Questioning numerical integration methods for microsphere (and microplane) constitutive equations

In the last few years, more and more complex microsphere models have been proposed to predict the mechanical response of various polymers. Similarly than for microplane models, they consist in deriving a one-dimensional force vs. stretch equation and to integrate it over the unit sphere to obtain a three-dimensional constitutive equation. In this context, the focus of authors is laid on the physics of the one-dimensional relationship, but in most of the case the influence of the integration method on the prediction is not investigated.Here we compare three numerical integration schemes: a classical Gaussian scheme, a method based on a regular geometric meshing of the sphere, and an approach based on spherical harmonics. Depending on the method, the number of integration points may vary from 4 to 983,040! Considering simple quantities, i.e. principal (large) strain invariants, it is shown that the integration method must be carefully chosen. Depending on the quantities retained to described the one-dimensional equation and the required error, the performances of the three methods are discussed. Consequences on stress–strain prediction are illustrated with a directional version of the classical Mooney–Rivlin hyperelastic model. Finally, the paper closes with some advices for the development of new microsphere constitutive equations.     

Influence of Bridgman solidification on microstructures and magnetic behaviors of a non-equiatomic FeCoNiAlSi high-entropy alloy

The non-equiatomic FeCoNiAlSi alloy is prepared by the Bridgman solidification (BS) technique at different withdrawal velocities (V = 30, 100, and 200 μm/s). Various characterization techniques have been used to study the microstructure and crystal orientation. The morphological evolutions accompanying the crystal growth of the alloy prepared at different withdrawal velocities are nearly the same, from equiaxed grains to columnar crystals. The transition of coercivity is closely related to the local microstructure, while the saturation magnetization changes little at different sites. The coercivity can be significantly reduced from the equiaxed grain area to the columnar crystal area when the applied magnetic field direction is parallel to the crystal growth direction, no matter what is the withdrawal velocity. In addition, the alloy possesses magnetic anisotropy when the applied magnetic field is in different directions.     

Assessing the cost-effectiveness of electric vehicles in European countries using integrated modeling

Electric vehicles (EVs) are considered alternatives to internal combustion engines due to their energy efficiency and contribution to CO₂ mitigation. The adoption of EVs depends on consumer preferences, including cost, social status and driving habits, although it is agreed that current and expected costs play a major role. We use a partial equilibrium model that minimizes total energy system costs to assess whether EVs can be a cost-effective option for the consumers of each EU27 member state up to 2050, focusing on the impact of different vehicle investment costs and CO₂ mitigation targets. We found that for an EU-wide greenhouse gas emission reduction cap of 40% and 70% by 2050 vis-à-vis 1990 emissions, battery electric vehicles (BEVs) are cost-effective in the EU only by 2030 and only if their costs are 30% lower than currently expected. At the EU level, vehicle costs and the capability to deliver both short- and long-distance mobility are the main drivers of BEV deployment. Other drivers include each state’s national mobility patterns and the cost-effectiveness of alternative mitigation options, both in the transport sector, such as plug-in hybrid electric vehicles (PHEVs) or biofuels, and in other sectors, such as renewable electricity.     

Chemically induced residual stresses in dental composites

In several European countries, dental composites are replacing mercury-containing amalgams as the most common restorative materials. One problem with dental composites is residual stresses which may lead to poor performance of the restoration. In the present study, a combined modeling and materials characterization approach is presented and predictions compare well with experimental data on residual stresses. The model takes stress relaxation into account through the complete relaxation time spectrum of the resin. The approach allows for detailed parametric studies where resin and composite composition as well as cure conditions may be tailored with respect to residual stress generation.     

A probabilistic model for cleavage fracture with a length scale--parameter estimation and predictions of stationary crack experiments

This study presents a large experimental investigation in the transition temperature region on a modified A508 steel. Tests were carried out on single-edge-notch-bend specimens with three different crack depth over specimen width ratios to capture the strong constraint effect on fracture toughness. Three test temperatures were considered, covering a range of 85 °C. All specimens failed by cleavage fracture prior to ductile tearing. A recently proposed probabilistic model for the cumulative failure by cleavage was applied to the comprehensive sets of experimental data. This modified weakest link model incorporates a length scale, which together with a threshold stress reduce the scatter in predicted toughness distributions as well as introduces a fracture toughness threshold value. Model parameters were estimated by a robust procedure, which is crucial in applications of probabilistic models to real structures. The conformity between predicted and experimental toughness distributions, respectively, were notable at all the test temperatures.     

Tracking-error model-based predictive control for mobile robots in real time

In this paper, a model-predictive trajectory-tracking control applied to a mobile robot is presented. Linearized tracking-error dynamics is used to predict future system behavior and a control law is derived from a quadratic cost function penalizing the system tracking error and the control effort. Experimental results on a real mobile robot are presented and a comparison of the control obtained with that of a time-varying state-feedback controller is given. The proposed controller includes velocity and acceleration constraints to prevent the mobile robot from slipping and a Smith predictor is used to compensate for the vision-system dead-time. Some ideas for future work are also discussed.     

Determination of instantaneous corrosion rates and runoff rates of copper from naturally patinated copper during continuous rain events

Instantaneous corrosion rates of naturally patinated copper of varying age (16 months, 138 and 145 years) have been determined during continuous rain events in the laboratory with electrochemical impedance spectroscopy using a two-electrode cell. The two-electrode cell was found to yield the same information in bulk rainwater as a conventional three-electrode cell.Relatively constant corrosion rates, between 0.2 and 0.6 μm/y, were determined for samples having a two-layer structure with an inner brownish layer of cuprous oxide and an outer greenish layer of basic copper salts (138, 145 years). Samples with cuprous oxide as the dominating phase of the patina (16 months) showed higher and somewhat increasing corrosion rates during a rain event (from 0.6 to 1.2 μm/y). During a continuous rain event, corrosion rates were found to be approximately 10 (brownish patina) and 25 times (greenish patina) lower than corresponding instantaneous runoff rates. The first flush phenomena of the runoff process, with an increased concentration during first flush and a relatively constant concentration during steady state, was indirectly seen as an increase in solution conductivity during the first rain volume followed by relative constant value. The contribution of the concentration in the first flush to the total annual runoff rate was significant for panels having a greenish layer (138, 145 years) whereas it was negligible for panels having a brownish layer (16 months).     

Interaction bounds in multivariable control systems

Time-domain limitations due to right half-plane zeros and poles in linear multivariable control systems are studied. Lower bounds on the interaction are derived. They show not only how the location of zeros and poles are critical in multivariable systems, but also how the zero and pole directions influence the performance. The results are illustrated on the quadruple-tank process, which is a new multivariable laboratory process.