Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method
نویسندگان
چکیده
Dynamic crack growth is simulated by implementing a cohesive zone model in the generalized interpolation material point (GIMP) method. Multiple velocity fields are used in GIMP to enable handling of discrete discontinuity on either side of the interface. Multilevel refinement is adopted in the region around the crack-tip to resolve higher strain gradients. Numerical simulations of crack growth in a homogeneous elastic solid under mode-II plane strain conditions are conductedwith the crack propagating along aweak interface. A parametric study is conducted with respect to varying impact speeds ranging from5m/s to 60m/s and cohesive strengths from 4 to 35MPa. Numerical results are compared qualitatively with the dynamic fracture experiments of Rosakis et al. [(1999) Science 284:1337–1340]. The simulations are capable of handling crack growth with cracktip velocities in both sub-Rayleigh and intersonic regimes. Crack initiation and propagation are the natural outcome of the simulations incorporating the cohesive zone model. For various impact speeds, the sustained crack-tip velocity falls either in the sub-Rayleigh regime or in the region between √ 2cS (cS is the shearwave speed) and cD (cD N. P. Daphalapurkar ·H. Lu ·D. Coker · R. Komanduri (B) School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078, USA e-mail: [email protected] is the dilatational wave speed) of the bulk material. The Burridge–Andrewsmechanism for transition of the crack-tip velocity from sub-Rayleigh to intersonic speed of the bulk material is observed for impact speeds ranging from 9.5 to 60m/s (for normal and shear cohesive strengths of 24MPa). Within the intersonic regime, sustained crack-tip velocities between 1.66 cS (or 0.82 cD) and 1.94 cS (or 0.95 cD)were obtained. For the cases simulated in this work, within the stable intersonic regime, the lowest intersonic crack-tip velocity obtained was 1.66 cS (or 0.82 cD).
منابع مشابه
Shock Waves Calculated Using Material Point Methods
One of the significant advantages of particle methods is their capability of computing large material deformation without the difficulty of mesh distortion. Often the large deformation of a material is caused by shock loading, therefore accurate calculation of shock waves is important for particle methods. In this work we study the numerical properties of four major versions of the material poi...
متن کاملThe Generalized Interpolation Material Point Method
The Material Point Method (MPM) discrete solution procedure for computational solid mechanics is generalized using a variational form and a Petrov– Galerkin discretization scheme, resulting in a family of methods named the Generalized Interpolation Material Point (GIMP) methods. The generalization permits identification with aspects of other point or node based discrete solution techniques whic...
متن کاملAuthor's personal copy An evaluation of explicit time integration schemes for use with the generalized interpolation material point method
The stability and accuracy of the generalized interpolation material point (GIMP) Method is measured directly through carefully-formulated manufactured solutions over wide ranges of CFL numbers and mesh sizes. The manufactured solutions are described in detail. The accuracy and stability of several time integration schemes are compared via numerical experiments. The effect of various treatments...
متن کاملExamination and Analysis of Implementation Choices within the Material Point Method (MPM)
The Material Point Method (MPM) has shown itself to be a powerful tool in the simulation of large deformation problems, especially those involving complex geometries and contact where typical finite element type methods frequently fail. While these large complex problems lead to some impressive simulations and solutions, there has been a lack of basic analysis characterizing the errors present ...
متن کاملA weighted least squares particle-in-cell method for solid mechanics
A novel meshfree method is proposed that incorporates features of the material point (MPM) and generalized interpolation material point (GIMP) methods and can be used within an existing MPM/GIMP implementation. Weighted least squares kernel functions are centered at stationary grid nodes and used to approximate field values and gradients. Integration is performed over cells of the background gr...
متن کامل