Constitutive Material Properties Research Articles

Determine the unique constitutive properties of elastoplastic materials from their plastic zone evolution under nanoindentation

The evolution of the plastic zone underneath the indenter is challenging to be described during nanoindentation, which is recently known to be crucial to establish a constitutive model that features the plastic properties of the substrate materials based on their indentation responses. Using molecular dynamics and axisymmetric finite element (FE) simulations in this study, we show that the plastic zone shape in the elastoplastic materials is hemispherical in a broad range of length scales under a three-sided pyramid-shaped Berkovich indenter. By considering the critical factors of the applied load–penetration depth (P–h) curve, dimensional analysis is performed to derive dimensionless functions regarding the radius of the hemispherical plastic zone. For the loading and unloading stages in extensive FE simulations, a set of polynomial functions are proposed by associating the instantaneous and residual plastic zone radii with constitutive parameters. In addition to Young's modulus and the hardening exponent, the ratio of the representative stress to the reduced modulus is found to be crucial for predicting the plastic deformation. Lastly, the proposed dimensionless function reveals that the plastic zone radii are drastically different for three representative materials with identical P–h curves as confirmed by three independent methods. This result suggests that the proposed plastic zone radius in the dimensionless analysis helps to overcome the challenging uniqueness issue for decades to determine the unique elastoplastic properties of materials based on nanoindentation responses.

Probing bonded interfaces with finite-element resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) has long been applied for non-destructive quantification of elasticity, geometry, and density in material samples. Improvements in mode imaging and finite element analysis now provide validation and predictive models for a growing range of sample types. We build on recent work which applied finite-element RUS to characterize layered samples. Our study takes a closer look at the utility of RUS to evaluate the bonded interface between layers, with extension to thin films. Forward modeling of bond properties provided insights into mode-dependent frequency shifts for various types of homogeneous bond changes such as thickness and stiffness. Experimental work consisted of RUS testing on Al-Ti samples diffusion-bonded at different pressures. Despite identical base materials, samples bonded at 2 MPa and 15 MPa exhibit spectral differences not explained by geometry variance alone, indicating sensitivity to the bond interface. Though highly geometry and material dependent, the sensitivity of RUS to interface properties appears to be roughly an order of magnitude smaller than to the constitutive material properties, emphasizing careful experimentation.

A complex-variable finite element method-based inverse methodology to extract constitutive parameters using experimental data

This paper presents the use of full-field kinematic measurements obtained using the digital image correlation (DIC) procedure and load–displacement data to determine constitutive material properties by solving an inverse finite element optimization problem. A key ingredient in the proposed approach is computing accurate sensitivities with respect to the unknown parameters. These sensitivities were used to solve the optimization problem using an accurate, efficient, gradient-based method, and were computed using the complex-variable finite element method, ZFEM. The use of ZFEM’s gradients to inversely determine material properties is demonstrated with two examples. First, the elastic–plastic material properties of DP-590 steel are obtained using a tensile test specimen. Second, the cohesive material parameters of an adhesive are determined using a double cantilever beam test. A significant outcome of this paper is that the use of a weighted residual formulation of the interfacial strain fields and the load–displacement data within the optimization procedure provides better estimates of the constitutive properties than using only the load–displacement data. This technique minimizes the relative error in both the strain fields and the load–displacement curve, which is important to obtain accurate interfacial properties.

Thermal oxidative aging of satin weave and thin‐ply polyimide composites

AbstractThe weight loss and damage development of satin weave and thin‐ply carbon fiber‐reinforced polyimide composites are studied during high temperature (288 and 320°C) aging in air. Two distinct regions are identified in the weight loss measurements—a rapid initial desorption and a subsequent slower weight loss, which is attributed to matrix degradation. The initial desorption stage is modeled by combining material constitutive properties from literature, micro‐mechanics and a one‐dimensional Fickian diffusion model. Two different damage patterns are observed by using optical microscopy and X‐ray computed tomography on specimens before and after aging. Crack clusters form a network in satin weave composites, while edge delaminations are observed in thin‐ply laminates, which are known for their enhanced resistance to matrix cracking.

