Both the positive and inverse problem of spherical waves propagating in concrete are studied. Using characteristics method, the nonlinear spherical waves in concrete, including the radial stress σr(r, t), circumferential stress σt(r, t), radial strain εr(r, t) and the circumferential strain εt(r, t) are calculated based on the ZWT constitutive relation. Numerical results illustrate that the viscosity effects and nonlinear effects in concrete cannot be ignored. Based on universal spherical wave conservation equations and combined with the rate-independent law of elastic volume deformation, the inverse analysis method for spherical waves (called ‘nv + T0/SW’) are developed to determine constitutive behavior of concrete when n particle velocity profiles are measured. The satisfactory agreement between the ‘characteristics solutions’ and the ‘nv + T0/SW’ inverse solutions confirms the validity of the proposed new method, which may be more suitable for studying the dynamic behavior of heterogeneous materials with large aggregates such as concretes and rocks et al.


In practical engineering problems, such as underground explosions and engineering blasts, there are often problems of point explosion, point impact and spherical cavity-walls subjected to explosion loading, where the spherical wave propagation should be dealt with (Wang 2005, Zukas et al. 1982). The dynamic response of concrete structures under explosive/impact loading is intrinsically dependent on the dynamic behavior of concrete materials involved in the structures. Thus the importance of research on the dynamic behavior of concrete materials under high strain rates (called strain rate effect for short) cannot be overemphasized.

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