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The subject of this article is the numerical simulation of concrete under explosive loading using a mesh-based and a meshfree discretization technique. The presented techniques are verified by experimental data. Experimental evidence suggests that the complete stress-strain history relation must be considered as a basis for constitutive modeling if concrete is subjected to high loading rates. These dynamic phenomena cause a retardation of damage activation which must be taken into account when constitutive modeling is pursued on mesolevel instead of microlevel. By including a dynamic relaxation formulation within the framework of a general three-dimensional coupled continuum damage-plasticity law, it is shown that the solution of the wave propagation problem in materials with strain-softening becomes independent of mesh size. As the simulation of concrete under contact detonation causes severe numerical problems because of the large deformations, special numerical spatial discretization techniques have to be used. In this article we compare the results of a concrete slab under contact detonation using the finite element method code LS-DYNA with an arbitrary Lagrangian Eulerian coupling and the results obtained by a MLSPH code developed at our institute with experimental data. The same constitutive model for concrete and the same equation of state for the explosive is implemented in the two codes. The results of the different numerical simulations and the experimental data agree with each other well. DOI: 10.1061/(ASCE)0733-9399(2007) 133:5(523) CE Database subject headings: Concrete slabs; Blasting; Strain rate; Constitutive equations; Simulation models; Numerical analysis; Experimental data.

Concrete strength is highly sensitive to loading procedure, especially in the range of high strain rates. On the basis of experimental results, it is demonstrated that the full loading history must be included in a dynamic constitutive model, not just consideration of the current strain rate. The rate effect is mainly attributed to internal inertia forces during microdamage evolution. A strain-history-dependent constitutive model is proposed based on this retarded activation of microdamage. A simplified version allows identification of material parameters for practical application. It is shown how this dynamic approach fits into the general framework of continuum damage mechanics.

A constitutive law to model the strain-rate-dependent compression behavior of concrete is proposed. It is derived from a mechanical model, where inertia effects influence damage formation. To verify this model an experimental method based on the split Hopkinson bar (SHB) technique is described, one that considers the special properties of concrete specimens. Compressive stress waves with varying peak values and durations were realized using an extended SHB device. Dynamic stress-strain relations - which differ considerably from the corresponding static relations - are derived for the investigated load histories and are modeled with the proposed dynamic constitutive law. While a number of compression load histories are sustained by the specimens, others result in failure. So a dynamic failure criterion is established, connecting failure occurrence, peak stress, and the time to reach the peak stress.