An efficient non-dominated sorting method for evolutionary algorithms

We present a new non-dominated sorting algorithm to generate the non-dominated fronts in multi-objective optimization with evolutionary algorithms, particularly the NSGA-II. The non-dominated sorting algorithm used by NSGA-II has a time complexity of O(MN(2)) in generating non-dominated fronts in one generation (iteration) for a population size N and M objective functions. Since generating non-dominated fronts takes the majority of total computational time (excluding the cost of fitness evaluations) of NSGA-II, making this algorithm faster will significantly improve the overall efficiency of NSGA-II and other genetic algorithms using non-dominated sorting. The new non-dominated sorting algorithm proposed in this study reduces the number of redundant comparisons existing in the algorithm of NSGA-II by recording the dominance information among solutions from their first comparisons. By utilizing a new data structure called the dominance tree and the divide-and-conquer mechanism, the new algorithm is faster than NSGA-II for different numbers of objective functions. Although the number of solution comparisons by the proposed algorithm is close to that of NSGA-II when the number of objectives becomes large, the total computational time shows that the proposed algorithm still has better efficiency because of the adoption of the dominance tree structure and the divide-and-conquer mechanism.     

Damage characterization and modeling of a 7075-T651 aluminum plate

In this paper, the damage-induced anisotropy arising from material microstructure heterogeneities at two different length scales was characterized and modeled for a wrought aluminum alloy. Experiments were performed on a 7075-T651 aluminum alloy plate using sub-standard tensile specimens in three different orientations with respect to the rolling direction. Scanning electron microscopy was employed to characterize the stereology of the final damage state in terms of cracked and or debonded particles. A physically motivated internal state variable continuum model was used to predict fracture by incorporating material microstructural features. The continuum model showed good comparisons to the experimental data by capturing the damage-induced anisotropic material response. Estimations of the mechanical stress–strain response, material damage histories, and final failure were numerically calculated and experimentally validated thus demonstrating that the final failure state was strongly dependent on the constituent particle morphology.     

Molecular dynamics simulations of deformation mechanisms of amorphous polyethylene

Molecular dynamics simulations were used to study deformation mechanisms during uniaxial tensile deformation of an amorphous polyethylene polymer. The stress-strain behavior comprised elastic, yield, strain softening and strain hardening regions that were qualitatively in agreement with previous simulations and experimental results. The chain lengths, number of chains, strain rate and temperature dependence of the stress-strain behavior was investigated. The energy contributions from the united atom potential were calculated as a function of strain to help elucidate the inherent deformation mechanisms within the elastic, yield, and strain hardening regions. The results of examining the partitioning of energy show that the elastic and yield regions were mainly dominated by interchain non-bonded interactions whereas strain hardening regions were mainly dominated by intra-chain dihedral motion of polyethylene. Additional results show how internal mechanisms associated with bond length, bond angle, dihedral distributions, change of free volume and chain entanglements evolve with increasing deformation.     

A general inelastic internal state variable model for amorphous glassy polymers

This paper presents the formulation of a constitutive model for amorphous thermoplastics using a thermodynamic approach with physically motivated internal state variables. The formulation follows current internal state variable methodologies used for metals and departs from the spring-dashpot representation generally used to characterize the mechanical behavior of polymers like those used by Ames et al. in Int J Plast, 25, 1495–1539 (2009) and Anand and Gurtin in Int J Solids Struct, 40, 1465–1487 (2003), Anand and Ames in Int J Plast, 22, 1123–1170 (2006), Anand et al. in Int J Plast, 25, 1474–1494 (2009). The selection of internal state variables was guided by a hierarchical multiscale modeling approach that bridged deformation mechanisms from the molecular dynamics scale (coarse grain model) to the continuum level. The model equations were developed within a large deformation kinematics and thermodynamics framework where the hardening behavior at large strains was captured using a kinematic-type hardening variable with two possible evolution laws: a current method based on hyperelasticity theory and an alternate method whereby kinematic hardening depends on chain stretching and material plastic flow. The three-dimensional equations were then reduced to the one-dimensional case to quantify the material parameters from monotonic compression test data at different applied strain rates. To illustrate the generalized nature of the constitutive model, material parameters were determined for four different amorphous polymers: polycarbonate, poly(methylmethacrylate), polystyrene, and poly(2,6-dimethyl-1,4-phenylene oxide). This model captures the complex character of the stress–strain behavior of these amorphous polymers for a range of strain rates.     

