Model-Free Data-Driven Viscoelasticity in the Frequency Domain

TL;DR

This paper introduces a novel data-driven method for simulating wave propagation in viscoelastic materials directly from experimental data in the frequency domain, bypassing traditional material modeling.

Contribution

It formulates a frequency domain approach that minimizes the difference between admissible stress-strain histories and experimental data using the flat-norm, enabling direct data utilization.

Findings

Successfully applied to polymeric truss with DMA data

Validated on 3D soft gel with MRE data

Demonstrated robustness and ease of implementation

Abstract

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.