Skip to main content
SpringerLink
Log in

Inverse analyses in fracture mechanics

  • Conference paper
Advances in Fracture Research

Abstract

The present purpose is a survey of some engineering-oriented research results which may be representative of the main issues in the title subject. Some recent or current developments are pointed out in the growing area of fracture mechanics centered on the calibration of cohesive fracture models for quasi-brittle materials, by approaches which combine experimentation, experiment simulation and minimisation of the discrepancy between measured and computed quantities. Specifically, reference is made herein to the following topics in calibration of fracture constitutive models: (a) deterministic characterisation of concrete-like materials by traditional three-point-bending tests (TPBTs), supplemented by optical measurements; (b) wedge-splitting tests (WST) and extended Kalman filter (EKF) for the stochastic estimation of fracture parameters; (c) in situ parameter identification for the local diagnosis of possibly deteriorated concrete dams on the basis of flat-jack tests; (d) fracture properties of ceramic materials and coating-substrate interfaces identified through indentation tests, imprint mapping and inverse analysis in micro-technologies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • ABAQUS/Standard (1998). Theory and User’s Manuals. Release 6.2-1, Pawtucket, RI (USA).

    Google Scholar 

  • Abdul-Baqi, A. and Van der Giessen, E. (2001). Indentation-induced interface delamination of a strong film on a ductile substrate. Thin Solid Films 381, 143–154.

    Article  Google Scholar 

  • Abdul-Baqi, A. and Van der Giessen, E. (2002). Numerical analysis of indentation-induced cracking of brittle coatings on ductile substrates. International Journal of Solids and Structures 39, 1427–1442.

    Article  Google Scholar 

  • Alvaredo, A.M. and Torrent, R.J. (1987). The effect of the shape of the strain-softening diagram on the bearing capacity of concrete beams. Materials and Structures 20, 448–454.

    Article  Google Scholar 

  • Ardito, R., Bartolotta, L., Ceriani, L. and Maier, G. (2004). Diagnostic inverse analysis of concrete dams with static excitation. Journal of the Mechanical Behavior of Materials 15(6), 381–389.

    Google Scholar 

  • Barenblatt, G.I. (1962). The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics 7, 55–129.

    MathSciNet  Google Scholar 

  • Bažant, Z.P. and Planas, J. (1998). Fracture and Size Effect in Concrete and Other Quasi-brittle Materials, CRC Press: Boca Raton, FL (USA).

    Google Scholar 

  • Bhattacharya, A.K. and Nix W.D. (1998). Finite element simulation of indentation experiments. International Journal of Solids and Structures 24, 881–891.

    Article  Google Scholar 

  • Bittanti, S., Maier, G. and Nappi, A. (1984). Inverse problems in structural elasto-plasticity: a Kalman filter approach. In: A. Sawczuck and G. Bianchi (eds.) Plasticity Today Elsevier Applied Science, London, pp. 311–329.

    Google Scholar 

  • Bocciarelli, M., Bolzon, G. and Maier, G. (2005). Parameter identification in anisotropic elastoplasticity by indentation and imprint mapping. Mechanics of Materials 37, 855–868.

    Article  Google Scholar 

  • Bolzon, G. and Cocchetti, G. (2003). Direct assessment of structural resistance against pressurized fracture. International Journal for Numerical and Analytical Methods in Geomechanics 27, 353–378.

    Article  Google Scholar 

  • Bolzon, G., Cocchetti, G., Maier, G., Novati, G. and Giuseppetti, G. (1994a). Boundary element and finite element fracture analysis of dams by the cohesive crack model: a comparative study. In: E. Bourdarot, J. Mazars and V. Sauma (eds.) Dam Fracture and Damage Balkema, Rotterdam, pp. 69–78.

    Google Scholar 

  • Bolzon, G. and Corigliano, A. (1997a). A discrete formulation for elastic solids with damaging interfaces. Computer Methods in Applied Mechanics and Engineering 140, 329–359.

    Article  Google Scholar 

  • Bolzon, G., Fedele, R. and Maier, G. (2002). Identification of cohesive crack models by Kalman filter. Computer Methods in Applied Mechanics and Engineering 191, 2847–2871.

