Modelling the Flow Behaviour of Al Alloy Sheets at Elevated Temperatures Using a Modified Zerilli-Armstrong Model and Phenomenological-Based Constitutive Models.

The flow behaviour of AA2060 Al alloy under warm/hot deformation conditions is complicated because of its dependency on strain rates (ε˙), strain (ε), and deformation modes. Thus, it is crucial to reveal and predict the flow behaviours of this alloy at a wide range of temperatures (T) and ε˙ using different constitutive models. Firstly, the isothermal tensile tests were carried out via a Gleeble-3800 thermomechanical simulator at a T range of 100, 200, 300, 400, and 500 °C and ε˙ range of 0.01, 0.1, 1, and 10 s-1 to reveal the warm/hot flow behaviours of AA2060 alloy sheet. Consequently, three phenomenological-based constitutive models (L-MJC, S1-MJC, S2-MJC) and a modified Zerilli-Armstrong (MZA) model representing physically based constitutive models were developed to precisely predict the flow behaviour of AA2060 alloy sheet under a wide range of T and ε˙. The predictability of the developed constitutive models was assessed and compared using various statistical parameters, including the correlation coefficient (R), average absolute relative error (AARE), and root mean square error (RMSE). By comparing the results determined from these models and those obtained from experimentations, and confirmed by R, AARE, and RMSE values, it is concluded that the predicted stresses determined from the S2-MJC model align closely with the experimental stresses, demonstrating a remarkable fit compared to the S1-MJC, L-MJC, and MZA models. This is because of the linking impact between softening, the strain rate, and strain hardening in the S2-MJC model. It is widely known that the dislocation process is affected by softening and strain rates. This is attributed to the interactions that occurred between ε and ε˙ from one side and between ε, ε˙, and T from the other side using an extensive set of constants correlating the constitutive components of dynamic recovery and softening mechanisms.

Need for transverse strain data for fitting constitutive models of arterial tissue to uniaxial tests.

The study deals with the process of estimation of material parameters from uniaxial test data of arterial tissue and focuses on the role of transverse strains. Two fitting strategies are analyzed and their impact on the predictive and descriptive capabilities of the resulting model is evaluated. The standard fitting procedure (strategy A) based on longitudinal stress-strain curves is compared with the enhanced approach (strategy B) taking also the transverse strain test data into account. The study is performed on a large set of material data adopted from literature and for a variety of constitutive models developed for fibrous soft tissues. The standard procedure (A) ignoring the transverse strain test data is found rather hazardous, leading often to unrealistic predictions of the model exhibiting auxetic behaviour. In contrast, the alternative fitting method (B) ensures a realistic strain response of the model and is proved to be superior since it does not require any significant demands of computational effort or additional testing. The results presented in this paper show that even the artificial transverse strain data (i.e., not measured during testing but generated ex post based on assumed Poisson's ratio) are much less hazardous than total disregard of the transverse strain response.

High-Temperature Compression Behaviors and Constitutive Models of a 7046-Aluminum Alloy.

High-temperature forming behaviors of a 7046-aluminum alloy were investigated by hot compression experiments. The microstructural evolution features with the changes in deformation parameters were dissected. Results indicated the formation of massive dislocation clusters/cells and subgrains through the intense DRV mechanism at low compression temperature. With an increase in deformation temperature, the annihilation of dislocations and the coarsening of subgrains/DRX grains became prominent, due to the collaborative effects of the DRV and DRX mechanisms. However, the growth of subgrains and DRX grains displayed the weakening trend at high strain rates. Moreover, two constitutive models involving a physically based (PB) model and a gate recurrent unit (GRU) model were proposed for predicting the hot compression features. By validation analysis, the predicted values of true stress perfectly fit with the experimental data, indicating that both the proposed PB model and the GRU model can accurately predict the hot compression behaviors of 7046-aluminum alloys.

A Fractional Creep Constitutive Model Considering the Viscoelastic-Viscoplastic Coexistence Mechanism.