Influence of Laser Welding on the Alumina Growth on a Thin FeCrAl-RE Foil at High Temperature

We study isothermal oxidation of laser welded FeCrAl-RE samples containing specific fractions of seams in a bead-on-plate configuration at approximately 900°C using thermogravimetric analysis (TGA), field emission scanning electron microscope (FEG-SEM), transmission electron microscope (TEM), electron probe microanalysis (EPMA) techniques. An important reduction in the alumina-growth rate over the fusion zone compared to the base material occurs at 900°C, thereby, suppressing the discontinuous increase in mass gain commonly observed for alumina-forming alloys when the temperature decreases from 1000°C to 900°C. This phenomenon is mainly related to the concomitant dramatic chromium carbide precipitation at the fusion zone/oxide film interface and possible earlier injection of the rare earth elements into the oxide layer. On one hand, chromium carbide precipitation, which is linked to the laser melting-induced high free carbon, contributes to improve the effectiveness of the diffusion barrier provided by the thermally growing scale. On the other hand, due to their initial high enrichment at the fusion zone surfaces, rare earth elements can penetrate in the oxide layer and promote the elimination of detrimental phase transformation of metastable platelets (γ,θ-Al₂O₃) to α-Al₂O₃ during the initial stages of oxidation.     

The location of atomic hydrogen in NiTi alloy: A first principles study

A first principles density functional theory study to investigate the H defect in NiTi alloy is presented. We have determined the interstitial H atom position in bulk B2 phase NiTi alloy. H positions on both the Ti and Ni terminated NiTi surfaces are calculated. Surface adsorptions of H atom on Ni/Ti terminated surfaces are calculated for a low surface coverage of 1.96 × 10¹⁴ cm^?2. We have also calculated the penetration barrier energy for an H atom from the surface site to the bulk lattice site.     

Atomistic simulations of fatigue crack growth and the associated fatigue crack tip stress evolution in magnesium single crystals

Using Large-scale Atomic Molecular Massively Parallel Simulator (LAMMPS), a classical molecular dynamics code, atomistic simulations were performed to investigate the fatigue crack growth rate and the evolution of the associated atomic stress fields near the crack tip during fatigue crack growth in magnesium single crystals. The interatomic bonds of atoms were described using the EAM potential. The specimens with initial edge cracks were subjected to uniaxial Mode I cyclic loading. For the sake of revealing the influence of the initial cracks’ crystal orientations, three different orientations were considered. The fatigue growth rate can be expressed by da/dN = cCTOD, where the values of constant c are determined by the atomistic simulations. Notably, the values of the constant c are much larger for magnesium single crystals than for FCC single crystals and vary widely from one orientation to another. The simulation results show that the evolution of atomic stress fields was highly dependent on the crystal orientations due to anisotropy and magnesium single crystals’ HCP structure. Interestingly, the von Mises stress or normal stress around the crack tip controlled the fatigue crack growth behaviors.     

Micromechanical analysis of thermoelastoplastic behavior of metal matrix composites

A micromechanics model based on the variational asymptotic method for periodic composites was developed using an incremental formulation to capture the coupled thermo-elasto-plastic behavior of metal matrix composites. Taking advantage of the small size of the microstructure, a variational statement of the unit cell through an asymptotic expansion of an functional of energy change was formulated to calculate the effective instantaneous tangential elasto-plastic matrix and thermal stress matrix of the composite materials. An iterative homogenization and localization technique was proposed to simulate the nonlinear thermo-elasto-plastic behavior of metal matrix composites. This model was implemented using the finite element method. For validation, a numerical example was examined to demonstrate the application and accuracy of this theory and companion code.     

Microporosity effects on cyclic plasticity and fatigue of LENS™-processed steel

Special microstructures of the newly developed Laser Engineered Net Shaping (LENS?)-processed steel induce a new variability in fatigue damage formation and evolution mechanisms. The microporosity and mechanism of fatigue damage formation and growth were invested using X-ray computed tomography and scanning electron microscopy. Systematic observations were made of the variations in the fracture surfaces according to three fatigue damage evolution stages: fatigue crack formation (incubation), microstructurally/physically small cracks, and long cracks. The fatigue crack was formed almost exclusively at the relatively large pores located at or near the specimen surface, with rare cases at incompletely melted power particles on the surface. Distributed cracks from large interior pores coalesced with each other in the microstructurally small crack regime to form the major critical crack that eventually fractured the specimen. This coalescence accelerated the fatigue crack growth, which in turn decreased the fatigue life but not significantly. In the long-crack regime, the fracture surface was rougher, but the overall surface tended to be perpendicular to the loading direction, indicating a Mode I type fracture. Cyclic strain-softening, with reduced strain-hardening, was also observed. The multistage fatigue model of McDowell et al. was used to capture the microstructure effects in the three fatigue damage evolution regimes, and the upper and lower bounds for the strain–life are predicted.