    Article  Google Scholar 

  • Bolzon, G., Ghilotti, D. and Maier, G. (1997b). Parameter identification of the cohesive crack model, In: H. Sol and C.W.J. Oomens (eds.) Material Identification Using Mixed Numerical Experimental Methods Kluwer Academic Publisher, Dordrecht, pp. 213–222.

    Google Scholar 

  • Bolzon, G. (1996). Hybrid finite element approach to quasi-brittle fracture. Computer and Structures 60, 733–741.

    Article  Google Scholar 

  • Bolzon, G. and Maier, G. (1998). Identification of cohesive crack models for concrete by three-point bending tests, In: R. de Borst, N. Bicanic, H. Mang and G. Meschke (eds.) Computational Modelling of Concrete Structures Balkema Publishers, Rotterdam, pp. 301–310.

    Google Scholar 

  • Bolzon, G., Maier, G. and Novati, G. (1994b). Some aspects of quasi-brittle fracture analysis as a linear complementarity problem, In: Z.P. Bažant, Z. Bittnar, M. Jirásek and J. Mazars (eds.) Fracture and Damage in Quasi-brittle Structures E and FN Spon, London, pp. 159–174.

    Google Scholar 

  • Bolzon, G., Maier, G. and Panico, M. (2004). Material model calibration by indentation, imprint mapping and inverse analysis. International Journal of Solids and Structures 41, 2957–2975.

    Article  Google Scholar 

  • Bolzon, G., Maier, G. and Tin-Loi, F. (1995). Holonomic and non-holonomic simulations of quasi-brittle fracture:a comparative study of mathematical programming approaches, In: F.H. Wittman (ed.) Fracture Mechanics of Concrete Structures Aedificatio Publishers, Freiburg, pp. 885–898.

    Google Scholar 

  • Bolzon, G., Maier, G. and Tin-Loi, F. (1997c). On multiplicity of solutions in quasi-brittle fracture computations. Computational Mechanics 19, 511–516.

    Article  Google Scholar 

  • Brühwiler, E. and Wittmann, F.H. (1990). Wedge-splitting test, a new method of performing stable fracture mechanics tests. Engineering Fracture Mechanics 35, 117–125.

    Article  Google Scholar 

  • Bui, H.D. (1994). Inverse Problems in the Mechanics of Materials: an Introduction, CRC Press, Boca Raton, FL (USA).

    Google Scholar 

  • Camacho, G.T. and Ortiz, M. (1996). Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures 33, 2899–2938.

    Article  Google Scholar 

  • Carpinteri, A. (1989). Softening and snap-back instability of cohesive solids. International Journal for Numerical Methods in Engineering 29, 1521–1538.

    Article  Google Scholar 

  • Carpinteri, A., Chiaia, B. and Invernizzi, S. (2001). Numerical analysis of indentation fracture in quasibrittle materials. Engineering Fracture Mechanics 71, 567–577.

    Article  Google Scholar 

  • CEB-FIP Model Code 1990 (1993). Design Code, Thomas Telford Ltd., London.

    Google Scholar 

  • Cen, Z. and Maier, G. (1992). Bifurcations and instabilities in fracture of cohesive-softening structures: a boundary element analysis. Fatigue and Fracture of Engineering Materials and Structures 15, 911–928.

    Google Scholar 

  • Cetinel, H., Uyulgan, B., Tekmen, C., Ozdemir, I. and Celik, E. (2003). Wear properties of functionally gradient layers on stainless steel substrates for high temperature applications. Surface and Coatings Engineering 174–175, 1089–1094.

    Article  Google Scholar 

  • Cheng, Y.T. and Cheng, C.M. (1999). Scaling relationships in conical indentation of elastic perfectly-plastic solids. International Journal of Solids and Structures 36, 1231–1243.

    Article  Google Scholar 

  • Cocchetti, G. and Maier, G. (2003). Elastic-plastic and limit-state analyses of frames with softening plastic-hinge models by mathematical programming. International Journal of Solids and Structures 40, 7219–7244.

