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A systematic account is given in part I of the use of dimensional analysis in constructing similarity conditions for models and structures. The analysis covers large deflections, buckling, plastic behavior, and materials with nonlinear stress-strain characteristics, as well as the simpler structural problems. (author)
Over the past decades, the prevalence of machine learning (ML) methods has made the development of ML-based constitutive models for granular materials undoubtedly a popular subject. Numerous studies have been made to feature the loading path or history-dependent stress-strain response of granular media using neural networks. In this work, a novel finite element method (FEM)–ML multiscale approach was developed by incorporating internal variables to improve the simulation accuracy of 3D history-dependent granular materials for the first time. To this end, a surrogate constitutive model based on the single-step-based multi-layer perceptron (MLP) neural network was used to replace representative volume element (RVE) simulations conducted by the discrete element method (DEM) in the multiscale FEM–DEM approach. Although the prediction principle of the MLP aligns with the FEM algorithm, artificially added internal variables are required to differentiate the loading history. To address this issue, history variables associated with the Frobenius norm are proposed to be fed into the MLP coupled with the strain tensor to extract the history-dependent behaviour of granular assemblies. The developed FEM–ML approach was demonstrated in 3D conventional triaxial compression (CTC) simulations. Compared to the multiscale FEM–DEM approach, the proposed FEM–ML method exhibits a significantly improved computational efficiency.
The predictive performance of a multimechanism GVIPS model with saturating hardening function is assessed against a set of high temperature cyclic experiments under both strain-control and stress-control at varying rates of loading as well as several complex interrupted cyclic responses. The material specimens were composed of the titanium alloy, TIMETAL 21S, and tested at 650 °C, see Lissenden et al., 2007. The model did a very good job of predicting the variety of tests, particularly given the fact that only monotonic loading tests (tensile, creep, relaxation) and a single fully reversed cycle was used for characterization. It was particularly interesting that the model was capable of reasonably capturing the rate of accumulated strain during ratchetting under tensile mean stress. Given complex interrupted cyclic response, the model was able to both qualitatively and even quantitatively predict reasonably well both the cyclic and associated relaxation periods (in all quadrants of the stress-strain space) thus confirming the validity of the chosen functional forms for both hardening and thermal recovery. The quantitative inaccuracy is associated with the fact that the material specimens tested by Lissenden et al., 2007 was significantly “softer” than those tested by Castelli in Saleeb et al., 1994 which were used for characterization of the GVIPS model parameters.
Developing sustainable solutions for single-use packaging is an important objective to combat the environmental crisis of plastics pollution. Most embodiments of cellulose-based packaging materials, including CellophaneTM, are completely biodegradable in both terrestrial and marine environments. However, petroleum-derived alternatives offer some performance advantages for metrics such as moisture barriers and mechanical properties. This project leverages molecular dynamics simulation to investigate how molecular modifications to cellulose-based polymer assemblies impact their material properties. An important performance criterion for the modified materials was to retain biodegradability; thus, modifications by naturally occurring, biodegradable additives were the focus of this study. Specifically, we developed models with xylan and lignin of varying monomeric compositions into the cellulose matrix. The mechanical properties were investigated by performing stress-strain simulations, and the water barrier and hydrophobicity were investigated by simulating the water contact angle. Our findings indicate that the incorporation of xylan into the cellulose matrix tends to increase the mechanical properties with an optimal loading of ~27 wt%. We also predict that orienting the nanoscale directionality of the xylan chains such that they are perpendicular to the cellulose fibrils will dramatically increase mechanical strength. In contrast, the incorporation of lignin tends to weaken the composite at all loadings investigated. Simulations of water contact angle predicted that coating polymers on the surface of the cellulose assembly creates a more hydrophobic surface than incorporating them throughout the matrix. Of the coatings investigated, lignin resulted in the most hydrophobic surface, followed by pectin and keratin, which both imparted modest increases in hydrophobicity. Future experimental work done by Futamura will focus on designing material prototypes to capitalize on the predictions of performance enhancement obtained from molecular modeling. While substantial progress was made by the simulations performed in this project, there still exists a vast parameter space that we were unable to investigate, including branching, functional group decoration, and degree of polymerization of polymer additives. However, the methods developed in this initial investigation will facilitate more rapid evaluation of the impact of molecular characteristics on the performance of biopolymer composite materials and thereby accelerate future materials discovery efforts in this area.
