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Homogenization theory has been well accepted by the applied mechanics modeling community for its ability to integrate small-scale microstructure phenomena into bulk continuum equations using convergent features of asymptotics. This paper describes an extension of the method to handle asymptotically small atomic scale systems at zero temperature embedded within a deforming continuum. A so-called inner displacement naturally arises in the formulation that enables the consideration of distributed anharmonic crystalline effects that would otherwise be unapproachable with bulk continuum methods alone. The result is a simple computational mechanics method that, first, maps instantaneous continuum deformation gradients to deforming defected crystalline arrangements then, second, provides convergent effective material properties to be used for consistent continuum calculations. The intended applications are those involving patterned defects, either in bulk or on surfaces, which allude to possible manufacturing scenarios. Simple 2-D examples are shown for in-plane deformation of graphene possessing various types of point defects. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

With advances in computer capabilities, cost of sheet metal forming has being reducing mainly due to the reduction of trial and error approaches. At the moment, a complete process can be simulated on computer and appropriate forming conditions optimized before actual industrial forming process is carried out. While formability predictions have improved, the problem of springback exhibited by most metal, including aluminum alloy AA6111-T4, after forming persist and often leads to significant part fit-up problems during assembly. There are a number of factors that affect springback and perhaps the most significant one is constitutive equation. In this paper springback predicted by six advanced kinematic models are evaluated. In addition an improved constitutive kinematic model is presented. It is shown that by adding stress correction term (SCT) to Armstrong-Frederick model a relatively simple and yet accurate stress prediction could be obtained. The SCT was developed with the assumption that the yield surface remains convex, yield center depends on translation, size and shape variations of the yield surface. The model is implemented in a commercial finite element code (ABAQUS/Standard) via its user material interface (UMAT). Numerical simulations of U-bending were performed using automotive aluminum sheet material (AA6111-T4). It was noted that springback has inverse relationship with residual stress. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

In this paper, we propose a multi-time scale modeling technique for analyzing cyclic plastic deformation in crystalline solids subject to periodic loading. An asymptotic expansion of the variables in the time domain, together with homogenization forms the basis of multi-time scaling. In the macroscopic scale analysis, the oscillatory behavior of the load is averaged out and neglected, and the rate of averaged material behavior is quite slow in cyclic deformation. Implicitly, this means that the periodicity of some variables may be assumed for the oscillatory potion of the material behavior may be approximated. In this formulation, the governing equations are divided into two initial-boundary value problems with two different time scale: one is long time scale problem for describing the smooth averaged solution (global problem) and the other is for the remaining oscillatory potion (local problem). For the global problem, long time increments, which are longer than one cycle period, can be used and this multi-time scaling becomes an effective integrator. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

In this paper, we propose a multi-time scale modeling technique for analyzing cyclic plastic deformation in crystalline solids subject to periodic loading. An asymptotic expansion of the variables in the time domain, together with homogenization forms the basis of multi-time scaling. In the macroscopic scale analysis, the oscillatory behavior of the load is averaged out and neglected, and the rate of averaged material behavior is quite slow in cyclic deformation. Implicitly, this means that the periodicity of some variables may be assumed for the oscillatory potion of the material behavior may be approximated. In this formulation, the governing equations are divided into two initial-boundary value problems with two different time scale: one is long time scale problem for describing the smooth averaged solution (global problem) and the other is for the remaining oscillatory potion (local problem). For the global problem, long time increments, which are longer than one cycle period, can be used and this multi-time scaling becomes an effective integrator. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

A molecular dynamics analysis model is proposed to study the effects of parameters on nanoimprint process, for example: taper angle, imprint depth and spring back. The nanoimprint process comprises one punch and one specimen at an isothermal state of 400K, while the deformed material is a copper FCC single crystal and the punch material is a nickel FCC single crystal. There were a total of 10,080 atoms in copper measuring 12.02 nm × 5.72 nm in length and height, respectively. There were a total of 4,200 atoms in nickel where the typical length and depth in punch tooth are 6.24 nm × 3.52 nm, respectively. Computer simulation codes based on Hamiltonian dynamics, periodical boundary conditions and Morse potential function were used to simulate the nanoimprint processes. By varying the punch taper angle and the imprinting depth, useful information for nanoimprint process has been obtained. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