Modeling of Dynamic Mechanical Response of Li-Ion cells with Homogenized Electrolyte-Solid Interactions

Several recent studies have revealed substantial strain-rate dependence of lithium-ion batteries subjected to dynamic mechanical loadings. This behavior has been shown to be strongly dependent on the cell type, geometry, and setting. While still far from being fully understood, this dependence is believed to be connected to the solid-liquid interactions between the porous solid materials inside the electrodes and separators and the liquid electrolyte. This understanding has been supported by tests on dry cells revealing a significantly simpler behavior, being determined primarily by the constitutive material properties as compared to wet cells. This paper provides a modeling approach for the fluid-solid interaction inside battery cells by utilizing a pore fluid movement feature originally developed for geo-materials. By applying this module to the dry cell structure, the essentials of the peculiar load displacement patterns observed with active cells could be reproduced for two types of cells, a prismatic and a pouch cell. It is believed that this procedure, elucidating the underlying physics, and yet being simple, effective, and less time consuming than potential alternative techniques, will be exceedingly useful for evaluating crash behavior of electric vehicles. It allows making realistic calculations feasible based on experiments performed only on dry cells quasi-statically.

An analytical approach of filament bundle swinging dynamics, Part II: identifying equivalent dynamic constitutive parameters of filament bundles

A filament bundle is a type of yarn, which is composed of nearly parallel and highly oriented polymer monofilaments. Due to its nonlinearity both in material constitutive properties and structure, the filament bundle possesses nonlinear viscoelastic properties. It is important to study the dynamic behavior of the filament bundle accurately during its high-speed movement. Therefore, an accurate expression of the constitutive relation of the filament bundle is an essential prerequisite for its dynamic simulation and analysis. Continued the previous study in Part I: modeling filament bundle method, in this paper, an approach was proposed to identify the equivalent dynamic constitutive parameters of the filament bundle considering frequency-dependent characteristics. Firstly, the identification formulas of the dynamic elastic modulus and viscoelastic coefficients were derived based on the Kelvin model. Then, a testing method of the cross-sectional parameters of the filament bundle under a certain tension was proposed, and the testing device was developed to obtain the area of the filament bundle; The dynamic loading test of the bundle filament was conducted in a DMA Q800 dynamic mechanical tester. Thirdly, the equivalent dynamic elastic modulus and viscoelastic coefficients were obtained through the experimental test. Finally, an analytical method was proposed to verify the correctness of experimental results through simulation. The results show that the excitation frequency has a significant influence on the dynamic elastic modulus and viscoelastic coefficient, and the curves of the equivalent dynamic elastic modulus and viscoelastic coefficient present nonlinear variation characteristics.

An accelerated three-dimensional coupled electromagnetic-mechanical model for electromagnetic pulse forming

Electromagnetic pulse technology (EMPT) is receiving growing attention from industry and academia in response to the rising demand for manufacturing with lightweight alloys. Further advances in this technology, however, relies to a large extent on the accuracy and efficiency of the computational models that can be used to provide insight to the fundamentals of the EMPT-based processes. This paper presents a multiphysics computational framework for efficient finite element simulation of these processes. A reduction coefficient, k, is proposed to account for the variation of the magnetic field intensity with both time (explicitly) and spatial distance (implicitly). Incorporation of the reduction coefficient allows for one-way coupling of the electromagnetic and mechanical domains, hence facilitating accurate and substantially efficient 3D numerical analysis of large domains and complex geometries, as compared to fully coupled electromagnetic-mechanical analysis. The reduction coefficient, modelled here as an explicit decaying exponential function of time, was validated and calibrated against the experimental results (final deformed geometry) obtained from a series of tube compression experiments. The paper also includes a discussion of the application of the model in evaluating high strain-rate constitutive properties of materials under complex loading conditions, which can be a basis for dynamic testing of metallic materials at the same time of processing.