A refined understanding of zirconium-based cladding thermomechanical performance during rapid transients is essential for enhancing the safety and operation of light-water reactors. Traditional models for zirconium alloys under accident conditions generally assume that creep dominates fuel cladding performance. Here, these historic models have largely remained unchanged and serve as the basis for safety criteria development. As the U.S. nuclear industry pursues higher burnup levels, the increased release of fission gases during transients raises the risk of cladding failure in the low-temperature hcp α-phase, making the fidelity of these models of greater importance. Creep testing was conducted from 550–700°C with 25–120 MPa applied hoop stresses to investigate Zircaloy-4 deformation at accident-relevant temperatures in the α-phase. Step-loading was employed to capture creep behavior across a wide stress range from a single sample. The stress-strain rate data at higher temperatures (650 and 700°C) were well-described by isotropic versions of the Erbacher and Kaddour models, while the lower temperature data (550 and 600°C) were underpredicted by both anisotropic and isotropic model variants. Greater strain rates during the initial loading step at 650 and 700°C were attributed to recrystallization and grain growth of sub-micron crystallites. Yet, texture analysis revealed the basal split texture remained after testing. These observations produced results suggesting Zircaloy-4 claddings experience higher creep rates across the α-phase than previously thought, possibly related to dynamic anisotropy due to temperature dependent activation of deformation mechanisms, effects of biaxial loading, and variation in material condition between the current testing used in previous model development.
The nonlinear hysteretic behavior of rocks under cyclic loading is a crucial area of study in geomechanics. The macroscopic response of a variety of materials has been found to be contingent upon the behavior of the micro-scale structure. This project aims to develop a functional and maintainable software package for generating a multi-phase numerical mesh and accompanying simulation files for finite element modeling used in computational mechanics solvers. Meshes generated from images often lack key preprocessing that reduces noise and prevents mesh element distortion that can increase computational cost. By incorporating user feedback throughout, grain2mesh ensures a high-fidelity mesh that can be used to model grain-scale interactions such as shearing, crack propagation, and interfacial material contrast. Scientific applications of this software include material fracturing, stress-strain analysis for natural and engineered materials, and nonlinear meso-scale analysis.
A more accurate procedure was developed for the determination of the inelastic behavior of structural components. The actual stress-strain curve for the mathematical of the structure was utilized to generate the force-deformation relationships for the structural elements, rather than using simplified models such as elastic-plastic, bilinear and trilinear approximations. relationships were generated for beam elements with various types of cross sections. In the generational of these curves, stress or load reversals, kinematic hardening and hysteretic behavior were taken into account. Intersections between loading and unloading branches were determined through an iterative process. Using the inelastic properties obtained, the plastic static response of some simple structural systems composed of beam elements was computed. Results were compared with known solutions, indicating a considerable improvement over response predictions obtained by means of simplified approximations used in previous investigations.
Finite element models of varying complexities were used to solve problems in solid mechanics. Particular emphasis was given to concrete which is nonisotropic at any level of deformation and is also nonlinear in terms of stress-strain relationships.
The limiting shear stress shear rheological model was applied to property measurements pursuant to the use of the constitutive equation and the application of the constitutive equation to elastrohydrodynamic (EHD) traction. Experimental techniques were developed to subject materials to isothermal compression which is similar to the history the materials were subjected to in EHD contacts. In addition, an apparatus was developed for measuring the shear stress-strain behavior of solid lubricating materials. Four commercially available materials were examined under pressure. They exhibit elastic and limiting shear stress behavior similar to that of liquid lubricants. The application of the limiting shear stress model to traction predictions was extended employing the primary materials properties measured in the laboratory. The shear rheological model was also applied to a Grubin-like EHD inlet analysis for predicting film thicknesses when employing the limiting shear stress model material behavior.
Elastomeric foam is an essential component in many industrial and technological settings, primarily as thermal insulators and as positional/mechanical support cushions. In particular, silicone foam is utilized in harsh environments due to exceptional thermal and chemical stability. Under service conditions within certain applications such material gets exposed to a high dosage of gamma radiation, which can permanently alter the material’s structural and mechanical response properties. Most studies on gamma-exposure under inert or oxidative atmosphere indicate hardening of silicone foam, which is attributed to radiation-induced enhancement in chemical cross-linking. Here we report two contrasting effects depending on whether (non-oxidative) radiation exposure is carried out with the foam under zero or finite compressive strain. While in the former case we observe radiation-hardening consistent with previous studies, in the latter case (50% porous foam under 30% uniaxial compression) we see a monotonic decrease in Young’s modulus with increasing dosage, although solvent swelling experiments on the constituent rubber indicate a net increase in cross-link density independent of the state of strain. We quantitatively model all dose-dependent data using the Ogden Hyperfoam strain-energy function within the framework of Tobolsky two-network scheme and attribute the above anomaly to a combined effect of radiation-induced thickness change (compression set) and inherent nonlinearity in the foam’s stress-strain response.
