Mesh‐size independent rigid‐body spring network for simulation of the dynamic fracture behavior of concrete

Abstract

In this study, a numerical approach is developed for simulating the rate‐dependent behaviors of concrete without mesh sensitivity. The rheological units (e.g., dashpot) are integrated with the six directional springs in the rigid‐body spring network (RBSN) elements to reflect the rate‐dependent behavior of concrete. Previously, the viscoplastic damage model was associated with the elemental degrees of freedom. However, in the present approach, a viscoelastic constitutive law is newly defined for the normal direction as a function of the strain rate, from which the internal forces can be updated from the regularized elemental stresses. Such improvements are validated through the numerical simulations of the direct tensile test and spalling test using the modified split‐Hopkinson pressure bar (SHPB). The simulated results show consistent structural responses without mesh dependence on the strain rate. In addition, the influences of the softening curve shapes on the crack localizations are examined. It is shown that the rheological parameters can be optimized and determined for consistent applications through virtual experiments. The proposed numerical approach enables the mesh construction procedure without concerning the mesh‐size sensitivity due to the strain rate, and various applications are expected for the simulations of detailed numerical models of concrete materials and structures under high loading rates.

Rigid‐body‐spring network model for failure simulation of reinforced‐concrete members under various loading rates

“…where 𝐹( ẇ) is a non-dimensional coefficient for expressing the rate dependency, 𝐶 1 and 𝐶 0 are non-dimensional material parameters, 𝑓 0 (𝑤)represent the computed stress along the softening curve under quasi-static conditions, and 𝜎(𝑤, ẇ) is rate dependent stress. Based on the results of numerical analyses using the RBSN model, Choo et al 19 modified Equation (18) as follows so that the fracture energy release rate increases proportionally as the strain rate increases:…”

“…Thus, element size dependency is produced by the damage factor contained in the degraded elastic modulus stated in Equation (16) when utilizing VPD as the rate dependence model of the normal direction spring. For the purpose of resolving the element size dependence issue that arose during the dynamic analysis, the viscoelastic damage model (VED) proposed in prior research 19 was utilized based on the crack width rate, $$\dot{w}$$. Bažant et al 15 .…”

“…presented the speed dependence of concrete using a viscoelastic model as follows: $$$$\begin{equation}\sigma \left( {w,\dot{w}} \right) = {f_0}\left( w \right)F\left( {\dot{w}} \right){\rm{ with }}F\left( {\dot{w}} \right) = 1 + {C_1}{\rm{asinh}}\left( {\frac{{\dot{w}}}{{{C_0}}}} \right)\end{equation}$$$$where $$F( {\dot{w}} )$$ is a non‐dimensional coefficient for expressing the rate dependency, C 1 and C 0 are non‐dimensional material parameters, $${f_0}( w )$$represent the computed stress along the softening curve under quasi‐static conditions, and $$\sigma ( {w,\dot{w}} )$$ is rate dependent stress. Based on the results of numerical analyses using the RBSN model, Choo et al 19 . modified Equation (18) as follows so that the fracture energy release rate increases proportionally as the strain rate increases: …”

“…Strain rate dependent crack opening width‐stress law applied to normal direction springs in the RBSN model 19 …”

“…The normal direction spring rate dependence of the concrete was considered by modifying the viscoelastic (VE) model defined by Bažant et al 15 . based on the crack width rate to avoid mesh dependence 19 . The VPD model consists of a dashpot and Coulombic friction component, and it was verified in previous studies 17,18,20–22 .…”