Response simulations of clamped circular steel plates under uniform impulse and effects of axisymmetric stiffener configurations

The paper presents Finite Element Analysis (FEA) and simulations of large deformations and observed ductile fracture failure modes of clamped circular plates subjected to uniform impulsive loads using phenomenological failure models for damage initiation and progression. The proposed numerical setup is founded on a well-defined model of the constitutive material properties based on inverse FEA simulations of the uniaxial tension test for the calibration of the material and failure parameters. The presented numerical model using the tri-axiality weighted accumulated plastic strain damage model in conjunction with a progressive degradation scheme for the evolution and progression of failure in the structure, is calibrated from a single uni-axial tension test. Published experimental results of large plastic deformations, onset of thinning and tearing at the boundary for clamped steel circular plates subjected to uniformly loaded air blasts have been used to assess the performance and efficacy of the proposed numerical scheme and procedure, with inclusion of temperature effects due to plastic dissipation. Towards improvement in the predictions by the numerical model, a hybrid damage model involving a two part ductile fracture locus has been proposed, which shows excellent correlation with the experimental results presented in terms of non-dimensional parameters over a wide range of impulsive loading and stress states, covering all the relevant failure modes. The validated numerical model has further been used to study the effect of flat bar axisymmetric stiffener configurations on the structural response and failure mechanisms of clamped circular plates, which has not been seen in the literature so far. The numerical simulations have also been used to gain insights into the evolution of plastic zones, damage progression and predicted failure modes in circumferentially oriented transversely stiffened steel plates with increasing intensity of impulsive loads.

Numerical investigation on RC T-beams strengthened in the negative moment region using NSM FRP rods at various depth of embedment

The application of Near Surface Mounted (NSM) method to strengthen reinforced concrete (RC) members in flexure through the use of Fiber Reinforced Polymer (FRP) rods has become a subject of interest to designers and researchers over the past few years. This technique has been extensively applied, and there is still a need for more experiments, analytical, and numerical studies to determine the effects of their parameters on the flexural performance of RC members. Therefore, a detailed 3D nonlinear finite element (FE) numerical model was developed in this study to predict the load-carrying capacity and the response of RC T-beams strengthened in the negative moment region accurately through the use of NSM FRP rods at different depth of embedment which are placed under three-point bending loading. The model was, however, designed with due consideration for the nonlinear constitutive material properties of concrete, yielding of steel reinforcement, NSM rods, and cohesive behaviors to simulate the contact between two neighboring materials. Moreover, the findings of the numerical simulations were compared with those from the experiments by other investigators which involve two specimens strengthened with NSM FRP rods added to one unstrengthened control specimen. The results, however, showed that the mid-span deflection responses of the predicted FE were in line with the corresponding data from the experiment for all the flexural loading stages. This was followed by the use of the validated FE models to analyze the effect of several properties of the FRP materials to provide more information than the limited experimental data available. It was discovered that the FE model developed is appropriate to be applied practically and economically with more focus on the parametric studies based on design to precisely model and analyze flexural negative moment strengthening for the RC members through the use of NSM FRP rods.

Nonlinear forced vibration of rotating composite laminated cylindrical shells under hygrothermal environment

Abstract This work aims to study nonlinear vibration of rotating composite laminated cylindrical shells under hygrothermal environment and radial harmonic excitation. Based on Love’s nonlinear shell theory, and considering the effects of rotation-induced initial hoop tension, centrifugal and Coriolis forces, the nonlinear partial differential equations of the shells are derived by Hamilton’s principle, in which the constitutive relation and material properties of the shells are both hygrothermal-dependent. Then, the Galerkin approach is applied to discrete the nonlinear partial differential equations, and the multiple scales method is adopted to obtain an analytical solution on the dynamic response of the nonlinear shells under primary resonances of forward and backward traveling wave, respectively. The stability of the solution is determined by using the Routh–Hurwitz criterion. Some interesting results on amplitude–frequency relations and nonlinear dynamic responses of the shells are proposed. Special attention is given to the combined effects of temperature and moisture concentration on nonlinear resonance behavior of the shells.

