A Regularized Inverse Framework for Stress and Strain Analysis of Viscoelastic Bodies via DIC–FEA Integration

Authors

DOI:

https://doi.org/10.31265/xqvwvr33

Abstract

A method for obtaining the strain and stress distributions in a viscoelastic body is proposed by combining digital image correlation with finite element analysis based on the principle of superposition. In this method, the boundary conditions within the measurement region are determined via inverse analysis so that the computed displacement fields match those obtained experimentally. A regularization scheme is introduced to mitigate the influence of measurement errors near the boundaries. The strain distributions are obtained simultaneously with the displacement fields. Meanwhile, the stress distributions are evaluated from the temporal evolution of the strain components, taking into account the time-dependent mechanical properties of the viscoelastic material. The effectiveness of the proposed method is demonstrated through a numerical simulation. Furthermore, as an application example, stress analyses around contact interfaces are presented. The proposed method alleviates difficulties in data processing during measurement and provides an effective approach for stress and strain analysis of viscoelastic bodies.

References

Knauss, W.G. A review of Fracture in Viscoelastic Materials. Int. J. Fract. 2015, 196, 99−146. https://doi.org/10.1007/s10704-015-0058-6

Yoneyama, S. and Takashi, M. Quantitative Characterization of Cracks and Contact Stresses Using Photoviscoelasticity. In Advances in Mechanics of Time-Dependent Materials (Altenbach, H., Kaplunov, J., Lu, H. and Nakada, M. eds.), Springer, 2023, 215−247.

https://doi.org/10.1007/978-3-031-22401-0_13

Shull, K.R. Contact Mechanics and the Adhesion of Soft Solids. Mater. Sci. Eng. 2002, 36, 1−45. https://doi.org/10.1016/S0927-796X(01)00039-0

Post, D., Han, B. and Ifju, P. High Sensitivity Moiré. Springer, 1994. https://doi.org/10.1007/978-1-4612-4334-2

Sutton, M.A., Orteu, J.-J. and Schreier, H.W. Image Correlation for Shape, Motion and Deformation Measurement. Springer, 2009.

Yoneyama, S. Computing Strain Distributions from Measured Displacements on a Three-dimensional Surface. J. JSEM 2010, 10, 113−118.

Segalman, D.J., Woyak, D.B. and Rowlands, R.E. Smooth Spline-like Finite-element Differentiation of Full-field Experimental Data Over Arbitrary Geometry. Exp. Mech. 1979, 19, 429−437. https://doi.org/10.1007/BF02326046

Yoneyama, S. Smoothing Measured Displacements and Computing Strains Utilizing Finite Element Method. Strain 2011, 47, 258−266. https://doi.org/10.1111/j.1475-1305.2010.00765.x

Sutton, M.A., Turner, J.L., Bruck, H. and Chae, T.A. Full-field Representation of Discretely Sampled Surface Deformation for Displacement and Strain Analysis. Exp. Mech. 1991, 31, 168−177. https://doi.org/10.1007/BF02327571

Nishioka, T., Kurio, K. and Nakabayashi, H. An Intelligent Hybrid Method to Automatically Detect and Eliminate Experimental Measurement Errors for Linear Elastic Deformation Fields. Exp. Mech. 2000, 40, 170−179. https://doi.org/10.1007/BF02325043

Yoneyama, S. and Arikawa, S. Identification of Boundary Condition from Measured Displacements for Linear Elastic Deformation Fields. Procedia IUTAM 2012, 4, 215−226. https://doi.org/10.1016/j.piutam.2012.05.023

Kubo, S. Inverse Problems (in Japanese), Baifukan,1992.

Christensen, R.M. Theory of Viscoelasticity, 2nd ed., Elsevier, 1982. https://doi.org/10.1016/B978-0-12-174252-2.50012-0

Hoshino, Y., Tamai, K., Zhang, Y. and Yoneyama, S. Direct Measurement and Master Curve Construction of Viscoelastic Poisson's ratio with Digital Image Correlation. Strain 2018, 54, e12294. https://doi.org/10.1111/str.12294

Parks, S.W. and Shapery, R.A. Methods of Interconversion between Linear Viscoelastic Material Functions. Part I-A Numerical Method Based on Prony Series. Int. J. Solids Struct. 1999, 36, 1653−1675. https://doi.org/10.1016/S0020-7683(98)00055-9

Williams, M.L., Landel, R.F. and Ferry, J.D. The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids. J. Am. Chem. Soc. 1955, 77, 3701−3707. https://doi.org/10.1021/ja01619a008

Johnson, K.L. Contact Mechanics, Cambridge University Press, 1985. https://doi.org/10.1017/CBO9781139171731

Sun, D., Taguchi, S., Niki, I., Iizuka, K. and Yoneyama, S., The Virtual Fields Method for Identifying Viscoelastic Properties Based on Stress Sensitivity Virtual Fields. Mech. Time-depend. Mater. 2025, 29, 43. https://doi.org/10.1007/s11043-025-09781-0

Yoneyama, S., Arikawa, S. and Kobayashi, Y. Linear and Nonlinear Algorithms for Stress Separation in Photoelasticity, Exp. Mech. 2012, 52, 529−538. https://doi.org/10.1007/s11340-011-9512-1

Yoneyama, S. Basic Principle of Digital Image Correlation for In-plane Displacement and Strain Measurement, Adv. Compos. Mater. 2016, 25, 105−123. https://doi.org/10.1080/09243046.2015.1129681

Downloads

Published

2026-08-26

How to Cite

[1]
S. Yoneyama, Y. Rai, and K. Iizuka, “A Regularized Inverse Framework for Stress and Strain Analysis of Viscoelastic Bodies via DIC–FEA Integration”, ATNRS, vol. 34, pp. 13–21, Aug. 2026, doi: 10.31265/xqvwvr33.