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A hybrid atomistic-continuum finite element modelling of nanoindentation and experimental verification for copper crystal

Dłużewski P., Maździarz M., Jurczak G., Traczykowski P., Niihara K., Nowak R., Kurzydłowski K.

Computer Assisted Mechanics and Engineering Sciences

2008

Vol. 15, No. 1

37-44

Problem of locally disordered atomic structure is solved by using a hybrid formulation in which nonlinear elastic finite elements are linked with discrete atomic interaction elements. The continuum approach uses nonlinear hyperelasticity based upon the generalized strain while the atomistic approach employs the Tight-Binding Second-Moment Approximation potential to create new type of elements. The molecular interactions yielding from constitutive models of TB-SMA were turned into interactions between nodes to solve a boundary value problem by means of finite element solver. In this paper we present a novel way of modelling materials behaviour where both discrete (molecular dynamics) and continuum (nonlinear finite element) methods are used. As an example, the nanoindentation of a copper sample is modelled numerically by applying a hybrid formulation. Here, the central area of the sample subject to nanoindentation process is discretised by an atomic net where the remaining area of the sample far from indenters tip is discretised by the use of a nonlinear finite element mesh.

Numerical simulation of atomic positions in quantum dot by means of molecular statics

Dłużewski P., Traczykowski P.

Archives of Mechanics

2003

Vol. 55, nr 5-6

393-406

Deformation of a crystal structure is considered here in terms of constitutive modelling based upon both the atomistic and continuum approaches. Atomistic calculations are made by using the Stillinger-Weber potential for the GaAs and CdTe structures. The stress-strain behaviour of the best-known anisotropic hyperelastic models are compared with the behaviour of the atomistic one in the uniaxial deformation test.