Data‐driven computing in dynamics

We formulate extensions to Data Driven Computing for both distance minimizing and entropy maximizing schemes to incorporate time integration. Previous works focused on formulating both types of solvers in the presence of static equilibrium constraints. Here formulations assign data points a variable relevance depending on distance to the solution and on maximum-entropy weighting, with distance minimizing schemes discussed as a special case. The resulting schemes consist of the minimization of a suitably-defined free energy over phase space subject to compatibility and a time-discretized momentum conservation constraint. We present selected numerical tests that establish the convergence properties of both types of Data Driven solvers and solutions.

[1]  Krishna Rajan.  Materials informatics part I: A diversity of issues , 2008 .

[2]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[3]  Trenton Kirchdoerfer,et al.  Data-driven computational mechanics , 2015, 1510.04232.

[4]  Jie Li,et al.  Data-intensive science: The Terapixel and MODISAzure projects , 2011, Int. J. High Perform. Comput. Appl..

[5]  Trenton Kirchdoerfer,et al.  Data Driven Computing with Noisy Material Data Sets , 2017, 1702.01574.

[6]  Christopher M. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .

[7]  Marc Bonnet,et al.  Inverse material identification in coupled acoustic-structure interaction using a modified error in constitutive equation functional , 2014, Computational mechanics.

[8]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[9]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[10]  Claude E. Shannon,et al.  The mathematical theory of communication , 1950 .

[11]  Bertrand Wattrisse,et al.  Elastoplastic Behavior Identification for Heterogeneous Loadings and Materials , 2008 .

[12]  L. Swiler,et al.  AN OVERVIEW OF INVERSE MATERIAL IDENTIFICATION WITHIN THE FRAMEWORKS OF DETERMINISTIC AND STOCHASTIC PARAMETER ESTIMATION , 2013 .

[13]  Magdalena Ortiz,et al.  Local maximum‐entropy approximation schemes: a seamless bridge between finite elements and meshfree methods , 2006 .

[14]  Arie Shoshani,et al.  A science data gateway for environmental management , 2016, Concurr. Comput. Pract. Exp..

[15]  Ana Azevedo.  Integration of Data Mining in Business Intelligence Systems , 2014 .

[16]  Marc Bonnet,et al.  Large Scale Parameter Estimation Problems in Frequency-Domain Elastodynamics Using an Error in Constitutive Equation Functional. , 2013, Computer methods in applied mechanics and engineering.

[17]  Pierre Feissel,et al.  Modified constitutive relation error identification strategy for transient dynamics with corrupted data : the elastic case , 2007 .

[18]  François Hild,et al.  Application of the virtual fields method to mechanical characterization of elastomeric materials , 2009 .

[19]  Surya R. Kalidindi,et al.  Data science and cyberinfrastructure: critical enablers for accelerated development of hierarchical materials , 2015 .

[20]  Krishna Rajan.  Informatics and integrated computational materials engineering: Part II , 2009 .

[21]  Pierre Feissel,et al.  A robust identification strategy for rate-dependent models in dynamics , 2008 .

[22]  Phillip B. Messersmith,et al.  Bioinspired antifouling polymers , 2005 .

[23]  Vasant Dhar,et al.  Editorial - Big Data, Data Science, and Analytics: The Opportunity and Challenge for IS Research , 2014, Inf. Syst. Res..

[24]  Alexander Tropsha,et al.  Materials Informatics , 2019, J. Chem. Inf. Model..

[25]  Krishna Rajan,et al.  Informatics derived materials databases for multifunctional properties , 2015, Science and technology of advanced materials.

[26]  Frederic Roger,et al.  Direct identification of nonlinear damage behavior of composite materials using the constitutive equation gap method , 2014 .

[27]  Krishna Rajan,et al.  Informatics for combinatorial materials science , 2008 .

[28]  Aleksandr Yakovlevich Khinchin,et al.  Mathematical foundations of information theory , 1959 .

[29]  Elisa D. Sotelino,et al.  Efficiency of group implicit concurrent algorithms for transient finite element analysis , 1989 .

[30]  Pierre Villon,et al.  Robust identification of elastic properties using the Modified Constitutive Relation Error , 2015 .

[31]  Krishna Rajan,et al.  Materials Informatics: The Materials ``Gene'' and Big Data , 2015 .

[32]  Surya R. Kalidindi,et al.  Materials Data Science: Current Status and Future Outlook , 2015 .

[33]  Biswanath Banerjee,et al.  Constitutive error based material parameter estimation procedure for hyperelastic material , 2015 .