دانلود رایگان مقاله فرمول بندی المان محدود ضمنی نظریه زنجیره مولتی رزولوشن

Abstract

The multiresolution continuum theory is a higher order continuum theory where additional kinematic variables account for microstructural inhomogeneities at several distinct length scales. This can be particularly important for localization problems. The strength of this theory is that it can account for details in the microstructure of a material without using an extremely fine mesh. The present paper describes the implementation and verification of a 3D elastic–plastic multiresolution element based on an implicit time stepping algorithm. It is implemented in the general purpose finite element program FEAP. The mesh independency associated with the length scale parameter is examined and the convergence rate of the element is also evaluated.

7. Conclusions and discussion

• The implementation of an implicit MRCT element into FEAP has been verified. It is a general formulation for higher order continuum theory and can accommodate several other types of formulations. It can accommodate multiple scales, as shown in the works by Liu and coworkers. • The merit of the implicit MRCT element compared to the explicit version is that no dynamic vibrations show up when modeling quasistatic problems. • The element shows second order convergence in the equilibrium iterations verifying the formulation of the element tangent matrix.• The element can be used to obtain mesh independent results in the case of deformation localization when choosing an appropriate length scale associated with the microdomain. The mesh needs to be refined to fully resolve the length scale. • The length scale of the microdomain should be related to the physics of the problem at hand. However, it can also be used as a numerical regularization parameter to obtain mesh independent results. It is not obvious how to calibrate the constitutive behavior of the microdomain. One can note from the evaluations above that the used properties must be related to the chosen length scale. In future work, the implicit MRCT element will be applied to the problem of fracturing of high strength steels where the constitutive behavior need to be addressed more in detail.