    Article  MathSciNet  Google Scholar 

  • Cocchetti, G., Maier, G. and Shen, X. (2002). Piecewise-linear models for interfaces and mixed mode cohesive cracks. Computer Methods in Engineering and Science 3, 279–298.

    Google Scholar 

  • Coleman, T.F. and Li, Y. (1996). An interior trust region approach for nonlinear minimisation subject to bounds. SIAM Journal on Optimization 6, 418–445.

    Article  MathSciNet  Google Scholar 

  • Comi, C., Maier, G. and Perego, U. (1992). Generalized variable finite element modeling and extremum theorems in stepwise holonomic elastoplasticity with internal variables. Computer Methods in Applied Mechanics and Engineering 96, 213–237.

    Article  MathSciNet  Google Scholar 

  • Corigliano, A. and Mariani, S. (2004). Parameter identification in explicit structural dynamics: performance of the extended Kalman filter. Computer Methods in Applied Mechanics and Engineering 193, 3807–3835.

    Article  Google Scholar 

  • Cottle, R.W., Pang, J.S. and Stone, R.E. (1992). The Linear Complementarity Problem, Academic Press, Boston.

    MATH  Google Scholar 

  • Denarié, E., Saouma, V., Iocco, A. and Varelas, D. (2001). Concrete fracture process zone characterization with fiber optics. ASCE Journal of Engineering Mechanics 127, 494–502.

    Article  Google Scholar 

  • Dirkse, S.P. and Ferris, M.C. (1995). The PATH solver: a non-monotone stabilization scheme for mixed complementarity problems. Optimization Methods and Software 5, 123–156.

    Google Scholar 

  • Elices, M., Guinea, G.V. and Planas, J. (1992). Measurement of the fracture energy using three-point bend tests: Part 3 — Influence of cutting the P-δ tail. Materials and Structures 25, 327–334.

    Article  Google Scholar 

  • Facchinei, F. and Pang, J.S. (2003). Finite-Dimensional Variational Inequalities and Complementarity Problems, Vol. II, Springer Series in Operations Research and Financial Engineering, Berlin.

    Google Scholar 

  • Fedele, R., Maier, G. and Miller, B. (2005). Identification of elastic stiffness and local stresses in concrete dams by in situ tests and neural networks. Structure and Infrastructure Engineering 1(3), 165–180.

    Google Scholar 

  • Fiacco, A.V., McCormick and G.P. (1968). Nonlinear Programming: Sequential Unconstrained Minimization Techniques, Wiley, New York (reprinted by SIAM Publications, Philadelphia, 1990).

    MATH  Google Scholar 

  • Frangi, A. and Maier, G. (2002). The symmetric Galerkin boundary element method in linear and nonlinear fracture mechanics, In: D. Beskos and G. Maier (eds.) Boundary Element Advances in Solid Mechanics CISM Lecture Notes, Vol. 440, Springer Verlag, Wien.

    Google Scholar 

  • Gioda, G. and Maier, G. (1980). Direct search solution of an inverse problem in elastoplasticity: identification of cohesion, friction angle and in situ stress by pressure tunnel tests. International Journal for Numerical Methods in Engineering 15, 1823–1848.

    Article  Google Scholar 

  • Goodman, R.E. (1980). Introduction to Rock Mechanics, John Wiley and Sons, New York.

    Google Scholar 

  • Guinea, G.V., Planas, J. and Elices, M. (1992). Measurement of the fracture energy using three-point bend tests: Part 1 — Influence of experimental procedures. Materials and Structures 25, 212–218.

    Article  Google Scholar 

  • Guinea, G.V., Planas, J. and Elices, M. (1994). A general bilinear fit for the softening curve of concrete. Materials and Structures 27, 99–105.

    Article  Google Scholar 

  • Haykin, S. (1999). Neural Networks. A Comprehensive Foundation, 2nd Edition, Prentice Hall, Upper Saddle River, NJ (USA).

    Google Scholar 

  • Hillerborg, A. (1991). Application of the fictitious crack model to different types of materials. International Journal of Fracture 51, 95–102.

