Negative compressibility property in hinging open-cell Kelvin structure

A new three-dimensional(3D)cellular model based on hinging open-cell Kelvin structure is proposed for its negative compressibility property.It is shown that this model has adjustable compressibility and does exhibit negative compressibility for some certain conformations.And further study shows that the images of compressibility are symmetrical about the certain lines,which indicates that the mechanical properties of the model in the three axial directions are interchangeable and the model itself has a certain geometric symmetry.A comparison of the Kelvin model with its anisotropic form with the dodecahedron model shows that the Kelvin model has stronger negative compressibility property in all three directions.Therefore,a new and potential method to improve negative compressibility property can be derived by selecting the system type with lower symmetry and increasing the number of geometric parameters.

Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method

This paper presents a quasi-static implicit generalized interpolation material point method(i GIMP)with B-bar approach for large deformation geotechnical problems.The i GIMP algorithm is an extension of the implicit material point method(iMPM).The global stiffness matrix is formed explicitly and the Newton-Raphson iterative method is used to solve the equilibrium equations.Where possible,the implementation procedure closely follows standard finite element method(FEM)approaches to allow easy conversion of other FEM codes.The generalized interpolation function is assigned to eliminate the inherent cell crossing noise within conventional MPM.For the first time,the B-bar approach is used to overcome volumetric locking in standard GIMP method for near-incompressible non-linear geomechanics.The proposed i GIMP was tested and compared with i MPM and analytical solutions via a 1 D column compression problem.Results highlighted the superiority of the i GIMP approach in reducing stress oscillations,thereby improving computational accuracy.Then,elasto-plastic slope stabilities and rigid footing problems were considered,further illustrating the ability of the proposed method to overcome volumetric locking due to incompressibility.Results showed that the proposed i GIMP with B-bar approach can be used to simulate geotechnical problems with large deformations.