An adaptive FE�MD model coupling approach

Shan, Wenzhe; Nackenhorst, Udo
September 2010
Computational Mechanics;Sep2010, Vol. 46 Issue 4, p577
Academic Journal
This contribution introduces an adaptively coupled finite element (FE)�molecular dynamics (MD) model based on the Quasicontinuum (QC) method. The idea for obtaining constitutive laws from the underlying lattice structure (local QC model) will be discussed in detail. The outline of the formulation for the quasi-static MD model (nonlocal QC model) will also be derived in the same mathematical structure. A new type of element is proposed to solve the boundary problems and to couple the FE and MD models. The interpolation techniques for the atomic stress and strain fields are introduced. A two-step adaptive mechanism is applied to the multiscale model, including the mesh refinement step for the FE model and the FE�MD conversion step. A 3D nanoindentation example is used for demonstrating accuracy and the efficiency of the coupled FE�MD model at the end.


Related Articles

  • A global-local higher order theory including interlaminar stress continuity and C0 plate bending element for cross-ply laminated composite plates. Wu Zhen; Chen Wanji // Computational Mechanics;Apr2010, Vol. 45 Issue 5, p387 

    A C0-type global-local higher order theory including interlaminar stress continuity is proposed for the cross-ply laminated composite and sandwich plates in this paper, which is able to a priori satisfy the continuity conditions of transverse shear stresses at interfaces. Moreover, total number...

  • Compactly supported non-tensor product form two-dimension wavelet finite element. Jian-ming Jin; Peng-xiang Xue; Ying-xiang Xu; Ya-li Zhu // Applied Mathematics & Mechanics;Dec2006, Vol. 27 Issue 12, p1673 

    Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor product form two dimension wavelet finite element was used to solve the...

  • Interpolation error estimates for mean value coordinates over convex polygons. Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit // Advances in Computational Mathematics;Aug2013, Vol. 39 Issue 2, p327 

    In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in Gillette et al. (Adv Comput Math 37(3), 417-439, ), we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is...

  • Interpolation functions in the immersed boundary and finite element methods. Xingshi Wang; Lucy T. Zhang // Computational Mechanics;Mar2010, Vol. 45 Issue 4, p321 

    In this paper, we review the existing interpolation functions and introduce a finite element interpolation function to be used in the immersed boundary and finite element methods. This straightforward finite element interpolation function for unstructured grids enables us to obtain a sharper...

  • Formation of a large scale spot-like structure of the total deposition due to a powerful elevated finite source. Skrynyk, O. Y.; Chernysh, R. I.; Hrytsyuk, Y. Y. // Advances in Science & Research;2010, Vol. 4, p37 

    The article discusses a study which focuses on the formation process of a large scale spot-like structure of the cumulative deposition pattern. The study has used numerical solutions of a model diffusion problem in identifying the formation process. It revealed that the solution used in the...

  • On the asymptotic behaviour of shells of revolution in free vibration. Artioli, Edoardo; da Veiga, Lourenco Beirão; Hakula, Harri; Lovadina, Carlo // Computational Mechanics;Jul2009, Vol. 44 Issue 1, p45 

    We consider the free vibration problem of thin shells of revolution of constant type of geometry, focusing on the asymptotic behaviour of the lowest eigenfrequency, as the thickness tends to zero. Numerical experiments are computed using two discretization methods, collocation and finite...

  • Interpolation error estimates for edge elements on anisotropic meshes. Lombardi, Ariel L. // IMA Journal of Numerical Analysis;Oct2011, Vol. 31 Issue 4, p1683 

    The classical error analysis for N�d�lec edge interpolation requires the so-called regularity assumption on the elements. However, in Nicaise (2001, SIAM J. Numer. Anal., 39, 784�816) optimal error estimates were obtained for the lowest order case under the weaker hypothesis of...

  • Analysis of Non-Prismatic Timoshenko Beams Using Basic Displacement Functions. Attarnejad, Reza; Shahba1,2, Ahmad; Semnani, Shabnam Jandaghi // Advances in Structural Engineering;Apr2011, Vol. 14 Issue 2, p319 

    Introducing the concept of Basic Displacement Functions (BDFs), an innovative method is presented which yields a mechanical based approach rather than a mathematical one for exact static analysis of arbitrarily tapered Timoshenko beams. Holding pure mechanical interpretations, BDFs are obtained...

  • Superconvergence estimates of finite element methods for American options. Lin, Qun; Liu, Tang; Zhang, Shuhua // Applications of Mathematics;Jun2009, Vol. 54 Issue 3, p181 

    In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. 39 (2001), 834–857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation...


Read the Article


Sign out of this library

Other Topics