined into one effective fiber using a finite element model. The interphase was modelled in a functionally graded manner to reflect the true nature of the portion of the polymer surrounding the carbon nanotube. The three phases of effective fiber, interphase and bulk polymer were then used in the micromechanical model to arrive at the mechanical properties of the nanocomposite. An orientation averaging integration was then applied on the results to better reflect macroscopic response of nanocomposites with randomly oriented nanotubes. The results were compared to other numerical and experimental findings in the literature.
@article{tacMicromechanicalModellingCarbon2019, title = {Micromechanical Modelling of Carbon Nanotube Reinforced Composite Materials with a Functionally Graded Interphase}, author = {Taç, Vahidullah and G{\"u}rses, Ercan}, year = {2019}, month = dec, journal = {Journal of Composite Materials}, volume = {53}, number = {28-30}, pages = {4337--4348}, issn = {0021-9983, 1530-793X}, doi = {10.1177/0021998319857126}, langid = {english}, url = {http://journals.sagepub.com/doi/10.1177/0021998319857126} }
2018
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Waheedullah Taj, and Demirkan CokerIOP Conference Series: Materials Science and Engineering, Jan 2018@article{tajDynamicFrictionalSliding2018, title = {Dynamic {{Frictional Sliding Modes}} between {{Two Homogenous Interfaces}}}, author = {Taj, Waheedullah and Coker, Demirkan}, year = {2018}, month = jan, journal = {IOP Conference Series: Materials Science and Engineering}, volume = {295}, number = {1}, pages = {012001}, issn = {1757-8981, 1757-899X}, doi = {10.1088/1757-899X/295/1/012001}, langid = {english}, url = {https://iopscience.iop.org/article/10.1088/1757-899X/295/1/012001/meta} }