In order to improve the accuracy and universality of the nonlinear viscoelastic-plastic mechanical behavior characterization method of asphalt mixture, a new criterion for the division of the creep process of materials was established based on the strain yield characteristics, and the coexistence mechanism of Viscoelastic-Viscoplastic strain was proposed in the subsequent yield phase; then, a viscoelastic element was constructed in the form of a parallel connection of two fractional viscoelastic elements based on fractional calculus theory, and its mathematical equations were derived; with novel viscoelastic elements, a constitutive model characterizing the whole creep process of asphalt mixtures was developed and its analytical expression was derived. The laboratory short-term creep test of Cement and Asphalt Mortar (CA mortar) and the simulation test data of asphalt mixtures from the references were used to verify the constitutive model. The results show that the creep constitutive model of asphalt mixture established in this paper has excellent fitting accuracy for different phases of the creep process of asphalt mixture under different stress levels, where the minimum fitting correlation values R2 for CA mortar, asphalt mixture (applied to pavement engineering), and asphalt sand are 0.9976, 0.981, and 0.979, respectively. Therefore, this model can be used to provide a theoretical reference for the study of the characterization of the mechanical behavior of asphalt materials.

A Constitutive Model for Describing the Tensile Response of Woven Polyethylene Terephthalate Geogrids after Damage.

A constitutive model was used to describe the tensile response of two woven Polyethylene Terephthalate (PET) geogrids, before and after mechanical damage. The model parameters of undamaged and damaged specimens were estimated via numerical regressions of test results. For each sample, the experimental and fitted tensile strengths were statistically compared using hypothesis tests. For each geogrid, tensile load-strain curves of damaged samples were drawn by applying scaling factors to the plot of the undamaged sample. The curve fittings resulted in high R2 values for undamaged and damaged specimens of the geogrids. For most samples, there was no significant mean difference between the experimental and fitted tensile strength. The model allowed us to describe the load-strain curve of a geogrid from its tensile properties: εmax, Tmax and Ji. Regardless of the type of damage (in laboratory or in situ), the model was able to describe the load-strain curves of damaged samples using data from undamaged samples and scaling factors.

A classification approach to improve out of sample predictability of structure-based constitutive models for ascending thoracic aortic tissue.

In this research, a pipeline was developed to assess the out-of-sample predictive capability of structure-based constitutive models of ascending aortic aneurysmal tissue. The hypothesis being tested is that a biomarker can help establish similarities among tissues sharing the same level of a quantifiable property, thus enabling the development of biomarker-specific constitutive models. Biomarker-specific averaged material models were constructed from biaxial mechanical tests of specimens that shared similar biomarker properties such as level of blood-wall shear stress or microfiber (elastin or collagen) degradation in the extracellular matrix. Using a cross-validation strategy commonly used in classification algorithms, biomarker-specific averaged material models were assessed in contrast to individual tissue mechanics of out of sample specimens that fell under the same category but did not contribute to the averaged model's generation. The normalized root means square errors (NRMSE) calculated on out-of-sample data were compared with average models when no categorization was performed versus biomarker-specific models and among different level of a biomarker. Different biomarker levels exhibited statistically different NRMSE when compared among each other, indicating more common features shared by the specimens belonging to the lower error groups. However, no specific biomarkers reached a significant difference when compared to the average model created when No Categorization was performed, possibly on account of unbalanced number of specimens. The method developed could allow for the screening of different biomarkers or combinations/interactions in a systematic manner leading the way to larger datasets and to more individualized constitutive approaches.

Temperature and Strain Rate Dependence on the Tensile Mechanical Properties, Constitutive Equations, and Fracture Mechanisms of MarBN Steel.

The effect of strain rate and temperature on the thermomechanical behavior and microstructure of MarBN steel is studied with the strain rates of 5 × 10-3 and 5 × 10-5 s-1 from room temperature (RT) to 630 °C. At high strain rates of 5 × 10-3 s-1, the Holloman and Ludwigson equations can better predict tensile plastic properties. In contrast, under low strain rates of 5 × 10-5 s-1, coupling of the Voce and Ludwigson equations appears to predict the flow relationship at RT, 430, and 630 °C. However, the deformation microstructures have the same evolution behavior under strain rates and temperatures. Geometrically necessary dislocations appear along the grain boundaries and increase the dislocation density, which results in the formation of the low-angle grain boundaries and a decrease in the number of twinning. The strengthening sources of MarBN steel include grain boundary strengthening, dislocation interactions, and multiplication. The fitted R2 values of these models (JC, KHL, PB, VA, ZA) to plastic flow stress at 5 × 10-5 s-1 are greater than 5 × 10-3 s-1 for MarBN steel. Due to the flexibility and minimum fitting parameters, the phenomenological models of JC (RT and 430 °C) and KHL (630 °C) give the best prediction accuracy under both strain rates.

Comparison of constitutive models for meniscus and their effect on the knee joint biomechanics during gait.

