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A study of the effect of prerelaxation on the nanoindentation process of crystalline copper

Maździarz M., Young T. D., Jurczak G.

Archives of Mechanics

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2011

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Vol. 63, nr 5-6

533-533

EN

This paper examines how prerelaxation effects the development of the mechanics of a nanoindentation simulation. In particular, the force-depth relation, indentation stress-strain curves, hardness and elastic modulus, are investigated through molecular statics simulations of a nanoindentation process, starting from initial relaxation by: (i) molecular dynamics and (ii) molecular statics. It is found that initial relaxation conditions change the quantitative response of the system, but not the qualitative response of the system. This has a significant impact on the computational time and quality of the residual mechanical behaviour of the system. Additionally, the method of determining of the elastic modulus is examined for the spherical and planar indenter; and the numerical results are compared. An overview of the relationship between the grain size and hardness of polycrystalline copper is examined and conclusions are drawn.

2

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

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2008

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Vol. 15, No. 1

37-44

EN

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.

3

Logarithmic strain measure in finite element modelling of anisotropic hyperelastic materials

Dłużewski P., Jurczak G., Antunez H.

Computer Assisted Mechanics and Engineering Sciences

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2003

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Vol. 10, No. 1

69-79

EN

A new finite element to analyze problems of anisotropic hyperelasticity is presented. The constitutive equations are derived by means of the energy method, which leads to the stress measure conjugate to the logarithmic strain. Equilibrium equation are integrated in the current configuration. Multiplicative - instead of additive - decomposition of the time derivative of a strain tensor function is applied as a crucial step that makes possible the formulation for anisotropic hyperelastic materials. Unlike previous known anisotropic large deformation models, the one here presented assures the energy conservation while using the anisotropic elastic constants and the logarithmic strain measure. It is underlined that for the first time a model including all these features is presented. Some numerical examples are shown to illustrate the results obtained with this model and to compare them with other known anisotropic models.