Thermomechanical postbuckling of higher order shear deformable CNT-reinforced composite plates with elastically restrained unloaded edges

Buckling and postbuckling behavior of carbon nanotube (CNT) reinforced thick composite plates resting on elastic foundations and subjected to thermomechanical loads are investigated in this paper. The plates are subjected to uniform uniaxial compression in a thermal environment or the combined action of nondestabilizing preexisting uniaxial compression and uniform temperature rise. CNTs are reinforced into matrix through functionally graded distributions. The properties of constitutive materials are assumed to be temperature dependent and effective properties of CNT-reinforced composite are determined according to an extended rule of mixture. Governing equations are based on a higher order shear deformation theory taking von Kárman nonlinearity, initial geometrical imperfection, elasticity of tangential restraints of unloaded edges and plate-foundation interaction into consideration. Analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain nonlinear load-deflection relations. Numerical analyses are carried out to show the effects of CNT distribution patterns, preexisting loads, initial imperfection, degree of in-plane constraint, and elastic foundations on the nonlinear thermomechanical stability of CNT-reinforced composite plates.

Experiments in measuring dynamic hydrostatic constitutive properties of soft materials

An experimental investigation is conducted to develop, analytically model, and test a novel facility to obtain the dynamic hydrostatic constitutive properties and behavior of soft materials. The novel facility is an underwater shock tube consisting of two aluminum sections and an optically-clear acrylic section in between, all filled with water. A striker-piston configuration is used to provide an axial shock loading to one end of the assembly. Dynamic pressure sensors provide pressure data along the entire length of the assembly, including at the specimen location in the acrylic section. 3D Digital Image Correlation (DIC) is used in conjunction with high-speed photography to provide full-field deformation data of the specimen to obtain volumetric strain. The mismatch in acoustic impedance between the aluminum and the acrylic sections causes a reduction in the amplitude of the pressure pulse by 33%. The pressure pulse also undergoes appreciable dispersion in the acrylic section. Fluid-structure interaction (FSI) models are considered and applied to understand the dispersion characteristics of the axially propagating pressure pulse. The dynamic hydrostatic constitutive response of closed-cell polyvinyl chloride (PVC) foam is obtained at a volumetric strain rate of 100s−1. The bulk modulus at this strain rate for H130 PVC foam is measured to be 106.97 ± 3.11MPa. This is more than double that of the quasi-static (0.001s−1) value of 46.71 ± 1.91MPa, indicating a strong effect of strain rate on the material's response. The buckling pressure is also found to be strain rate dependent, with the dynamic buckling occurring at 3.09 ± 0.12MPa and quasi-static buckling occurring at 1.39 ± 0.17MPa.

Anisotropic finite element modelling of traumatic brain injury: A voxel-based approach

A computationally efficient 3D human head finite element model was constructed. The model includes the mesoscale geometrical details of the brain including the distinction between white and grey matter, sulci and gyri, ventricular system, foramen magnum, and the cerebrospinal fluid. We incorporate the heterogeneity and anisotropy from diffusion tensor imaging data by applying a one-to-one voxel-based correspondence between diffusion voxels and finite elements. The voxel resolution of the model was optimized to obtain a trade-off between reduced computational cost and higher geometrical details. Three sets of constitutive material properties were extracted from the literature to validate the model against intra-cranial pressure and relative motion test data within the brain. The model exhibited good agreement at pressure tests in frontal and occipital lobes with peak pressure magnitudes of only 8% and 6% higher which occurred 0.5-3 ms earlier than those of the experimental curves at coup and countercoup sites, respectively. In addition, the evaluation of the relative displacement at six locations within the brain indicated acceptable agreement with experimental data, with our model’s performance exhibiting the highest overall score compared to several previous models by using the correlation and analysis rating method.

