The experimental stress-strain curves from the standardized tests of Tensile, Plane Stress, Compression, Volumetric Compression, and Shear, are normally used to obtain the invariant λi and constants of material C_i that will define the behavior elastomers. Obtaining these experimental curves requires the use of expensive and complex experimental equipment. For years, a direct method called model updating, which is based on the combination of parameterized finite element (FE) models and experimental force-displacement curves, which are simpler and more economical than stress-strain curves, has been used to obtain the C_i constants. Model updating has the disadvantage of requiring a high computational cost when it is used without the support of any known optimization method or when the number of standardized tests and required C_i constants is high. This paper proposes a methodology that combines the model updating method, the mentioned standardized tests and the multi-response surface method (MRS) with desirability functions to automatically determine the most appropriate C_i constants for modeling the behavior of a group of elastomers. For each standardized test, quadratic regression models were generated for modeling the error functions (ER), which represent the distance between the force-displacement curves that were obtained experimentally and those that were obtained by means of the parameterized FE models. The process of adjusting each C_i constant was carried out with desirability functions, considering the same value of importance for all of the standardized tests. As a practical example, the proposed methodology was validated with the following elastomers: nitrile butadiene rubber (NBR), ethylene-vinyl acetate (EVA), styrene butadiene rubber (SBR) and polyurethane (PUR). Mooney–Rivlin, Ogden, Arruda–Boyce and Gent were considered as the hyper-elastic models for modeling the mechanical behavior of the mentioned elastomers. The validation results, after the C_i parameters were adjusted, showed that the Mooney–Rivlin model was the hyper-elastic model that has the least error of all materials studied (MAEnorm = 0.054 for NBR, MAEnorm = 0.127 for NBR, MAEnorm = 0.116 for EVA and MAEnorm = 0.061 for NBR). The small error obtained in the adjustment of the C_i constants, as well as the computational cost of new materials, suggests that the methodology that this paper proposes could be a simpler and more economical alternative to use to obtain the optimal C_i constants of any type of elastomer than other more sophisticated methods.

The exhaustion of natural resources has increased petroleum prices and the environmental impact of oil has stimulated the search for an alternative source of energy such as biodiesel. Waste cooking oil is a potential replacement for vegetable oils in the production of biodiesel. Biodiesel is synthesized by direct transesterification of vegetable oils, which is controlled by several inputs or process variables, including the dosage of catalyst, process temperature, mixing speed, mixing time, humidity and impurities of waste cooking oil that was studied in this case. Yield, turbidity, density, viscosity and higher heating value are considered as outputs. This paper used multi-response surface methodology (MRS) with desirability functions to find the best combination of input variables used in the transesterification reactions to improve the production of biodiesel. In this case, several biodiesel optimization scenarios have been proposed. They are based on a desire to improve the biodiesel yield and the higher heating value, while decreasing the viscosity, density and turbidity. The results demonstrated that, although waste cooking oil was collected from various sources, the dosage of catalyst is one of the most important variables in the yield of biodiesel production, whereas the viscosity obtained was similar in all samples of the biodiesel that was studied.

To ensure realistic results when modeling welded joints using the finite element method (FEM), it is essential to appropriately characterize the thermo-mechanical behavior of the elastic-plastic Finite Element (FE) models. This task is complex. Any small differences between the actual welded joints and the welded joints based on FEM can be amplified enormously in the presence of nonlinearities. Due to the intense concentration of heat on a small area to create such joints, the regions near the weld line undergo severe thermal cycles. These generate significant angular distortion due mainly to the residual stresses. This paper proposes a method to determine the parameters that are most appropriate for modeling the Butt joint single V-groove welded joint FE models’ thermo-mechanical behavior that were created by the one-pass Gas Metal Arc Welding (GMAW). The method is based on experimental data, as well as genetic algorithms (GA) with multi-objective functions. As a practical example, the proposed methodology is validated with three different welded joints specimens that are manufactured by different voltages and currents (26 volts and 140 amps, 28 volts and 210 amps, and 35 volts and 260 amps). The electrode orientation, shielding gas flow rate, distance between nozzle and plate, and welding speed were considered to be constant for all of the specimens that were studied, and their values were 80°, 20.0 L/min, 4.0 mm, and 6 mm/s, respectively. The base material was EN 235JR low carbon steel, whereas the weld bead was ER70S-6 for the three specimens that were welded. An agreement between the temperature field and the angular distortion that was obtained by the adjusted FE models and those that were obtained experimentally demonstrates that the proposed methodology may be valid for automatically determining the most appropriate parameters.

The kinematic behavior of models that are based on the finite element method (FEM) for modeling the human body depends greatly on an accurate estimate of the parameters that define such models. This task is complex, and any small difference between the actual biomaterial model and the simulation model based on FEM can be amplified enormously in the presence of nonlinearities. The current paper attempts to demonstrate how a combination of the FEM and the MRS methods with desirability functions can be used to obtain the material parameters that are most appropriate for use in defining the behavior of Finite Element (FE) models of the healthy human lumbar intervertebral disc (IVD). The FE model parameters were adjusted on the basis of experimental data from selected standard tests (compression, flexion, extension, shear, lateral bending, and torsion) and were developed as follows: First, three-dimensional parameterized FE models were generated on the basis of the mentioned standard tests. Then, 11 parameters were selected to define the proposed parameterized FE models. For each of the standard tests, regression models were generated using MRS to model the six stiffness and nine bulges of the healthy IVD models that were created by changing the parameters of the FE models. The optimal combination of the 11 parameters was based on three different adjustment criteria. The latter, in turn, were based on the combination of stiffness and bulges that were obtained from the standard test FE simulations. The first adjustment criteria considered stiffness and bulges to be equally important in the adjustment of FE model parameters. The second adjustment criteria considered stiffness as most important, whereas the third considered the bulges to be most important. The proposed adjustment methods were applied to a medium-sized human IVD that corresponded to the L3–L4 lumbar level with standard dimensions of width = 50 mm, depth = 35 mm, and height = 10 mm. Agreement between the kinematic behavior that was obtained with the optimized parameters and that obtained from the literature demonstrated that the proposed method is a powerful tool with which to adjust healthy IVD FE models when there are many parameters, stiffnesses, and bulges to which the models must adjust.

A method to find the optimum process parameters for manufacturing nickel-based superalloy Inconel 738LC by laser powder bed fusion (LPBF) technology is presented. This material is known to form cracks during its processing by LPBF technology; thus, process parameters have to be optimized to get a high quality product. In this work, the objective of the optimization was to obtain samples with fewer pores and cracks. A design of experiments (DoE) technique was implemented to define the reduced set of samples. Each sample was manufactured by LPBF with a specific combination of laser power, laser scan speed, hatch distance and scan strategy parameters. Using the porosity and crack density results obtained from the DoE samples, quadratic models were fitted, which allowed identifying the optimal working point by applying the response surface method (RSM). Finally, five samples with the predicted optimal processing parameters were fabricated. The examination of these samples showed that it was possible to manufacture IN738LC samples free of cracks and with a porosity percentage below 0.1%. Therefore, it was demonstrated that RSM is suitable for obtaining optimum process parameters for IN738LC alloy manufacturing by LPBF technology.