Constitutive equations for concrete materials subjected to high rate of loading

University dissertation from Institutionen för systemteknik

Abstract: Continuum mechanics is used to model the mechanical behaviour of concrete structures subjected to high rates of loading in defence applications. Large deformation theory is used and an isotropic elastic-plastic constitutive equation with isotropic hardening, damage and strain rate dependent loading surface. The hydrostatic pressure is governed by an equation of state. Numerical analysis is performed using the finite element method and the central difference method for the time integration.Projectile penetration is studied and it is concluded that it is not suitable to use material description of the motion of both the target and the projectile together with an erosion criterion. Instead, the material description should be used only for the projectile and the spatial description for the target. In this way the need for an erosion criterion is eliminated. Also, in the constitutive model used it is necessary to introduce a scaling of the softening phase in relation to the finite element size, in order to avoid strain localization.Drop weight testing of reinforced concrete beams are analysed, where a regularisation is introduced that renders mesh objectivity regarding fracture energy release. The resulting model can accurately reproduce results from material testing but the regularisation is not sufficient to avoid strain localization when applied to an impact loaded structure. It is finally proposed that a non-local measure of deformation could be a solution to attain convergence.The third study presents the behaviour of a concrete constitutive model in a splitting test and a simplified non-local theory applied in a tensile test. The splitting test model exhibits mesh dependency due to a singularity. In the tensile test the non-local theory is shown to give a convergent solution. The report concluded with a discussion on how to better model concrete materials.

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