Abstract
A new inverse problem formulation is developed using the Airy stress function. Inverse methods are used to determine the constitutive properties of a graphite/epoxy laminated composite loaded vertically by processing measured values of v-displacement component with an Airy stress function in complex variables. Displacements are recorded using digital image correlation. The traction-free conditions on the symmetrically located sided notches are satisfied analytically using conformal mappings and analytic continuation. The traction-free on the vertical free edge and a symmetrical condition on horizontal line of symmetry are imposed discretely. The primary advantage of this new formulation is the direct use of displacement data, eliminating the need for numerical differentiation when strain data is required. The inverse method algorithm determined the constitutive properties with errors range from 2% to 10%. Selection of Airy coefficients, test geometry configuration and comparison with other inverse methods will be addressed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alshaya, A.A.: Experimental, analytical and numerical analyses of orthotropic materials and biomechanics application. PhD thesis, University of Wisconsin-Madison (2017)
Alshaya, A., Rowlands, R.: Experimental stress analysis of a notched finite composite tensile plate. Compos. Sci. Technol. 144, 89–99 (2017.) ISSN 0266-3538, http://dx.doi.org/10.1016/j.compscitech.2017.03.007. (http://www.sciencedirect.com/science/article/pii/S0266353816312143)
Ju, S.H., Rowlands, R.E.: Thermoelastic determination of KI and KII in an orthotropic graphite–epoxy composite. J. Compos. Mater. 37(22), 2011–2025 (2003)
Ju, S.H., Rowlands, R.E.: Mixed-mode thermoelastic fracture analysis of orthtropic composites. Int. J. Fract. 120(4), 601–621 (2003)
Lin, S.T., Rowlands, R.E.: Thermoelastic stress analysis of orthotropic composites. Exp. Mech. 35(3), 257–265 (1995)
Alshaya, A., Shuai, X., Rowlands, R.: Thermoelastic stress analysis of a finite orthotropic composite containing an elliptical hole. Exp. Mech. 56(8), 1373–1384 (2016)
Rhee, J., Rowlands, R.E.: Thermoelastic-numerical hybrid analysis of holes and cracks in composites. Exp. Mech. 39(4), 349–355 (1999)
Hawong, J.S., Lin, C.H., Lin, S.T., Rhee, J., Rowlands, R.E.: A hybrid method to determine individual stresses in orthotropic composites using only measured isochromatic data. J. Compos. Mater. 29(18), 2366–2387 (1995)
Baek, T.H., Rowlands, R.E.: Experimental determination of stress concentrations in orthotropic composites. J. Strain Anal. Eng. Des. 34(2), 69–81 (1999)
Baek, T., Rowlands, R.: Hybrid stress analysis of perforated composites using strain gages. Exp. Mech. 41(2), 195–203 (2001)
Avril, S., Pierron, F.: General framework for the identification of constitutive parameters from full-field measurements in linear elasticity. Int. J. Solids Struct. 44(14–15), 4978–5002 (2007)
Le Magorou, L., Bos, F., Rouger, F.: Identification of constitutive laws for wood-based panels by means of an inverse method. Compos. Sci. Technol. 62(4), 591–596 (2002)
Molimard, J., Le Riche, R., Vautrin, A., Lee, J.-R.: Identification of the four orthotropic plate stiffnesses using a single open-hole tensile test. Exp. Mech. 45(5), 404–411 (2005)
Genovese, K., Lamberti, L., Pappalettere, C.: Improved global–local simulated annealing formulation for solving non-smooth engineering optimization problems. Int. J. Solids Struct. 42(1), 203–237 (2005)
Considine, J.M., Vahey, D.W., Matthys, D., Rowlands, R.E., Turner, K.T.: An inverse method for analyzing defects in heterogeneous materials. In: Proulx, T. (ed.) Application of Imaging Techniques to Mechanics of Materials and Structures, Volume 4: Proceedings of the 2010 Annual Conference on Experimental and Applied Mechanics, pp. 339–346. Springer New York, New York (2013)
Lekhnitskii, S.G.: Anisotropic Plates. Gordon & Breach Scientific Publishers, New York (1968)
Bisshopp, F.: Numerical conformal mapping and analytic continuation. Q. Appl. Math. 41, 125–142 (1983)
Challis, N.V., Burley, D.M.: A numerical method for conformal mapping. IMA J. Numer. Anal. 2(2), 169–181 (1982)
Lekhnitskii, S.G.: Theory of Elasticity of an Anisotropic Elastic Body. Holden-Day, San Francisco (1963)
Lin, S.T., Rowlands, R.E.: Hybrid stress analysis. Opt. Lasers Eng. 32(3), 257–298 (1999)
Muskhelishvili, N.: Some Basic Problems of the Mathematical Theory of Elasticity. Springer, Leyden (1977)
Savin, G.N.: Stress Concentration Around Holes. Pergamon Press 1961
Bowie, O.L., Freese, C.E.: Central crack in plane orthotropic rectangular sheet. Int. J. Fract. Mech. 8(1), 49–57 (1972)
Gerhardt, T.D.: A hybrid/finite element approach for stress analysis of notched anisotropic materials. J. Appl. Mech. 51(4), 804–810 (1984)
Huang, Y.-M.: Determination of individual stresses from thermoelastically measured trace of stress tensor. PhD thesis, University of Wisconsin-Madison
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Alshaya, A., Considine, J.M., Rowlands, R. (2018). Determination of Constitutive Properties in Inverse Problem Using Airy Stress Function. In: Baldi, A., Considine, J., Quinn, S., Balandraud, X. (eds) Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 8. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-62899-8_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-62899-8_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-62898-1
Online ISBN: 978-3-319-62899-8
eBook Packages: EngineeringEngineering (R0)