Experimental and Numerical investigations on the cyclic load behavior of beams with rectangular web openings strengthened using FRP sheets

This study assesses experimentally and numerically the cyclic loading response of reinforced concrete beams with web openings and shear-flexure strengthened carbon fiber reinforced polymer (CFRP) sheets using an external bonded technique. The influence of the beams on the reverse cyclic effect including the parameters of the hysteretic failure modes, stiffness degradation performance, energy dissipation, pinching width ratio, and ductility, are discussed. A numerical approach is employed to evaluate an innovative rectangular web opening and external bonding strengthening with an FRP sheet. A numerical model was used to validate the results of the tested specimens. Appropriate simulation techniques, which characterize the properties of constitutive materials, and a concrete damaged plasticity model were used for modeling development. Further, they are incorporated to apply models with new parameters. The results indicated that the use of CFRP as a strengthening system around the opening can significantly improve the overall stiffness capacity and beam behavior under cyclic loading. In particular, the increase in the load-carrying capacity over the control beam reached 63.43% for the beam with an opening in the shear zone and 73% for that with an opening in the flexural zone. The load–displacement hysteresis loops of the tested specimens were compared with those simulated by numerical models. Good convergence between the predicted and measured results was observed under all cyclic loading rates.

Interfacial failure and arching of the CRTS II slab track reinforced by post-installed reinforcement bars due to thermal effects

To prevent damage of the China Railway Track System (CRTS) II slab track induced by thermal effects, post-installed reinforcement (PIR) bars between the prefabricated slabs and the concrete base have been utilized in the track. This work presents a study on the interfacial failure and arching of the CRTS II slab track reinforced by PIR bars due to the effects of temperature change. To this end, a novel finite element model of the track was established, in which the non-linear interfacial interaction between the track slabs and the cement asphalt (CA) mortar layer was simulated by a cohesive zone model, the non-linear constitutive material properties of track concrete were represented by a concrete damaged plasticity (CDP) model, and the non-linear bond-slip relationship between PIR bars and track concrete was characterized by non-linear spring elements. Comparison between simulation results and experimental data indicates that the proposed modelling technique is capable of evaluating the performance of the track reinforced by PIR bars. The combined action of insufficient bond strength between PIR bars and concrete, and insufficient bond strength between track slabs and CA mortar layer, was analyzed. Numerical analysis results show: (1) The temperature rise of interface failure between the concrete slabs and the CA mortar layer can be improved by 6 °C after PIR bars installation. (2) The PIR bars are effective in reducing arching displacement of slabs caused by temperature rise in both lateral direction and longitudinal direction of track slabs. (3) Both PIR bond strength and interface bond strength influence the maximum arching displacement of track slabs significantly.

Acoustics modelling of open-cell foam materials from microstructure and constitutive properties.

The dynamic relations for highly porous fibrous materials, having analytical expressions for dynamic viscous drag forces and oscillatory solid-to-fluid heat transfer, are now extended towards open-cell foam materials where the struts of the foam are considered to be primarily cylindrical except in the region of the joints. By also including analytical expressions for the stiffness of the foam cell, an entirely analytically-based model is presented for the acoustics of highly-porous, open-celled foam materials. This approach is extremely efficient, requiring only the mean cell size, mean strut diameter, and constitutive properties of the solid foam material and the surrounding viscous fluid as input. The acoustic performance prediction of not only isotropic foam cell designs, but also anisotropic ones may be performed rapidly and virtually, without the need for the determination of poroelastic material properties from existing material samples. The steps required for the development of the analytical foam-cell model are presented, along with the acoustic performance prediction of a typical Melamine foam cell, yielding very promising results in comparison against measurements. In order to understand the suitability of the cylindrical foam strut assumption, a viscous drag force comparison with foam struts having square and triangular cross-sectional profiles is also presented.

Tamped Richtmyer–Meshkov Instability Experiments to Probe High-Pressure Material Strength

Dynamic interface instabilities such as Rayleigh–Taylor, Kelvin–Helmholtz, and Richtmyer–Meshkov are important in a number of physical phenomena. Besides meriting study because of their role in natural events and man-made applications, they can also be used to study constitutive properties of materials in extreme conditions. Both RTI and RMI configurations have been used to study the strength of solids at high strain rates, though RMI has largely been limited to zero or ambient pressure. Recently, advances in imaging have allowed tamped RMI experiments to be performed in which the pressure is maintained above ambient. In this study, we examine the tamped RMI for determining material strength. Through simulation, we explore the behavior of the jetting material and examine the sensitivity of jetting to material properties. We identify simple scaling laws that relate the key physical parameters controlling jetting, which are compared to previous results from the literature. We use these scaling law and other considerations to examine issues associated with tamped RMI experiments.

