GEW soft strip

Compute guided elastic waves (GEWs) in a soft strip.

This code computes dispersion curves of an anisotropic waveguide with rectangular cross-section. It uses the spectral collocation method (SCM) and is an extension to "GEW dispersion script".

Three cases are included: 1. strip_elastic_SCM.m: linear-elastic (possibly anisotropic) strip with free boundaries. 2. strip_elastic_clamped_SCM.m: same but with the lateral boundaries clamped. 3. strip_elastic_SA_SCM.m: free strip with symmetry conditions (SS, SA, AA, AS). 4. strip_soft_viscoAE_SCM.m: includes acoustoelasticity and viscosity for a soft, nearly-incompressible strip.

Acoustoelasticity and viscosity are inherently present in common soft matter, such as biological tissues. Acoustoelasticity describes the effect of pre-stress on the wave propagation, which we account for using a compressible Mooney-Rivlin hyperelastic material model. Viscoelastic losses are included with a fractional Kelvin-Voigt model. The difficulty relies in the interdependence of both effects.

The methods have been presented in:

A. Delory, D. A. Kiefer, M. Lanoy, A. Eddi, C. Prada, and F. Lemoult, “Viscoelastic dynamics of a soft strip subject to a large deformation,” Soft Matter, Jan. 2024, doi: 10.1039/D3SM01485A.

Code repository: https://github.com/dakiefer/gewsoftstrip

How to use

1. Change into the GEW_soft_strip folder or add it to the Matlab path.
2. Execute the desired script, i.e., strip_elastic_SCM.m, strip_elastic_SA_SCM.m,strip_elastic_clamped_SCM.m or strip_soft_viscoAE_SCM.
3. If you want to implement a different hyperviscoelastic material model, you can create it by adapting initiateTensor.nb and createTensorForMatlab.nb and running the latter in Mathematica. Copy the output of the last command as plain text and replace the marked block in customTensor.m with the code you copied.

Limitations

Mixed boundary conditions (Dirichlet and Neumann) as used in strip_elastic_clamped_SCM.m lead to instabilities at the corners. Depending on the parity of the number of collocation points, either the in-plane or the out-of-plane waves are, nonetheless, well represented. Switch to another discretization method, e.g., Finite Elements, if this is still an issue.

Mathematical background

The SCM discretizes boundary-value problems based on the strong form. The two-dimensional implementation that we use is explained in

J. A. Weideman and S. C. Reddy, “A MATLAB Differentiation Matrix Suite,” ACM Trans. Math. Softw., vol. 26, no. 4, pp. 465–519, 2000, doi: 10.1145/365723.365727.

Dependencies

chebdif.m from DMSUITE is bundled and can be found at

J.A.C Weideman (2022). DMSUITE (https://www.mathworks.com/matlabcentral/fileexchange/29-dmsuite), MATLAB Central File Exchange. Retrieved August 18, 2022.

ToMatlab.m is bundled from

Harri Ojanen (1999). Mathematica Expression to Matlab m-file Converter (https://library.wolfram.com/infocenter/MathSource/577/), Wolfram Library Archive. Retrieved June 23rd, 2022.

Citing this software

If this code is useful to you, please cite it as (always including the DOI):

D. A. Kiefer, A. Delory, and F. Lemoult. GEW soft strip (2023), doi 10.5281/zenodo.10372576. https://github.com/dakiefer/GEWsoftstrip

together with the related publication:

A. Delory, D. A. Kiefer, M. Lanoy, A. Eddi, C. Prada, and F. Lemoult, “Viscoelastic dynamics of a soft strip subject to a large deformation,” Soft Matter, Jan. 2024, doi: 10.1039/D3SM01485A.

Authors

Code created 2022–2023 by

Daniel A. Kiefer, Institut Langevin, ESPCI Paris, Université PSL, France
daniel.kiefer@espci.fr   ●   dakiefer.net   ●   Google Scholar   ●   Follow me on ResearchGate!

Alexandre Delory, Institut Langevin, ESPCI Paris, Université PSL, France
delory.alexandre@free.fr   ●   Google Scholar.

Fabrice Lemoult, Institut Langevin, ESPCI Paris, Université PSL, France
fabrice.lemoult@espci.psl.eu   ●   Google Scholar.