Concrete Viscoplasticity
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Impact behaviour of concrete: a computational approach F. Barpi * Department of Structural and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy Received 21 February 2003; received in revised form 2 June 2003; accepted 17 November 2003 Abstract The purpose of this study is to examine the numerical simulation of concrete specimens under high loading rates in tension. The data found in the literature are described: they show an increase in compressive and tensile strength as a function of the loading rate. To study this behaviour, we focused our attention on the assessment of the consistency model through the simulation of many experimental results related to a wide range of strain rates. In particular, the tests on unnotched and notched specimens performed at Delft University in recent years are examined. The proposed model is able to describe the increase in strength due to a high loading rate by an appropriate choice of the viscosity parameter. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Concrete; Hopkinson bar; Impact; Softening; Strain rates; Viscoplasticity 1. Introduction Concrete is a rate-dependent material, i.e., its properties (ultimate strength, Young modulus, fracture energy) are highly dependent on the loading rate. For this reason, knowledge of the constitutive rela- tionship for a wide range of strain rates is required to develop a realistic material law. High loading rates are frequently encountered in engineering problems. Some structures have to be designed directly for impacts or impulsive loading: shelters, ammunition bunkers, structures to protect mou nta in roads fro m falling rocks, str uct ure s to protect bri dge s aga inst impact of shi ps, acc idental explosions. The aim of this work is to evaluate the capabilities of the consistency model , developed at Delft Uni- versity in recent years, concerning the impact tensile behaviour of concrete. In the consistency model the viscoplastic contribution is incorporated in the loading function by using a scalar para meter. The contr i- bution of viscosity makes it possible to overcome the problems ( mesh dependence and, in general, non- objectivity of the numerical response) encountered by using standard softening plasticity models. * Tel.: +39-11-564-488 6; fax: +39-11-56 4-4899. E-mail address: [email protected] (F. Barpi). 0013-7944/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfracmech.2003.11.007 Engineering Fracture Mechanics 71 (2004) 2197–2213 www.elsevier.com/locate/engfracmech
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