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Model-free Data-Driven viscoelasticity in the frequency domain

Salahshoor, Hossein and Ortiz, Michael (2023) Model-free Data-Driven viscoelasticity in the frequency domain. Computer Methods in Applied Mechanics and Engineering, 403 (Pt. A). Art. No. 115657. ISSN 0045-7825. doi:10.1016/j.cma.2022.115657.

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We develop a Data-Driven framework for the simulation of wave propagation in viscoelastic solids directly from dynamic testing material data, including data from Dynamic Mechanical Analysis (DMA), nano-indentation, Dynamic Shear Testing (DST) and Magnetic Resonance Elastography (MRE), without the need for regression or material modeling. The problem is formulated in the frequency domain and the method of solution seeks to minimize a distance between physically admissible histories of stress and strain, in the sense of compatibility and equilibrium, and the material data. We metrize the space of histories by means of the flat-norm of their Fourier transform, which allows consideration of infinite wave trains such as harmonic functions. Another significant advantage of the flat norm is that it allows the response of the system at one frequency to be inferred from data at nearby frequencies. We demonstrate and verify the approach by means of two test cases, a polymeric truss structure characterized by DMA data and a 3D soft gel sample characterized by MRE data. The examples demonstrate the ease of implementation of the Data-Driven scheme within conventional commercial codes and its robust convergence properties, both with respect to the solver and the data.

Item Type:Article
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URLURL TypeDescription ItemDiscussion Paper
Salahshoor, Hossein0000-0002-7264-7650
Ortiz, Michael0000-0001-5877-4824
Additional Information:Support for this work from the U.S. National Institutes of Health through Grant No. 1RF1MH117080 is gratefully acknowledged. MO is also grateful for support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via project 211504053 - SFB 1060; project 441211072 - SPP 2256; and project 390685813 - GZ 2047/1 - HCM.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)211504053 - SFB 1060
Deutsche Forschungsgemeinschaft (DFG)441211072 - SPP 2256
Deutsche Forschungsgemeinschaft (DFG)390685813 - GZ 2047/1
Issue or Number:Pt. A
Record Number:CaltechAUTHORS:20221117-155430600.5
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117903
Deposited By: Research Services Depository
Deposited On:30 Nov 2022 19:03
Last Modified:30 Nov 2022 19:03

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