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CivilComp Proceedings
ISSN 17593433 CCP: 81
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 137
A Discrete QuasiStatic Cyclic Material Model Incorporating Hysteresis for QuasiBrittle Materials S. Mertens+, K. De Proft* and J. Vantomme+
+Department of Civil and Materials Engineering, Royal Military Academy, Brussels, Belgium *Department IW&T, XIOS Hogeschool Limburg, Diepenbeek, Belgium S. Mertens, K. De Proft, J. Vantomme, "A Discrete QuasiStatic Cyclic Material Model Incorporating Hysteresis for QuasiBrittle Materials", in B.H.V. Topping, (Editor), "Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 137, 2005. doi:10.4203/ccp.81.137
Keywords: hysteresis, hysteretic, Preisach, damage, plasticity, cohesive crack, partition of unity (PUM).
Summary
Cyclic quasistatic test results of quasibrittle materials reveal hysteretic loops during unloading and reloading in the postpeak region. Physically, this region corresponds with a cracked state of the material and the hysteretic loops are formed due to the frictional sliding of the crack faces. Such a hysteretic loop can be considered as a thermodynamic cycle and thus can be considered as an irreversible thermodynamic process. According to the second law of thermodynamics, this is accompanied with energy dissipation.
It is generally known that an accurate constitutive model is required to assure an accurate FEMprediction of the structure. This means that the constitutive model in the post peakregion should incorporate the hysteretic phenomena. The constitutive model used is in fact an extension of a combined damageplasticity model proposed by De Proft [1]. This model is capable of capturing the observed permanent deformations and the observed reduction of Young's modulus. The hysteretic loops are included by the coupling of the Preisach hysteresis model with the combined damageplasticity model. The Preisach hysteresis model is capable of simulating a single hysteretic loop. It originates from electromagnetism and corresponds with the opening and closing of small relays simulating the orientation effects of small magnetic particles. This model was extended to a general mathematical hysteresis model as shown in [2]. The coupling of the Preisach hysteresis model and the combined damageplasticity model is realized by the physical origin of the hysteretic loops. As mentioned before, the hysteretic phenomenon is caused by the sliding of the crack faces, the hysteretic phenomena can therefore be coupled with the number and size of the cracks. In its turn, the number and size of the cracks are coupled with the amount of damage. Consequently, it can be concluded that the combined damageplasticity model and the Preisach hysteresis model are coupled by the damage parameter. Subsequently, the model generated is been implemented in the PUMFEM algorithm. This algorithm is chosen because of the fact that it is capable of simulating discrete cracks in a meshindependent fashion (the kind of cracks that occur in quasibrittle materials). However, before the implementation has been done, the continuum constitutive model has been discretised, to allow its implementation in the PUMFEM model. Furthermore, the numerical test results obtained with the PUMFEM algorithm of a double notched test specimen under cyclic tensile loading are compared with the published experimental test results by Gopalaratnam, et al. [3]. It can be concluded that the observed phenomena can be simulated. However, a more advanced parameter study of the numerical material model is required to obtain a good matching of the numerical results with the experimental results. References
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