A recently developed micro-tensile sample preparation technique was implemented to evaluate the tensile strengths of the buffer, IPyC, and buffer-IPyC interlayer regions of the unirradiated and irradiated AGR-2 TRISO fuel particles. Understanding the mechanical properties of the buffer-IPyC interlayer is essential for developing thermomechanical models of buffer-IPyC separation, yet there is a lack of experimental data on its micro-tensile properties. TEM analysis was conducted on these regions to determine the microstructural changes relevant to the samples' tensile properties. In the unirradiated TRISO particle samples, the buffer layer demonstrated the weakest tensile strength, while the IPyC layer exhibited the highest. Conversely, in the irradiated TRISO particle samples, the buffer-IPyC interlayer region showed the lowest tensile strength, with the IPyC layer being the strongest. Fractures in the samples from the buffer-IPyC region predominantly occurred either in the buffer layer or at the buffer-IPyC interface. However, some buffer-IPyC interlayer samples displayed stress-strain and fracture behaviors more akin to the IPyC layer than the buffer layer. Analysis of diffraction patterns suggests that irradiation may have increased anisotropy in the three regions tested. Despite this suggested increase in anisotropy, there was no evidence that it affected the measured strengths. The irradiated TRISO particles demonstrated a considerable increase in void space and a decrease in ultimate tensile strength within the buffer-IPyC interlayer region due to the densification and contraction of the buffer layer. Minor variations in diffraction ring patterns were also observed. These changes, coupled with a significant reduction in the Weibull modulus/shape parameter, imply that irradiation-induced densification leads to tearing between the buffer and IPyC layers at locations of elevated porosity in the buffer-IPyC interlayer region.
Here, the present study examines the thermal energy storage (TES) effectiveness and printability of microencapsulated phase-change material (MEPCM) combined with thermoplastic polyurethane (TPU) for fused filament fabrication (FFF). Two formulations were assessed: 24D MEPCM, which changes phase at 24 ° C, compounded with TPU pellets and 43D MEPCM, which changes phase at 43 ° C, integrated with TPU powder. These combinations are designed to evaluate the effectiveness of the form of the TPU (pellets versus powder) in the FFF process. The investigation includes a comprehensive analysis of thermal characteristics, encompassing phase-change temperature, latent heat of fusion, thermal conductivity, and thermal decomposition, which are assessed through differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). Additionally, mechanical properties, including stress-strain behavior, are examined to evaluate material suitability for TES applications, while microstructural visualization is used to provide deeper insights into material performance, structural integrity, and the quality of printed components. The 24D MEPCM and TPU pellets formulation experienced a significant loss of approximately 39.6% of PCM during filament extrusion and printing, resulting in a reduced effective latent heat. Therefore, further characterization of the pellet formulation was discontinued due to excessive leakage. In contrast, the 43D MEPCM and TPU powder formulation demonstrated minimal PCM loss, with the 60 wt.% composition achieving an effective latent heat of 132 J/g. This value represents the highest effective latent heat currently documented in the literature for PCM-polymer-composite materials produced using an FFF-based additive manufacturing process.
This document outlines a method for processing functional output (i.e., curves) for the ultimate purpose of sampling curves under specified input conditions for use in modeling and simulation uncertainty quantification (UQ) studies. A set of benchmark curves sufficiently representative of the relevant scenario(s) being simulated are provided to the process and formatted as described in Section 1. Principal Component Analysis (PCA) is utilized to discover the components of uncertainty in the benchmark curves and is outlined in Section 2. Section 3 describes the application of uncertainty quantification to the PCA results for the purpose of sampling curves to be used in UQ analysis. Section 4 applies these techniques to an example benchmark dataset. Concluding remarks are provided in the final section.
The microstructural characteristics and morphology of interfaces in metals can be crucial in governing the initiation of plasticity and early deformation mechanisms under extreme conditions. During high-strain-rate deformation, these interfaces significantly affect dislocation nucleation, twinning, and other mechanisms that directly impact material strength and failure. Despite their importance, a substantial knowledge gap remains between the observed macroscopic material behavior and the underlying role of bimetal interfaces in plasticity initiation. Here, to address this gap, large-scale molecular dynamics simulations are performed on Al/Ti bimetal structures to examine the effect of interface characteristics on the onset of plasticity under uniaxial compression. Specifically, this study investigates how interface roughness (flat vs waveform interfaces) modifies the initiation of plastic events in the microstructure. Atomistic simulations indicate that interface roughness (a microscopic behavior) reduces the stress required for dislocation nucleation, thereby reducing the peak stress relative to a flat interface. For the square interface, the step height strongly influences plasticity initiation by setting the separation of locally flat regions. Varying the interface rotation relative to the loading direction (macroscopic behavior) reveals that the peak stress for both flat and waveform interfaces initially decreases and then increases with rotation, accompanied by a shift in dominant mechanisms—from Al twinning (flat) to interface sliding and Ti-dominated phase transformation and twinning at lower angles. The change in the stress-strain slope during initial compression reflects how rotation alters the resolved shear stress and activates different slip systems. Overall, the study provides valuable insights into the role of bimetal interfaces in controlling plasticity initiation and early deformation pathways for Al/Ti under extreme loading conditions.
