In physical viscosity SPH method with low Reynolds number,density reinitialization is performed with reproducing kernel particle method(RKPM).It can avoid numerical dissipation resulting from artificial viscosity.Numerical stability of physical viscosity SPH method with low Reynolds number is improved.Taking dam-break problem for example,it is shown that the method can remove numerical instability efficiently.The method can be applied to problems with higher Reynolds numbers or viscous fluid.

Conversion criterion and time step control are corrected for smoothed particle hydrodynamics-finite element method (SPH-FEM) conversion algorithm. Impact of a 7.62 mm rifle bullet against a special heat treated 30CrMnSiA steel target plate is simulated in full-size in 3D using the corrected SPH-FEM conversion algorithm, in which distorted finite elements of the bullet are converted into SPH particles. An elastic-plasticity model is used for bullet, and corrected Johnson-Cook and Gruneisen EOS are used for target. Two destroyed modes of disc-shape plastic deformation and plugging perforation are calculated for different initial velocities of bullet. Good agreement between numerical results and experimental observations shows that the corrected SPH-FEM conversion algorithm could use finite elements and SPH particles efficiently, which provides an effective tool for simulation of a soft core bullet impacting on a hard plate.

Modified equations for surface tension are derived by modifying normal and curvature with corrected smoothed particle method(CSPM).It is based on smoothed particle hydrodynamics(SPH) method with surface tension proposed by Morris.Both Morris and our method are tested via a semicircular problem.Factors that affect accuracy are investigated including surface definition,normal and curvature calculation.Smoothed length in curvature calculation is also confirmed reasonable.Furthermore,formation of a liquid drop with initial square shape under surface tension is simulated.Compared with Morris method and grid-based volume of fluid method,it is proved that the accuracy of our method is higher and particle distribution is more homogeneous.Finally,coalescence process of two oil drops in water under surface tension is simulated.

A cohesive zone model is employed in finite element formulation using nonlinear explicit dynamic algorithm.A 4-node tetrahedron element and a 6-node triangular prism element are chosen as volumetric and cohesive stress/displacement element,respectively.A bilinear constitutive equation is used to describe cohesive tractions and displacement jumps.Interfacial penetration of adjacent layers after complete rupture is avoided.A damage criterion is formulated in displacement jump space.The final displacement jump is calculated with Benzeggagh-Kenane's propagation criterion.The onset displacement jump is calculated with Turon's initial damage surface criterion.The code(CVFEM) can simulate material interface delamination under mixed-mode ratio loading in 3D.Three examples are shown.Numerical predictions are compared with those obtained by Abaqus 6.7.

SPH (smoothed particle hydrodnamics) method with fully variable smoothing lengths is proposed. Different from existing adaptive kernel SPH methods, fully variable smoothing lengths are considered based on an adaptive symmetrical kernel estimation. An evolution equation of density is derived which implicitly couples with a variable smoothing length equation. Based on Springel' s fully conservative formulation SPH momentum equation and energy equation are derived by using symmetrical kernel estimation instead of scatter kernel estimation. An additional iteration process is employed to solve evolution equations of density and variable smoothing lengths equation. SPH momentum equation and energy equation are solved explicitly. Computation cost added by iteration is little. The equations and algorithm are tested via three ID shock-tube problems and a 2D Sedov problem. It is showed that conservation of momentum and energy is improved substantially and variable smoothing lengths effect is corrected, especially in the 2D Sedov problem. Pressure peak position and pressure at center are more accurate than those by Springel's scheme. The method deals with large density gradient and large smoothing length gradient problems well, such as large deformation and serious distortion problems in high velocity impact and blasting.