Fused Deposition Modelling of Fibre Reinforced Polymer Composites: A Parametric Review

Fused deposition modelling (FDM) is a widely used additive layer manufacturing process that deposits thermoplastic material layer-by-layer to produce complex geometries within a short time. Increasingly, fibres are being used to reinforce thermoplastic filaments to improve mechanical performance. This paper reviews the available literature on fibre reinforced FDM to investigate how the mechanical, physical, and thermal properties of 3D-printed fibre reinforced thermoplastic composite materials are affected by printing parameters (e.g., printing speed, temperature, building principle, etc.) and constitutive materials properties, i.e., polymeric matrices, reinforcements, and additional materials. In particular, the reinforcement fibres are categorized in this review considering the different available types (e.g., carbon, glass, aramid, and natural), and obtainable architectures divided accordingly to the fibre length (nano, short, and continuous). The review attempts to distil the optimum processing parameters that could be deduced from across different studies by presenting graphically the relationship between process parameters and properties. This publication benefits the material developer who is investigating the process parameters to optimize the printing parameters of novel materials or looking for a good constituent combination to produce composite FDM filaments, thus helping to reduce material wastage and experimental time.

Modeling Strategies of Finite Element Simulation of Reinforced Concrete Beams Strengthened with FRP: A Review

Fiber-reinforced polymer (FRP) composites do not only possess superior mechanical properties, but can also be easy to tailor, install, and maintain. As such, FRPs offer novel and attractive solutions to facilitate strengthening and/or retrofitting of aging, weakened, and upgraded structures. Despite the availability of general code provisions, the design and analysis of FRP-strengthened concrete structures is both tedious and complex—especially in scenarios associated with unique loading conditions. As such, designers often leverage advanced finite element (FE) simulation as a mean to understand and predict the performance of FRP-strengthened structures. In order to narrow this knowledge gap, this paper details suitable strategy for developing and carrying out advanced FE simulations on FRP-strengthened concrete structures. The paper also covers techniques related to simulating adhesives (bonding agents), material constitutive properties and plasticity (cracking/crushing of concrete, yielding of steel reinforcement, and delamination of FRP laminates), as well as different material types of FRP (CFRP, GFRP, and their hybrid combinations), and FRP strengthening systems (sheets, plates, NSM, and rods) under various loading conditions including ambient, earthquake, and fire. The principles, thumb rules, and findings of this work can be of interest to researchers, practitioners, and students.

Variations in Constitutive Properties of the Fluid Elicit Divergent Vibrational and Pressure Response Under Shock Wave Loading.

We performed a characterization of the shock wave loading on the response of the specimen representing a simplified head model. A polycarbonate cylinder (2-in. outer diameter, wall thickness: 0.06 or 0.12 in.) was filled with two fluids: pure de-ionized water and 40% glycerol in water, which differ only slightly in their constitutive material properties. These two fluids were selected to represent the cerebrospinal fluid and cerebral blood, using their high strain rate viscosity as a primary selection criterion. The model specimen was exposed to a single shock wave with two nominal intensities: 70 and 130 kPa overpressure. The response of the model was measured using three strain gauges and three pressure sensors, one mounted on the front face of the cylinder and two embedded in the cylinder to measure the pressure inside of the fluid. We noted several discriminant characteristics in the collected data, which indicate that the type of fluid is strongly influencing the response. The vibrations of the cylinder walls are strongly correlated with the fluid kind. The similarity analysis via the Pearson coefficient indicated that the pressure waveforms in the fluid are only moderately correlated, and these results were further corroborated by Euclidean distance analysis. Continuous wavelet transform of pressure waveforms revealed that the frequency response is strongly correlated with the properties of the fluid. The observed differences in strain and pressure modalities stem from relatively small differences in the properties of the fluids used in this study.