Material Point Method Calculations with Explicit Cracks
نویسنده
چکیده
A new algorithm is described which extends the material point method (MPM) to allow explicit cracks within the model material. Conventional MPM enforces velocity and displacement continuity through its background grid. This approach is incompatible with cracks which are displacement and velocity discontinuities. By allowing multiple velocity fields at special nodes near cracks, the new method (called CRAMP) can model cracks. The results provide an “exact” MPM analysis for cracks. Comparison to finite element analysis and to experiments show it gets good results for crack problems. The intersection of crack surfaces is prevented by implementing a crack contact scheme. Crack contact can be modeled using stick or sliding with friction. All results are two dimensional, but the methods can be extended to three dimensional problems. keyword: Material point method, cracks, fracture, numerical methods, contact
منابع مشابه
Material Point Method Calculations with Explicit Cracks, Fracture Parameters, and Crack Propagation
A new particle-based method, the material point method (MPM), has recently been extended to handle explicit cracks in a new algorithm called CRAMP or “CRAcks with Material Points.” This new method has several advantages for numerical work on fracture. Compared to finite element analysis, CRAMP can handle cracks with similar algorithmic efficiency, but is better at handling crack surface contact...
متن کاملCalculation of J-Integral and Stress Intensity Factors using the Material Point Method
The Material Point Method (MPM), which is a particle-based, meshless method that discretizes material bodies into a collection of material points (the particles), is a new method for numerical analysis of dynamic solid mechanics problems. Recently, MPM has been generalized to include dynamic stress analysis of structures with explicit cracks. This paper considers evaluation of crack-tip paramet...
متن کاملCracking Elements Method for Simulating Complex Crack Growth
The cracking elements method (CEM) is a novel numerical approach for simulating fracture of quasi-brittle materials. This method is built in the framework of conventional finite element method (FEM) based on standard Galerkin approximation, which models the cracks with disconnected cracking segments. The orientation of propagating cracks is determined by local criteria and no explicit or implic...
متن کاملThree-Dimensional Dynamic Fracture Analysis Using the Material Point Method
This paper describes algorithms for threedimensional dynamic stress and fracture analysis using the material point method (MPM). By allowing dual velocity fields at background grid nodes, the method provides exact numerical implementation of explicit cracks in a predominantly meshless method. Crack contact schemes were included for automatically preventing crack surfaces from interpenetration. ...
متن کاملA descent method for explicit computations on curves
It is shown that the knowledge of a surjective morphism $Xto Y$ of complex curves can be effectively used to make explicit calculations. The method is demonstrated by the calculation of $j(ntau)$ (for some small $n$) in terms of $j(tau)$ for the elliptic curve with period lattice $(1,tau)$, the period matrix for the Jacobian of a family of genus-$2$ curves complementing the classi...
متن کامل