A Dynamic Model For Concrete With Finite Deformation

摘要

The analysis of concrete material under dynamic loading becomes more and more important in the current time. Because the dynamic behavior of concrete structure is closely related to the strain rate, the viscoplastic law should be used to describe the material behavior in this model, which is established on the basis of publishing experimental results. The first feature of the model is non-linear and rate-dependent. It is developed from Ottosen's four parameter criterion, where the Lord's angle was applied to determine the stress status, and the influence of hydrostatic pressure on yield surface was also considered. A scalar damage parameter is introduced here, and it is controlled by plastic strain rate and volume strain rate. The expansion and contraction of the load surfaces of material are considered respectively. Both theoretical and empirical improvements are made to model the stress status of concrete under dynamic loading. The model is extended here for encompassing the finite deformation of concrete. The differences of constitutive models between infinitesimal deformations and finite deformations are listed here. The framework of constitutive relations for concrete is postulated in terms of the finite deformation theory, where Green strain and deformational rate could be applied in an updated formula. Green-Naghdi objective -rate is introduced to avoid the physically unreasonable responses for certain loading paths when using Jaumann objective -rate. Some integral techniques of the deformation rates and stress-rates are also given in the paper, which could be easily implemented in finite element software. An updated Runge-Kutta method with adaptive step-control algorithm is presented for avoiding the time-consuming differential computation of the high-order tensors. The methodology is particularly suitable to the complicated constitutive laws, such as the one in current paper. The correctness of the model is evaluated in the end of the paper.