    Google Scholar 

  • Jayaraman, S., Hahn, G.T., Oliver, W.C., Rubin, C.A. and Bastias, P.C. (1998). Determination of monotonic stress-strain curve of hard materials from ultra-low-load indentation tests. International Journal of Solids and Structures 35, 365–381.

    Article  Google Scholar 

  • Jirasek, M. and Bažant, Z.P. (2001). Inelastic Analysis of Structures, John Wiley and Sons, New York.

    Google Scholar 

  • Karihaloo, B. (1995). Fracture Mechanics and Structural Concrete, Longman Scientific and Technical, Burnt Mill, Harlow.

    Google Scholar 

  • Kleiber, M., Antunez, H., Hien, T.D. and Kowalczyk, P. (1997). Parameter Sensitivity in Nonlinear Mechanics. Theory and Finite Element Computations, John Wiley and Sons, New York.

    Google Scholar 

  • Li, W. and Siegmund, T. (2004). An analysis of the indentation test to determine the interface toughness in a weakly bonded thin film coating-substrate system. Acta Materialia 52, 2989–2999.

    Article  Google Scholar 

  • Luo, Z.Q., Pang, J.S. and Ralph, D. (1996). Mathematical Programs with Equilibrium Constraints, Cambridge University Press, Cambridge (UK).

    Google Scholar 

  • Maier, G. (1968). On softening flexural behaviour of beams in elasto-plasticity. Rendiconti dell’Istituto Lombardo di Scienze e Lettere 102, 648–677, (in Italian).

    Google Scholar 

  • Maier, G. (1970). A matrix structural theory of piecewise-linear plasticity with interacting yield planes. Meccanica 5, 55–66.

    Google Scholar 

  • Maier, G., Ardito, R. and Fedele, R. (2004). Inverse analysis problems in structural engineering of concrete dams. In: Z.H. Yao, M.W. Yuan e and W.X. Zhong (eds.) Computational Mechanics Tsinghua University Press & Springer-Verlag, Beijing, pp. 97–107.

    Google Scholar 

  • Maier, G. and Comi, C. (2000). Energy properties of solutions to quasi-brittle fracture mechanics problems with piecewise linear cohesive crack models, In: A. Benallal (ed.) Continuous Damage and Fracture Elsevier, Amsterdam, pp. 197–205.

    Google Scholar 

  • Maier, G., Giannessi, F. and Nappi, A. (1982). Identification of yield limits by mathematical programming. Engineering Structures 4, 86–98.

    Article  Google Scholar 

  • Maier, G., Novati, G. and Cen, Z. (1993). Symmetric Galerkin boundary element method for quasibrittle fracture and frictional contact problems. Computational Mechanics 13, 74–89.

    Google Scholar 

  • Mröz, Z. and Stavroulakis, G.E. (eds.) (2005). Identification of Materials and Structures, CISM Lecture Notes, Vol. 469, Springer-Verlag, Wien.

    Google Scholar 

  • Nakamura, T., Yu, G., Prchlik, L., Sampath, S. and Wallace, J. (2003). Micro-indentation and inverse analysis to characterize elastic-plastic graded materials. Materials Science and Engineering A 345, 223–233.

    Article  Google Scholar 

  • Nash, J.F. (1951). Non-cooperative games. Annals of Mathematics 54, 286–295.

    Article  MathSciNet  Google Scholar 

  • Norgaard, M., Pulsen, N. and Ravn, O. (2000). New developments in state estimation for nonlinear systems. Automatica 36, 1627–1638.

    Article  Google Scholar 

  • Ohring, M. (1991). The Materials Science of Thin Films, Academic Press, New York.

    Google Scholar 

  • Ortiz, M. and Pandolfi, A. (1999). Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. International Journal for Numerical Methods in Engineering 44, 1267–1282.

    Article  Google Scholar 

  • Pang, J.S. and Tin-Loi, F. (2001). A penalty interior point algorithm for a parameter identification problem in elasto-plasticity. Mechanics of Structures and Machines 29, 85–99.

    Article  Google Scholar 

  • Planas, J., Elices, M. and Guinea, G.V. (1992). Measurement of the fracture energy using three-point bend tests: Part 2-Influence of bulk energy dissipation. Materials and Structures 25, 305–312.

