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A deep learning framework for solution and discovery in solid mechanics [article]

Ehsan Haghighat, Maziar Raissi, Adrian Moure, Hector Gomez, Ruben Juanes
2020 arXiv   pre-print
We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics.  ...  We explain how to incorporate the momentum balance and constitutive relations into PINN, and explore in detail the application to linear elasticity, and illustrate its extension to nonlinear problems through  ...  Conclusions We study the application of a class of deep learning, known as Physics-Informed Neural Networks (PINN), for solution and discovery in solid mechanics.  ... 
arXiv:2003.02751v2 fatcat:xuiydxnlyvbbtf4ubfugmg4lbm

Meshless physics-informed deep learning method for three-dimensional solid mechanics [article]

Diab W. Abueidda, Qiyue Lu, Seid Koric
2021 arXiv   pre-print
Data generation usually is the main bottleneck in most data-driven models. The deep learning model is trained to learn the model's parameters yielding accurate approximate solutions.  ...  We have considered different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with large deformation, and von Mises plasticity with isotropic and kinematic hardening.  ...  Acknowledgment The authors would like to thank the National Center for Supercomputing Applications (NCSA) Industry Program and the Center for Artificial Intelligence Innovation.  ... 
arXiv:2012.01547v2 fatcat:hcpfovszhfchjedvo3cg6vmjaa

PhySRNet: Physics informed super-resolution network for application in computational solid mechanics [article]

Rajat Arora
2022 arXiv   pre-print
However, technical challenges still remain in developing a high-fidelity SR model for application to computational solid mechanics, especially for materials undergoing large deformation.  ...  This work aims at developing a physics-informed deep learning based super-resolution framework (PhySRNet) which enables reconstruction of high-resolution deformation fields (displacement and stress) from  ...  The author also thank Ankit Shrivastava, research associate at Sandia National Laboratories, for useful discussions and comments on the manuscript.  ... 
arXiv:2206.15457v1 fatcat:74lbqtgnyzhnzaucvkk3gpowae

Teaching Solid Mechanics to Artificial Intelligence: a fast solver for heterogeneous solids [article]

Jaber Rezaei Mianroodi, Nima H. Siboni, Dierk Raabe
2021 arXiv   pre-print
We propose a deep neural network (DNN) as a fast surrogate model for local stress (and in principle strain) calculation in inhomogeneous non-linear material systems.  ...  The results reveal a completely new and highly efficient approach to solve non-linear mechanical boundary value problems and/or augment existing solution methods in corresponding hybrid variants, with  ...  Introducing a deep learning alternative for a physics-based solution scheme should be carried out with stringent assessment of the performance in quality of the solutions (see Refs.  ... 
arXiv:2103.09147v1 fatcat:dwjzkrfyhbhl3kzktdzgep6wxu

Artificial Intelligence and Machine Learning in Design of Mechanical Materials

Kai Guo, Zhenze Yang, Chi-Hua Yu, Markus J. Buehler
2021 Materials Horizons  
Artificial intelligence, especially machine learning (ML) and deep learning (DL) algorithms, is becoming an important tool in the fields of materials and mechanical engineering, attributed to its power  ...  His research interests focus on fracture mechanics in solids and structures, multiscale modeling of complex alloys and composites, and using advanced deep learning models to study bioinspired structural  ...  distribution in complex solutions (Fig. 9 ). 176 n a recent work by Samaniego et al., deep neural networks based on the variational form of the boundary value problems were implemented as solvers for  ... 
doi:10.1039/d0mh01451f pmid:34821909 fatcat:as7gd4u6rzfflgdra5iemzinh4

Materials Informatics for Mechanical Deformation: A Review of Applications and Challenges

Karol Frydrych, Kamran Karimi, Michal Pecelerowicz, Rene Alvarez, Francesco Javier Dominguez-Gutiérrez, Fabrizio Rovaris, Stefanos Papanikolaou
2021 Materials  
In this fast-growing field, we focus on reviewing advances at the intersection of data science with mechanical deformation simulations and experiments, with a particular focus on studies of metals and  ...  In the design and development of novel materials that have excellent mechanical properties, classification and regression methods have been diversely used across mechanical deformation simulations or experiments  ...  Acknowledgments: We would like to thank Mikko Alava for inspiring discussions and fruitful suggestions and Paweł Sobkowicz for showing us the inspiring motivation for this work.  ... 
doi:10.3390/ma14195764 pmid:34640157 fatcat:o5csvoojpbhazfo63rcv4ersf4

Correlative image learning of chemo-mechanics in phase-transforming solids [article]

Haitao D. Deng, Hongbo Zhao, Norman L. Jin, Lauren Hughes, Benjamin Savitzky, Colin Ophus, Dimitrios Fraggedakis, András Borbély, Young-Sang Yu, Eder Lomeli, Rui Yan, Jueyi Liu (+5 others)
2021 arXiv   pre-print
In this work, we developed a generalizable, physically-constrained image-learning framework to algorithmically learn the chemo-mechanical constitutive law at the nanoscale from correlative four-dimensional  ...  One such relationship is between composition and eigenstrain, which governs the chemo-mechanical expansion in solids.  ...  For example, the compositioneigenstrain relation in solids, such as the linear response postulate in Vegard's law 7, 8 , governs chemo-mechanics 9-12 -that is, how a material changes shape with compositional  ... 
arXiv:2107.06192v1 fatcat:6i62lx3bsjdjngj33lcqmqyuwu

Exploring the 3D architectures of deep material network in data-driven multiscale mechanics