Mechanical behavior of meniscus can be modeled using constitutive material models of varying complexity, such as isotropic elastic or fibril reinforced poroelastic (FRPE). However, the FRPE material is complex to implement, computationally demanding in 3D geometries, and simulation is time-consuming. Hence, we aimed to quantify the most suitable and efficient constitutive model of meniscus for simulation of cartilage responses in the knee joint during walking. We showed that simpler constitutive material models can reproduce similar cartilage responses to a knee model with the FRPE meniscus, but only knee models that consider orthotropic elastic meniscus can also reproduce meniscus responses adequately.

Applicability of a Material Constitutive Model Based on a Transversely Isotropic Behaviour for the Prediction of the Mechanical Performance of Multi Jet Fusion Printed Polyamide 12 Parts.

Multi Jet Fusion (MJF), an innovative additive manufacturing (AM) technique in the field of Powder Bed Fusion (PBF) developed by Hewlett-Packard (HP) Inc. (Palo Alto, CA, USA), has been designed to produce polymer parts using thermoplastic-based powders, primarily focusing on polyamide 12 (PA12). Employing a layer-by-layer approach, MJF enables the rapid production of intricate components, reportedly up to 10 times faster than other AM processes. While the mechanical properties of MJF-printed PA12 and the impact of build orientation on those properties have already been explored in various studies, less attention has been given to the mechanical performance of MJF-printed PA12 components under complex loads and accurate predictive models. This contribution aims to assess the applicability of a constitutive model based on a transversely isotropic behaviour under linear elastic deformation for predicting the mechanical response of MJF-printed PA12 parts through numerical simulations. Both uniaxial tensile and shear tests were carried out on printed samples to determine the elastic properties of MJF-printed PA12, with additional testing on printed complex handle-shaped parts. Finally, a numerical model was developed to simulate the mechanical tests of the handles. Results from tests on printed samples showed that MJF-printed PA12, to some extent, behaves as a transversely isotropic material. Furthermore, using a constitutive model that assumes a transversely isotropic behaviour under linear elastic deformation for predicting the mechanical response of MJF-printed PA12 parts in numerical simulations could be a reasonable approach, provided that the material stress levels remain within the linear range. However, the particularities of the stress-strain curve of MJF-printed PA12 complicate determining the elasticity-to-plasticity transition point.

Viscoelastic Characterization of a Thermoplastic Elastomer Processed through Material Extrusion.

Objective. We aim to characterize the viscoelastic behavior of Polyether-Block-Amide (PEBA 90A), provide reference values for the parameters of a constitutive model for the simulation of mechanical behaviors, and paying attention to the influence of the manufacturing conditions. Methods. Uniaxial relaxation tests of filaments of PEBA were used to determine the values of the parameters of a Prony series for a Quasi-Linear Visco-Elastic (QLVE) model. Additional, fast cyclic loading tests were used to corroborate the adequacy of the model under different test criteria in a second test situation. Results. The QLVE model predicts the results of the relaxation tests very accurately. In addition, the behavior inferred from this model fits very well with the measurements of fast cyclic loading tests. The viscoelastic behavior of PEBA under small strain polymer fits very well to a six-parameter QLVE model.

Finite Element Analysis and Modeling in Pharmaceutical Tableting.

Finite element analysis (FEA) is a computational method providing numerical solutions and mathematical modeling of complex physical phenomena that evolve during compression tableting of pharmaceutical powders. Since the early 2000s, FEA has been utilized together with various constitutive material models in a quest for a deeper understanding and unraveling of the complex mechanisms that govern powder compression. The objective of the present review paper is to highlight the potential and feasibility of FEA for implementation in pharmaceutical tableting in order to elucidate important aspects of the process, namely: stress and density distributions, temperature evolution, effect of punch shape on tablet formation, effect of friction, and failure of the tablet under stress. The constitutive models and theoretical background governing the above aspects of tablet compression and tablet fracture under diametral loading are also presented. In the last sections, applications of FEA in pharmaceutical tableting are demonstrated by many examples that prove its utilization and point out further potential applications.

A comparison between constitutive models for the municipal solid waste.

