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Keywords: Hybrid-Trefftz elements, cohesive crack, fracturing.

Summary

The analysis of crack initiation and propagation in materials is necessary for the effective design of reliable, high performance structural components. Furthermore, in computationally demanding analyses, such as where computational homogenisation demands the micromechanical modelling of heterogeneous materials (involving multiple fractures, crack-branching and crack-crossing), an accurate and efficient modelling framework for fracture is essential.

This paper presents the use of hybrid-Trefftz elements [1,2] , which are characterised by the fact that stresses are approximated within the domain of the element and the stiffness is expressed via a boundary integral. Thus, compared to their FEM counterpart, hybrid-Trefftz elements exhibit faster convergence of the stress fields. Furthermore, the displacements are approximated on the boundary of each element and the displacement basis is defined independently on each inter-element surface. Thus, the overall bandwidth of the stiffness matrix is very small and computationally efficient to solve.

This paper presents a formulation for a hybrid-Trefftz element for modelling fracture in quasi-brittle materials; it is ideally suited to these problems since the significant nonlinearities are restricted to the inter-element surface. The cohesive crack model adopted by Wells [3] is used for the interface material model. Efficient imposition of constraints using the Uzawe Method [4] is presented. Performance of the formulation is demonstrated on a numerical example of a three-point bending test.

References

1: J.A. Teixeira de Freitas, "Formulation of elstostatic hybrid-Trefftz stress elements", Comput. Methods Appl. Mech. Engrg., 153, 127-151, 1998. doi:10.1016/S0045-7825(97)00042-X
2: A. Matuszak, "Partial material replacement without stress redistribution in plane problems of elasticity", PhD Thesis, Cracow University of Technology, 2003 (in polish).
3: G.N. Wells, "Discontinuous modelling of strain localisation and failure", PhD Thesis, Technische Universiteit Delft, 2001.
4: Kok-Kwang Phoon, et al. "Fast iterative solution of large undrained soil-structure interaction problems", Int. J. Numer. Anal. Meth. Geomech., 27, 159-181, 2003. doi:10.1002/nag.268

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 85 PROCEEDINGS OF THE FIFTEENTH UK CONFERENCE OF THE ASSOCIATION OF COMPUTATIONAL MECHANICS IN ENGINEERING Edited by: B.H.V. Topping Paper 29 Hybrid-Trefftz Elements for Cohesive Crack Propagation in Quasi-Brittle Materials L. Kaczmarczyk and C.J. Pearce Department of Civil Engineering, University of Glasgow, United Kingdom doi:10.4203/ccp.85.29 purchase the full-text of this paper Full Bibliographic Reference for this paper L. Kaczmarczyk, C.J. Pearce, "Hybrid-Trefftz Elements for Cohesive Crack Propagation in Quasi-Brittle Materials", in B.H.V. Topping, (Editor), "Proceedings of the Fifteenth UK Conference of the Association of Computational Mechanics in Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 29, 2007. doi:10.4203/ccp.85.29 Keywords: Hybrid-Trefftz elements, cohesive crack, fracturing. Summary The analysis of crack initiation and propagation in materials is necessary for the effective design of reliable, high performance structural components. Furthermore, in computationally demanding analyses, such as where computational homogenisation demands the micromechanical modelling of heterogeneous materials (involving multiple fractures, crack-branching and crack-crossing), an accurate and efficient modelling framework for fracture is essential. This paper presents the use of hybrid-Trefftz elements [1,2] , which are characterised by the fact that stresses are approximated within the domain of the element and the stiffness is expressed via a boundary integral. Thus, compared to their FEM counterpart, hybrid-Trefftz elements exhibit faster convergence of the stress fields. Furthermore, the displacements are approximated on the boundary of each element and the displacement basis is defined independently on each inter-element surface. Thus, the overall bandwidth of the stiffness matrix is very small and computationally efficient to solve. This paper presents a formulation for a hybrid-Trefftz element for modelling fracture in quasi-brittle materials; it is ideally suited to these problems since the significant nonlinearities are restricted to the inter-element surface. The cohesive crack model adopted by Wells [3] is used for the interface material model. Efficient imposition of constraints using the Uzawe Method [4] is presented. Performance of the formulation is demonstrated on a numerical example of a three-point bending test. References 1 J.A. Teixeira de Freitas, "Formulation of elstostatic hybrid-Trefftz stress elements", Comput. Methods Appl. Mech. Engrg., 153, 127-151, 1998. doi:10.1016/S0045-7825(97)00042-X 2 A. Matuszak, "Partial material replacement without stress redistribution in plane problems of elasticity", PhD Thesis, Cracow University of Technology, 2003 (in polish). 3 G.N. Wells, "Discontinuous modelling of strain localisation and failure", PhD Thesis, Technische Universiteit Delft, 2001. 4 Kok-Kwang Phoon, et al. "Fast iterative solution of large undrained soil-structure interaction problems", Int. J. Numer. Anal. Meth. Geomech., 27, 159-181, 2003. doi:10.1002/nag.268 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £75 +P&P)
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