Research on the tensile behavior of additively manufactured 316L stainless steel coupon specimens at increasing strain rates was conducted over the past year at Penn State. Dynamic loading rates into the 1000 1/s loading rates were performed on specimens with nearly 1.32” gage lengths. Stress-strain plots show ductile and plastic behavior well beyond 12% strain with necked specimens, having smaller effective gage lengths showing up to 56% ultimate strain. Additional tests performed on compact tension specimens helped with simulation work to understand the deformation behavior. Using finite elements, it was possible to determine the feasibility of a comprehensive experimental validation study towards an improved model for AM material failure – specifically, the Bai-Wierzbicki approach which accounts for lode angle and triaxiality. A non-significant number of tests are projected for eight specific failure nodes, with additional replicates to provide strain-rate capabilities to the existing formulation. One such correction factor is explored for quasi-static, notched specimens. Finally, stress intensity factor was explored using a set of compact-tension specimens which would also provide useful validation data for any simulation work.
Uranium mononitride (UN) is a promising advanced nuclear fuel due to its high thermal conductivity and high fissile density. However, many aspects of its mechanical behavior, particularly at reactor-relevant conditions, remain unclear. In this study, molecular dynamics (MD) simulations were employed to investigate the deformation behavior and dislocation motion in UN. We found that the Kocevski potential predicts the principal slip system as $\frac{1}{2}$ $\langle110\rangle${110}, aligning with experimental data. On the other hand, the Tseplyaev potential predicts slip to primarily occur on $\frac{1}{2}$ $\langle110\rangle${111}. MD simulations of stress–strain behavior were used to estimate the nanoindentation hardness, revealing that the Kocevski potential accurately predicts hardness even though it fails to model dynamic plasticity. Complete dislocation mobility functions have been fitted for the edge and screw dislocations in both the thermally activated and phonon-drag regimes. The 300 K linear mobility of the edge dislocation using the Tseplyaev potential was found to be 817 Pa -1 ·s -1 , whereas that of the screw dislocation using the Kocevski potential was found to be 4546 Pa -1 ·s -1 . At intermediate stresses, we observed that the subsonic steady-state motion of the edge dislocation in UN is intermittently interrupted by velocity jumps, reaching the average sound velocity. Finally, the threshold Schmid stress is calculated as 179–197 MPa, which gives an upper-limit estimate of the uniaxial yield stress of polycrystalline UN of 548–603 MPa. These findings, including the fitted dislocation mobility function, provide essential input for future plasticity and dislocation dynamics models of nuclear fuels.
A study was made to estimate the magnitudes of elastic stresses and elastic-plastic stresses and strains in sheet or foil laminar composites. Using a model tungsten/80Ni + 20Cr laminar composite and assuming cooling or heating through a temperature range of 80-2000 deg F (26.5-1093.5 deg C), calculated elastic stresses exceeded published or estimated strengths of the constituents. Elastic-plastic stress-strain solutions resulted in lower estimated stress levels but with the concomitant occurrence of sufficiently large strain ranges to suggest possible thermal fatigue problems. Limited experimental studies using tungsten/80Ni + 20Cr foil and sheet laminar composites, slowly cycled between 80 and 2000 deg F (26.5-1093.5 deg C) or rapidly cycled between 80 and 1600 deg F (26.5-871 deg C) produced varying degrees of observable structural damage in from 1 to 11 cycles depending upon temperature transition rate and laminae thickness; these particular results might not occur with other combinations of materials.
Theoretical equations are derived and analytical procedures are presented for the interpretation of experimental measurements of large plastic strains in the surface of a plate. Orthogonal gage lengths established on the metal surface are measured before and after deformation. The change in orthogonality after deformation is also measured. Equations yield the principal strains, deviatoric stresses in the absence of surface friction forces, true stresses if the stress normal to the surface is known, and the orientation angle between the deformed gage line and the principal stress-strain axes. Errors in the measurement of nominal strains greater than 3 percent are within engineering accuracy. Applications suggested for this strain measurement system include the large-strain-stress analysis of impact test models, burst tests of spherical or cylindrical pressure vessels, and to augment small-strain instrumentation tests where large strains are anticipated.