Studies On Impact Problems Of Ceramics And Concrete Based On Material Point Method

Impact problems involve large deformation and damage of structures, along withgeometric nonlinearity, material nonlinearity and boundary condition nonlinearity. Nu-merical simulation is a powerful tool for solving these problems. Material point method(MPM) discretizes a material domain by using a collection of particles, which carry allstate variables such as position, velocity, stress, strain, etc and can describe load carry-ing and deformation of the material domain, so this method is suited for histo-ry-dependent material models. MPM, which can effectively simulate impact problems,solves momentum equations and computes spatial derivative using regular backgroundgrid, so it eliminates the drawbacks of mesh distortion in Lagrangian description anddifficulties of tracking material interface and dealing with convection term in Euleriandescription. The brittle materials, ceramics and concrete, whose strength increases as thepressure increases, are widely used for armor and protective structures. In this thesis,ceramics and concrete material models are implemented in MPM and then numericalsimulation is made for impact problems, so as to analyze the protective property ofstructures.Three types of constitutive models, including hyper-elasticity and hypo-elasticity,are introduced. For hyper-elasticity stress-strain equation is derived and quantitative re-lations of material parameters are shown. When it comes to hypo-elasticity, stress ratemust be an objective tensor to meet the principle of objectivity of the constitutive equa-tions. The stress update procedure and radial return of Drucker-Prager materialmodel, for example, are also introduced.In order to validate the stress update procedure, JH-2model, for ceramics material,is implemented in our explicit FE code EFEM, and the comparison of results, such asstress, strain, damage and so on, between EFEM and commercial finite element soft-ware LS-DYNA, is made by using single element model under different loading cases.Then crash and penetration problems are simulated to analyze material property of ce-ramics based on MPM.HJC and RHT material models are adopted to describe the behavior of concrete.The results show that in LS-DYNA pressure is cut off without dealing with damage andthere is an obvious error of calculating the yield stress when validation is done for HJC model in the similar way for JH-2. The RHT material model, together with P-α EOS(Equation of State), is implemented in our three-dimensional explicit materialpoint method code MPM3D, and the results from simulating projectile pene-trating targets are in good agreement with those from experiments.