    Article  Google Scholar 

  • RILEM Draft Recommendation (1985). Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams. Materials and Structures 18, 285–290.

    Google Scholar 

  • Rose, J.H., Ferrante, J. and Smith, J.R. (1981). Universal binding energy curves for metals and bimetallic interfaces. Physical Review 18, 675–678.

    Google Scholar 

  • Spearing, S.M. (2000). Materials issues in microelectromechanical systems (MEMS). Acta Materialia 48, 179–196.

    Article  Google Scholar 

  • Stavroulakis, G.E. (2000). Inverse and Crack Identification Problems in Engineering Mechanics, Kluwer Academic Publishers, Durtrecht.

    Google Scholar 

  • Stavroulakis, G.E., Bolzon, G., Waszczyszyn, Z. and Ziemanski, L. (2003). Inverse Analysis, In: B. Karihaloo, R.O. Ritchie and I. Milne (eds.) Comprehensive Structural Integrity Vol. 3, Elsevier Science, Oxford.

    Google Scholar 

  • Tin-Loi, F. and Que, N.S. (2001a). Parameter identification of quasi-brittle materials as a mathematical program with equilibrium constraints. Computer Methods in Applied Mechanics and Engineering 190, 5819–5836.

    Article  Google Scholar 

  • Tin-Loi, F. and Que, N.S. (2002a). Identification of cohesive crack fracture parameters by evolutionary search. Computer Methods in Applied Mechanics and Engineering 191, 5741–5760.

    Article  Google Scholar 

  • Tin-Loi, F. and Que, N.S. (2002b). Nonlinear programming approaches for an inverse problem in quasibrittle fracture. International Journal of Mechanical Sciences 44, 843–858.

    Article  Google Scholar 

  • Tin-Loi, F. and Xia, S.H. (2001b). Non-holonomic elastoplastic analysis involving unilateral frictionless contact as a mixed complementarity problem. Computer Methods in Applied Mechanics and Engineering 190, 4551–4568.

    Article  Google Scholar 

  • Volinsky, A.A., Moody N.R. and Gerberich, W.W. (2002). Interfacial toughness measurement for thin film on substrates. Acta Materialia 50, 441–466.

    Article  Google Scholar 

  • Waszczyszyn, Z. (ed.) (1999). Neural Networks in the Analysis and Design of Structures, CISM Lectures Notes, Vol. 404, Springer Verlag, Wien.

    Google Scholar 

  • Wittmann, F.H. and Hu, X. (1991). Fracture process zone in cementitious materials. International Journal of Fracture 51, 3–18.

    Article  Google Scholar 

  • Xiaodong, L., Dongfeng, D. and Bhushan, B. (1997). Fracture mechanisms of thin amorphous carbon films in nano-indentation. Acta Materialia 45, 4453–4461.

    Article  Google Scholar 

  • Xu, X.P. and Needleman, A. (1994). Numerical simulation of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids 42, 1397–1434.

    Article  Google Scholar 

  • Zhi-He, J., Glaucio, H., Paulino, R.H. and Dodds, J. (2003). Cohesive fracture modeling of elastic-plastic crack growth in functionally graded materials. Engineering Fracture Mechanics 70, 1885–1912.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Structural Engineering, Technical University (Politecnico) of Milan, Milan, Italy

    G. Maier, M. Bocciarelli, G. Bolzon & R. Fedele

Authors
  1. G. Maier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Bocciarelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Bolzon
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. Fedele
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Politecnico di Torino, Torino, Italy

    Alberto Carpinteri

  2. University of Sydney, Sydney, Australia

    Yiu-Wing Mai

  3. University of California, Berkeley, USA

    Robert O. Ritchie

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer

About this paper

Cite this paper

Maier, G., Bocciarelli, M., Bolzon, G., Fedele, R. (2006). Inverse analyses in fracture mechanics. In: Carpinteri, A., Mai, YW., Ritchie, R.O. (eds) Advances in Fracture Research. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5423-5_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-5423-5_6

  • Received:

  • Accepted:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-4626-1

  • Online ISBN: 978-1-4020-5423-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation