Finite strain logarithmic hyperelasto-plasticity with softening: a strongly non-local implicit gradient framework

This paper addresses the extension of a Eulerian logarithmic finite strain hyperelasto-plasticity model in order to incorporate an isotropic plastic damage variable that leads to softening and failure of the plastic material. It is shown that a logarithmic elasto-plastic model with a strongly non-local degrading yield stress exactly preserves the structure of its infinitesimal counterpart. The strongly non-local nature of the model makes it an attractive framework for the numerical solution of softening plasticity problems. Consistent constitutive tangent operators are derived for the particular case of hyperelasto-J2-plasticity, which are exactly equal to the corresponding infinitesimal tangent operators. The finite element implementation, along with the geometrically nonlinear contributions and the incremental solution strategy, is outlined. A benchmark example is solved, illustrating the main differences between the purely elasto-plastic case and the case with plastic damage. Finally, the main model characteristics and its practical use are emphasized

Enhanced solution control for physically and geometrically non-linear problems, Part I : The subplane control approach

\u3cp\u3eGeometrically or physically non-linear problems are often characterized by the presence of critical points with snapping behaviour in the structural response. These structural or material instabilities usually lead to inefficiency of standard numerical solution techniques. Special numerical procedures are therefore required to pass critical points. This paper presents a solution technique which is based on a constraint equation that is defined on a subplane of the degrees-of-freedom (dof's) hyperspace or a hyperspace constructed from specific functions of the degrees-of-freedom. This unified approach includes many existing methods which have been proposed by various authors. The entire computational process is driven from only one control function which is either a function of a number of degrees-of-freedom (local subplane method) or a single automatically weighted function that incorporates all dof's directly or indirectly (weighted subplane method). The control function is generally computed in many points of the structure, which can be related to the finite element discretization. Each point corresponds to one subplane. In the local subplane method, the subplane with the control function that drives the load adaptation is selected automatically during the deformation process. Part I of this two-part series of papers fully elaborates the proposed solution strategy, including a fully automatic load control, i.e. load estimation, adaptation and correction. Part II presents a comparative analysis in which several choices for the control function in the subplane method are confronted with classical update algorithms. The comparison is carried out by means of a number of geometrically and physically non-linear examples. General conclusions are drawn with respect to the efficiency and applicability of the subplane solution control method for the numerical analysis of engineering problems.\u3c/p\u3

Multiscale modeling of microstructure-property relations

The recent decades have seen significant progress in linking the mechanical performance of materials to their underlying microstructure. This article presents an overview of some of these achievements, trends, and challenges. Attention is given to methods initially developed for micromechanics and their gradual evolution toward powerful multiscale methods. Various methods have been proposed for bridging scales in mechanics of materials, all aiming for efficiency and accuracy. Computational homogenization is one of these powerful approaches, now used systematically for the assessment of structure–property relations. Novel solution methods and model reduction techniques provide tools to speed up the structure–property analysis, whereby large-scale computations have been made possible. Truly fast analyses of microstructures may be expected in the near future

Mechanical shape correlation:a novel integrated digital image correlation approach

\u3cp\u3eMechanical Shape Correlation (MSC) is a novel integrated digital image correlation technique, used to determine the optimal set of constitutive parameters to describe the experimentally observed mechanical behavior of a test specimen, based on digital images taken during the experiment. In contrast to regular digital image correlation techniques, where grayscale speckle patterns are correlated, the images used in MSC are projections of the sample contour. This enables the analysis of experiments for which this was previously not possible, because of restrictions due to the speckle pattern. For example, analysis becomes impossible if parts of the specimen move or rotate out of view as a result of complex and three-dimensional deformations and if the speckle pattern degrades due to large deformations. When correlating on the sample outline, these problems are overcome. However, it is necessary that the outline is large with respect to the structure volume and that its shape changes significantly upon deformation, to ensure sufficient sensitivity of the images to the model parameters. Virtual experiments concerning stretchable electronic interconnects, which because of their slender wire-like structure satisfy the conditions for MSC, are executed and yield accurate results in the objective model parameters. This is a promising result for the use of the MSC method for tests with stretchable electronics and other (micromechanical) experiments in general.\u3c/p\u3

Characterization of the mechanical properties of leptin receptor-deficient mice vertebrae, using nanoindentation tests

In order to investigate the eects of leptin receptor-deciency on the intrinsic material properties of vertebral mice bones, a total of twenty L4-vertebrae from the leptin receptor-decient (db/db) and wild-type (wt) mouse phenotype were tested, using the nanoindentation method. Each of the twenty samples was indented on cortical and trabecular bone regions, allowing for comparison between these two bone types. No signicant dierences were found in intrinsic material properties of vertebrae between leptin receptor-decient and wild-type mouse phenotypes, within cortical and trabecular bone. The reduced elastic modulus of cortical bone was found to be 24:351 3:179 [GPa] versus 20:2382:364 [GPa] for trabecular bone. From this result, the former bone type is regarded to be stier than the latter. The hardness parameters were found to be: 1:055 0:135 [GPa] and 0:997 0:103 [GPa] for cortical and trabecular bone, respectively. From this result, the two bone types are not concluded to signicantly dier in hardness. Since the intrinsic material properties of hormonal controlled (db/db) and wild-type (control group) mouse phenotypes are found to be equal, it is concluded that the bonemineral density of both mouse species are equal as well, and therefore µCT-scan based bone-mineral density (BMD) measurements become a quantitative measure of density, rather than a qualitative measure of relative bone volume.

Mechanical shape correlation: a novel integrated digital image correlation approach

Mechanical Shape Correlation (MSC) is a novel Integrated Digital Image Correlation (IDIC) based technique used for parameter identification. Digital images taken during an experiment are correlated and coupled to a Finite Element model of the specimen, in order to find the correct parameters in this numerical model. In contrast to regular IDIC techniques, where the images consist of a grayscale speckle pattern applied to the sample, in MSC the images are projections based on the contour lines of the test specimen only. This makes the technique suitable in cases where IDIC cannot be used, e.g., when large deformations and rotations cause parts of the sample to rotate in or out-of-view, or when the speckle pattern degrades due to large or complex deformations, or when application of the pattern is difficult because of small or large specimen dimensions. The method targets problems for which the outline of the specimen is large with respect to the volume of the structure and changes significantly upon deformation. The technique is here applied to virtual experiments with stretchable electronic interconnects, for identification of both elastic and plastic properties. Furthermore, attention is paid to the influence of algorithmic choices and experimental issues. The method reveals good convergence and adequate initial guess robustness. The results are promising and indicate that the method can be used in cases of either large, complex or three-dimensional displacements and rotations on any scale

Intergranular thermal fatigue damage evolution in SnAgCu lead-free solder

At present, SnAgCu appears to be the leading lead-free solder in the electronics industry. Driven by miniaturization, decreasing the component size leads to a stronger influence of microstructure on the observed lifetime properties. The present study concentrates on the thermal fatigue response of a near-eutectic SnAgCu solder alloy with the objective ofcorrelating damage mechanisms with the underlying microstructure, on the basis of whicha thermo-mechanical fatigue damage evolution model is characterized. Bulk Sn4Ag0.5Cu specimens are thermally cycled between 40 and 125 C up to 4000 cycles. As a result of the intrinsic thermal anisotropy of the beta-Sn phase, thermal fatigue loading causes localizeddeformations, especially along Sn grain boundaries. Mechanical degradation of test specimens after temperature cycling is identified from a reduction of the global elasticity modulus measured at very low strains. Using OIM scans, the test specimens are modeled including the local grain orientations and the detailed microstructure. A traction-separationbased cohesive zone formulation with a damage variable that traces the fatigue historyis used to model interfacial interactions between grains. Damage evolution parameters areidentified on the basis of the experimentally obtained global elastic moduli after a certainnumber of cycles. The resulting damage evolution law is applied to a number of numericalexamples and the mismatch factor is discussed in detail. Finally, the damage evolution lawcharacterized in this study is exploited towards the fatigue life prediction of a 2D microstructure-incorporated BGA solder ball

Experimental analysis of the evolution of thermal shock damage using transit time measurement of ultrasonic waves

Thermal shock is a principal cause of catastrophic wear of the refractory lining of high temperature installations in metal making processes. To investigate thermal shock experimentally with realistic and reproducible heat transfer conditions, chamotte and corund refractory samples of ambient temperature were subjected to surface contact with molten aluminium followed by passive cooling in ambient air. The evolution of damage was characterized by measuring the transit time of ultrasonic longitudinal waves at various sample locations after each test cycle. The mechanical validity of transit time measurement was confirmed in independent experiments. The single test cycle performed with chamotte material indicated the reproducibility and reliability of the experimental set-up and damage characterization method. Multiple test cycles performed with corund material yielded a reliable set of data, to be used for model validation purposes. Both non-uniform damage due to temperature gradients as well as uniform damage due to exposure to a uniform temperature were determined experimentally. The interaction between both damage mechanisms requires further investigation as well as the possible shielding of heat transport by damage. © 2008 Elsevier Ltd. All rights reserved