This paper compares the behavioural models of municipal solid waste (MSW) using the corresponding experimental data. To do so, the proposed models are first reviewed and, then, the algorithms and codes of different models are written. After obtaining each model's algorithm, the same experimental data are considered as input, and the strain-stress curve is plotted for each model. In the first method, the total strain in the waste is obtained based on the summation of the elastic, plastic, biological, and creep strains. Afterward, the equivalent stress is obtained. In this method, using biological changes over time, the age of the waste is calculated as an effective parameter in MSW behaviour. Moreover, the effect of creep on the waste is considered independently. In the second algorithm, MSW is considered as fibre and paste material, and the strain-stress curve is obtained. In this method, the waste is considered as a soil model, and the effect of different parameters are calculated. Due to the complexity of the MSW behaviour and considering various parameters, such as the age of the waste, E changes over time, creep, and biological changes, the Krase model has less error than the other models. Using the soil behaviour model for the waste has a significant error, indicating the difference between the results for the behaviours of the two substances.

An Experimental Investigation of Viscoelastic Flow in a Contraction Channel.

In order to assess the predictive capability of the S-MDCPP model, which may describe the viscoelastic behavior of the low-density polyethylene melts, a planar contraction flow benchmark problem is calculated in this investigation. A pressure-stabilized iterative fractional step algorithm based on the finite increment calculus (FIC) method is adopted to overcome oscillations of the pressure field due to the incompressibility of fluids. The discrete elastic viscous stress splitting (DEVSS) technique in combination with the streamline upwind Petrov-Galerkin (SUPG) method are employed to calculate the viscoelastic flow. The equal low-order finite elements interpolation approximations for velocity-pressure-stress variables can be applied to calculate the viscoelastic contraction flows for LDPE melts. The predicted velocities agree well with the experimental results of particle imagine velocity (PIV) method, and the pattern of principal stress difference calculated by the S-MDCPP model has good agreement with the results measured by the flow induced birefringence (FIB) device. Numerical and experimental results show that the S-MDCPP model is capable of accurately capturing the rheological behaviors of branched polymers in complex flow.

Residual Mechanical Properties and Constitutive Model of High-Strength Seismic Steel Bars through Different Cooling Rates.

In this study, the high-temperature test (i.e., temperature to 1000 °C) is conducted on 600 MPa seismic steel bars, and its residual mechanical properties and constitutive relations are investigated though three cooling rates, i.e., under air, furnace, and water-cooling conditions. Results show that three cooling methods have significant effects on the apparent characteristics of 600 MPa steel bars, when the heating temperature is greater than 600 °C. In addition, the ultimate and yield strength of steel bars have been significantly affected by different cooling methods, with increasing heating temperature. However, the elastic modulus is significantly not affected by temperature. Furthermore, the elongation rate after fracture and the total elongation rate at the maximum force do not change significantly, when the heating temperature is less than 650 °C. The elongation rate, after fracture, and the total elongation rate, at the maximum force, have different changes for three cooling methods. The degeneration of the stress-strain curves occurs when the heating temperature is high. The two-fold line, three-fold line, and Ramberg-Osgood models are developed based on the stress-strain curve characteristics of steel bars after cooling. The fire resistance of 600 MPa steel bars of reinforced concrete structure is analyzed, which provides a basis for post-disaster damage assessment, repair, and reinforcement of the building structure.

Confinement Effect and Efficiency of Concentrically Loaded RACFCST Stub Columns.

Recycled aggregate concrete-filled steel tubular (RACFST) columns are widely recognized as efficient structural members that can reduce the environmental impact of the building industry and improve the mechanical behavior of recycled aggregate concrete (RAC). The objective of this study is to investigate the behavior of recycled aggregate concrete-filled circular steel tubular (RACFCST) stub columns subjected to the axial loading. Three-dimensional finite element (FE) models were established using a triaxial plastic-damage constitutive model of RAC considering the replacement ratio of recycled aggregates. The FE analytical results revealed that the decreased ultimate bearing capacity of RACFCST stub columns compared with conventional concrete infilled steel tubular (CFST) columns was mainly due to the weakened confinement effect and efficiency. This trend will become more apparent with the larger replacement ratio of recycled aggregates. A practical design formula of the ultimate bearing capacity of RACFCST stub columns subjected to axial load was proposed on the basis of the reasonably simplified cross-sectional stress nephogram at the ultimate state. The derivation process incorporated the equilibrium condition and the superposition theory. The proposed equation was evaluated by comparing its accuracy and accessibility to some well-known design formulae proposed by other researchers and some widely used design codes.

Characterization of rat tail lymphatic contractility and biomechanics: incorporating nitric oxide-mediated vasoregulation.