The work is devoted to functional polycrystalline material design, which is currently an important research field in Material Science. The problem of searching for deformation regimes leading a billet to a product with a rational crystallographic texture is considered. To solve such problems, an approach based on multilevel modeling and statistical crystal elasto-visco-plasticity theories is proposed. In this article, a framework developed for simulating mechanical treatment processes and analyzing textures being formed is presented. [ABSTRACT FROM AUTHOR]

The anisotropic macro-scale mechanical behavior of polycrystalline metals is characterized by incorporating the micro-scale constitutive model of single crystal plasticity into the two-scale modeling based on the mathematical homogenization theory. The two-scale simulations are conducted to analyze the macro-scale anisotropy induced by micro-scale plastic deformation of the polycrystalline aggregate. In the simulations, the micro-scale representative volume element (RVE) of a polycrystalline aggregate is uniformly loaded in one direction, unloaded to macroscopically zero stress in a certain stage of deformation and then re-loaded in the different directions. The last re-loading calculations provide different macro-scale responses of the RVE, which can be the appearance of material anisotropy. We then try to examine the effects of the intergranular and intragranular behaviors on the anisotropy by means of various illustrations of plastic deformation process in stead of the use of pole figures for the change of crystallographic orientations. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

Over the last several years, significant progress has been made in the use of crystal level material models in simulations of forming operations. However, in Lagrangian finite element approaches simulation capabilities are limited in many cases by mesh distortion associated with deformation heterogeneity. Contexts in which such large distortions arise include: bulk deformation to strains approaching or exceeding unity, especially in highly anisotropic or multiphase materials; shear band formation and intersection of shear bands; and indentation with sharp indenters. Investigators have in the past used Eulerian finite element methods with material response determined from crystal aggregates to study steady state forming processes. However, Eulerian and Arbitrary Lagrangian-Eulerian (ALE) finite element methods have not been widely utilized for simulation of transient deformation processes at the crystal level. The advection schemes used in Eulerian and ALE codes control mesh distortion and allow for simulation of much larger total deformations. We will discuss material state representation issues related to advection and will present results from ALE simulations. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

The crystallographic texture evolution induced by plastic deformation in the sheet metal forming process has a great influence on its formability. In the present study, a dynamic explicit finite element (FE) analysis code is newly developed by introducing a crystallographic homogenization method to estimate the polycrystalline sheet metal formability, such as the extreme thinning and “earing.” This code can predict the plastic deformation induced texture evolution at the micro scale and the plastic anisotropy at the macro scale, simultaneously. This multi-scale analysis can couple the microscopic crystal plasticity inhomogeneous deformation with the macroscopic continuum deformation. In this homogenization process, the stress at the macro scale is defined by the volume average of those of the corresponding microscopic crystal aggregations in satisfying the equation of motion and compatibility condition in the micro scale “unit cell,” where the periodicity of deformation is satisfied. This homogenization algorithm is implemented in the conventional dynamic explicit finite element code by employing the updated Lagrangian formulation and the rate type elastic/viscoplastic constitutive equation. At first, it has been confirmed through a texture evolution analyses in cases of typical deformation modes that Taylor’s “constant strain homogenization algorithm” yields extreme concentration toward the preferred crystal orientations compared with our homogenization one. Second, we study the plastic anisotropy effects on “earing” in the hemispherical cup deep drawing process of pure ferrite phase sheet metal. By the comparison of analytical results with those of Taylor’s assumption, conclusions are drawn that the present newly developed dynamic explicit crystallographic homogenization FEM shows more reasonable prediction of plastic deformation induced texture evolution and plastic anisotropy at the macro scale. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]