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2. The Tonti diagram for the HW is shown in Fig. C. 1: Tonti Diagram for Hu-Washizu, (Cervenka, J. 3 Discretization of the Variational Statement for the HW Variational Principle 6–5 The discretization of the three variational statements defined in Equation ?? will be performed on an element domain Ωe using the procedures described in Chapter 2 of (Zienkiewicz and Taylor 1989) assembly of the discrete element equations into a discrete global system of equations is straightforward and will be omitted from this discussion.
This model is among the most widely used in non-linear fracture mechanics finite element analysis, however due to the computational complexity, few “engineering” structures have been analyzed. In addition, 1. There is an inflection point in the descending branch. (a) The first part has been associated with (unconnected) microcracking ahead of the stress-free crack (b) The second part with bridging of the crack by aggregates 2. The area under the curve, termed the fracture energy GF (not to be confused with Gc or critical energy release rate), is a measure of the energy that needs to be spent to generate a unit surface of crack.
1 Numerical Evaluation 3–3 where n1 and n2 are the components of n, which is a unit vector normal to the contour line at the Gauss point under consideration. 8. Having defined all the terms of J, we substitute in Eq. 2 to obtain the contribution to J from a particular Gauss point within an element. 9) ds 1 = −1 Idη 9. 10) q=1 where Wq is the weighting factor corresponding to ηq and N GAU S is the order of integration (2 or 3). 10. Stresses σx , σy , τxy are readily available at the Gauss points.