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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 86
Edited by: B.H.V. Topping
Paper 98

Numerical Experiment for Determination of Critical Hole Length

P.G. Papadopoulos, P. Lambrou and D. Plasatis

Department of Civil Engineering, Aristotle University of Thessaloniki, Greece

Full Bibliographic Reference for this paper
P.G. Papadopoulos, P. Lambrou, D. Plasatis, "Numerical Experiment for Determination of Critical Hole Length", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 98, 2007. doi:10.4203/ccp.86.98
Keywords: critical hole length, hole mouth opening displacement, truss model, mesh refinement, global load-deformation curve, yield concentration.

The usual finite elements have complicated stiffness matrices and present particular difficulties in handling nonlinear problems [1]. Alternatively, truss models can be used for the analysis of structures [2,3]. A bar of a truss is the finite element with the simplest local stiffness matrix. And a truss has a simple global stiffness matrix.

The bars of a truss model obey nonlinear uniaxial stress-strain laws; so, the whole truss can, in a simple way, describe material nonlinearities. On the other hand, by writing the equilibrium conditions with respect to the deformed truss, we can, in a simple way too, take into account geometric nonlinearities.

The proposed truss model can be proved as a simple and useful computational tool in fracture mechanics. A numerical experiment is performed on a typical problem of fracture mechanics, that of a plate with central hole, subject to uniaxial tension [4,5], for five gradually increasing values of the hole length.

A local mesh refinement of the truss is simply constructed around and near the hole, in order to study, in more detail, the stress and strain concentrations in this region. It is observed that this local mesh refinement plays a role similar to that of other defects (voids, cracks, stiffer or more flexible inclusions), which cause stress concentrations; thus it slightly reduces the global stiffness and the strength of the plate.

The value of the critical hole length of the plate under consideration is detected in three ways:

  1. In the global load-displacement curves, for hole lengths larger than the critical value, the stiffness and strength of the specimen are significantly reduced, much lower than the corresponding values of the ligament.
  2. In the distributions of tensile stresses along the ligament at failure, for a hole length smaller than its critical value, a global yield of the specimen is observed. Whereas, for a hole length larger than its critical value, the plastic yield is concentrated at the hole tip region.
  3. The deformed configuration of a specimen at failure shows more clearly that, for hole length smaller than its critical value, the global deformation of the specimen is mainly due to global yield and a very small part of it is due to hole extension. On the contrary, for a hole length larger than its critical value, the global deformation of the specimen is mainly due to hole extension.

Argyris J.H., Editor. "F.E.No.Mech. (Finite Elements in Nonlinear Mechanics)", International Conferences, Institute for Statics and Dynamics, University of Stuttgart, I. 1978, II. 1981, III. 1984.
Fraternali F., Angelilo M., Fortunato A.. "A lumped stress method for planar elastic problems and their discrete-continuum approximation", International Journal of Solids and Structures, Vol. 39, p. 6211-6240, 2002. doi:10.1016/S0020-7683(02)00472-9
Papadopoulos P.G., Xenidis H., "A truss model with structural instability for the confinement of concrete columns", Journal of E.E.E., (European Earthquake Engineering), II, p. 57-80, 1999.
Gdoutos E., Fracture Mechanics - An Introduction, Second edition, Springer 2006.
Sanford R.G., Principles of Fracture Mechanics, Prentice Hall, 2003.

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