Retrieving the constitutive properties of a concrete target from a single instrumented penetration test

Abstract

Penetration into concrete is an important problem that attracted many researches who developed analytical models and numerical solutions. Most of the advanced methods account for the material properties through their constitutive equations, combined from the failure envelope and the equation of state. These properties are rarely available in many cases, and in different experimental reports it is missing. For lack of any other option, analysts borrow available equations that were developed for other concrete types, with the doubt of their suitability. In a limited number of tests, instrumented projectiles are used and the deceleration time history is recorded. Rarely, the constitutive properties are also provided and analysis can be conducted. Otherwise, analysis cannot be carried out and prediction and validation of the recorded deceleration curve cannot be conducted. The present article refers to such instrumented tests where the constitutive properties are not available. It aims at unveiling the relationship between the deceleration curve and the constitutive properties and at solving, for the first time, the inverse problem of a penetration problem in order to retrieve major constitutive equation parameters from the acceleration time-history record. The major new feature of the present article is identification of the failure envelope parameters in the Mohr–Coulomb form as well as the parameters of the Shock Hugoniot equation of state for which procedures have been developed. The present approach allows to retrieve required information regarding the equation of state and failure envelope from a single instrumented experiment that provides the projectile deceleration time-history record. It is shown that the retrieved parameters of the failure envelope and the equation of state are in good agreement with reported constitutive parameters that are based on experimental data. The retrieved data allow to carry out penetration time-history predictions of different projectiles at different impact velocities on the same concrete.