The lymphatic system transports lymph from the interstitial space back to the great veins via a series of orchestrated contractions of chains of lymphangions. Biomechanical models of lymph transport, validated with ex vivo or in vivo experimental results, have proved useful in revealing novel insight into lymphatic pumping; however, a need remains to characterize the contributions of vasoregulatory compounds in these modelling tools. Nitric oxide (NO) is a key mediator of lymphatic pumping. We quantified the active contractile and passive biaxial biomechanical response of rat tail collecting lymphatics and changes in the contractile response to the exogenous NO administration and integrated these findings into a biomechanical model. The passive mechanical response was characterized with a three-fibre family model. Nonlinear regression and non-parametric bootstrapping were used to identify best-fit material parameters to passive cylindrical biaxial mechanical data, assessing uniqueness and parameter confidence intervals; this model yielded a good fit (R2 = 0.90). Exogenous delivery of NO via sodium nitroprusside (SNP) elicited a dose-dependent suppression of contractions; the amplitude of contractions decreased by 30% and the contraction frequency decreased by 70%. Contractile function was characterized with a modified Rachev-Hayashi model, introducing a parameter that is related to SNP concentration; the model provided a good fit (R2 = 0.89) to changes in contractile responses to varying concentrations of SNP. These results demonstrated the significant role of NO in lymphatic pumping and provide a predictive biomechanical model to integrate the combined effect of mechanical loading and NO on lymphatic contractility and mechanical response.

Comparative Analysis of Fatigue EnergyCharacteristics of S355J2 Steel Subjected toMulti-Axis Loads.

In this study, a novel test system for estimating bending and torsion fatigue under selectable kinematic and dynamic loading modes was constructed. Using S355J2 steel specimens, a series of tests were conducted to determine material sensitivity to different load paths and loading modes. The experimental results were supplemented with the results of numerical analyses, on the basis of which the components of strain and stress tensors for subsequent analyses were determined in the entire working part of the specimen. An original method for determining specific strain energy components was used. The experimental results showed the grouping of data according to the mode of loading chosen. This could signify that the selected fatigue models are sensitive to certain loading scenarios. We performed in- depth data analysis and complex numerical simulations, formulating likely explanations for the observed effect.

A comparative study of hyperelastic constitutive models for colonic tissue fitted to multiaxial experimental testing.

For colonic stents design, the interaction with colonic tissue is essential in order to characterize the appropriate radial stiffness which provides a minimum lumen for intestinal transit to be maintained. It is therefore important to develop suitable constitutive models allowing the mechanical behavior of the colon tissue to be characterized. The present work investigates the biomechanical behavior of colonic tissue by means of biaxial tests carried out on different parts of the colonic tract taken from several porcine specimens. Samples from the colonic tract were quasi-statically tensioned using a load-controlled protocol with different tension ratios between the circumferential and the axial directions. Fitting techniques were then used to adjust specific hyperelastic models accounting for the multilayered conformation of the colonic wall and the fiber-reinforced configuration of the corresponding tissues. It was found that the porcine colon changed from a more isotropic to a more anisotropic tissue and became progressively more flexible and compliant in circumferential direction depending on the position along the duct as it approaches the rectum. The best predictive capability of mechanical behavior corresponds to the Four Fiber Family model showing mean values of coefficient of determination R2=0.97, and a normalized root mean square error of εNRMS=0.0814 for proximal spiral samples, and R2=0.89 , ÎµNRMS=0.1600 and R2=0.94 , ÎµNRMS=0.1227 for distal spiral and descending colon samples, respectively. The other analyzed models provide good results for proximal spiral colon specimens, which have a lower degree of anisotropy. The analyzed models with the fitted elastic parameters can be used for more realistic and reliable FE simulations, providing the appropriate framework for the design of optimal devices for the treatment of colonic diseases.

Verification of Continuum Mechanics Predictions with Experimental Mechanics.

The general goal of the study is to connect theoretical predictions of continuum mechanics with actual experimental observations that support these predictions. The representative volume element (RVE) bridges the theoretical concept of continuum with the actual discontinuous structure of matter. This paper presents an experimental verification of the RVE concept. Foundations of continuum kinematics as well as mathematical functions relating displacement vectorial fields to the recording of these fields by a light sensor in the form of gray-level scalar fields are reviewed. The Eulerian derivative field tensors are related to the deformation of the continuum: the Euler-Almansi tensor is extracted, and its properties are discussed. The compatibility between the Euler-Almansi tensor and the Cauchy stress tensor is analyzed. In order to verify the concept of the RVE, a multiscale analysis of an Al-SiC composite material is carried out. Furthermore, it is proven that the Euler-Almansi strain tensor and the Cauchy stress tensor are conjugate in the Hill-Mandel sense by solving an identification problem of the constitutive model of urethane rubber.