Zeliang Liu, C.T. Wu
2019 Journal of the mechanics and physics of solids  
The complete learning and extrapolation procedures of DMN establish a reliable data-driven framework for multiscale material modeling and design.  ...  With linear elastic data generated by direct numerical simulations on a representative volume element (RVE), the network can be effectively trained in the offline stage using stochastic gradient descent  ...  The global framework of deep material network Preliminaries The global framework of deep material network is presented in Figure 1 .  ... 
doi:10.1016/j.jmps.2019.03.004 fatcat:e53dbpiv55frrk2v6xwn2gwn7y

Mechanical meta-materials

Amir A. Zadpoor
2016 Materials Horizons  
A review of mechanical meta-materials that offer unusual mechanical properties and new functionalities.  ...  In this paper, we will particularly focus on meta-materials with a rare or unprecedented range of elastic mechanical properties including both the linear elastic behavior described by the elasticity tensor  ...  Crystals with negative line and area compressibility have been identified 47 including recent discovery of negative linear compressibility in methanol monohydrate, which is a relatively simple molecular  ... 
doi:10.1039/c6mh00065g fatcat:jvjakes6znd5lisj5vfrkjyvhu

A Survey of Datasets, Preprocessing, Modeling Mechanisms, and Simulation Tools Based on AI for Material Analysis and Discovery

Imran Imran, Faiza Qayyum, Do-Hyeun Kim, Seon-Jong Bong, Su-Young Chi, Yo-Han Choi
2022 Materials  
Recently, machine learning-based mechanisms have been adapted for material science applications, meeting traditional experiments' challenges in a time and cost-efficient manner.  ...  This study presents a comprehensive survey of state-of-the-art benchmark data sets, detailed pre-processing and analysis, appropriate learning model mechanisms, and simulation techniques for material discovery  ...  • Deep learning is explored for modeling mechanisms; however, deep learning-based optimization mechanisms must be explored for stable material and material with maximum performance index properties  ... 
doi:10.3390/ma15041428 pmid:35207968 pmcid:PMC8875409 fatcat:43rsdj5gnnf6rhqfr6qlnm2syq

Computational Mechanics in Science and Engineering – Quo Vadis

Peter Wriggers
2018 Razred za tehničke znanosti (HAZU od 1991 -)  
Computational Mechanics has many applications in science and engineering. Its range of application has been enlarged widely in the recent decades.  ...  Hence, nowadays areas such as biomechanics and additive manufacturing are among the new research topics, in which computational mechanics helps solve complex problems and processes.  ...  Machine learning and manifold learning, and, notably, deep learning techniques, have contributed to an unprecedented growth in the wide range of engineering applications as well.  ... 
doi:10.21857/ypn4oc8nw9 fatcat:rbdveguuonfljo3yruxuzzzy2e

A nonlocal physics-informed deep learning framework using the peridynamic differential operator [article]

Ehsan Haghighat, Ali Can Bekar, Erdogan Madenci, Ruben Juanes
2020 arXiv   pre-print
The Physics-Informed Neural Network (PINN) framework introduced recently incorporates physics into deep learning, and offers a promising avenue for the solution of partial differential equations (PDEs)  ...  We apply nonlocal PDDO-PINN to the solution and identification of material parameters in solid mechanics and, specifically, to elastoplastic deformation in a domain subjected to indentation by a rigid  ...  Recently, PINN has been applied for inversion and discovery in solid mechanics [14] .  ... 
arXiv:2006.00446v1 fatcat:2i2mpp54evh55nh4fuktnt7r4y

An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications [article]

Esteban Samaniego, Cosmin Anitescu, Somdatta Goswami, Vien Minh Nguyen-Thanh, Hongwei Guo, Khader Hamdia, Timon Rabczuk, Xiaoying Zhuang
2019 arXiv   pre-print
The energy of a mechanical system seems to be the natural loss function for a machine learning method to approach a mechanical problem.  ...  the solution of a PDE.  ...  In the deep learning Tensorflow framework, a variety of optimizers are available to help to gain an optimal solution, and the Adam and LBFGS optimizers are mainly adopted in numerical examples.  ... 
arXiv:1908.10407v2 fatcat:nkpln2dkffa7hoz72hyisas7sy

Data-driven discovery of quasi-disordered mechanical metamaterials failed progressively [article]

Akash Singh Bhuwal, Yong Pang, Ian Ashcroft, Wei Sun, Tao Liu
2022 arXiv   pre-print
A data-driven approach has been developed, combining deep-learning and global optimization algorithms, to tune the distribution of the disorderliness to achieve the damage tolerant QTM designs.  ...  Our results suggest a novel design pathway for architected materials to improve damage tolerance.  ...  The QTM design space for two-and three-dimensional topologies A deep learning framework to map design space to output space The input and output databases were generated to feed into deep learning neural  ... 
arXiv:2207.05001v2 fatcat:tkhbxucvprazfitlfdz44afgxe

Unsupervised discovery of interpretable hyperelastic constitutive laws

Moritz Flaschel, Siddhant Kumar, Laura De Lorenzis
2021 Computer Methods in Applied Mechanics and Engineering  
Sparsity of the solution is achieved by ℓ p regularization combined with thresholding, which calls for a non-linear optimization scheme.  ...  We propose a new approach for data-driven automated discovery of isotropic hyperelastic constitutive laws.  ...  computational solid mechanics.  ... 
doi:10.1016/j.cma.2021.113852 fatcat:a2adag6qszegbmg3rwdm4mfjby
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