Constitutive Model Research Articles

Isolated Rib Response and Fracture Prediction for Young Mid-Size Male, Enabled by Population Specific Material Models and Rib Cross-Sectional Geometry.

Thorax injury remains a primary contributor to mortality in car crash scenarios. Although human body models can be used to investigate thorax response to impact, isolated rib models have not been able to predict age- and sex-specific force-displacement response and fracture location simultaneously, which is a critical step towards developing human thorax models able to accurately predict injury response. Recent advancements in constitutive models and quantification of age- and sex-specific material properties, cross-sectional area, and cortical bone thickness distribution offer opportunities to improve rib computational models. In the present study, improved cortical and trabecular bone constitutive models populated with age-specific material properties, age- and sex-specific population data on rib cross-sectional area, and cortical bone thickness distribution were implemented into an isolated 6th rib from a contemporary human body model. The enhanced rib model was simulated in anterior-posterior loading for comparison to experimental age- and sex-specific (twenty-three mid-size males, age range of 22- to 57-year-old) population force-displacement response and fracture location. The improved constitutive models, populated with age-specific material properties, proved critical to predict the rib failure force and displacement, while the improved cortical bone thickness distribution and cross-sectional area improved the fracture location prediction. The enhanced young mid-size male 6th rib model was able to predict young mid-size male 6th rib experimental force-displacement response and fracture location (overpredicted the displacement at failure by 35% and underpredicted the force at failure by 8% but within ±1 SD). The results of the present study can be integrated into full body models to potentially improve thorax injury prediction capabilities.

Prediction of single cell mechanical properties in microchannels based on deep learning

Traditional methods for measuring single-cell mechanical characteristics face several challenges, including lengthy measurement times, low throughput, and a requirement for advanced technical skills. To overcome these challenges, a novel machine learning (ML) approach is implemented based on the convolutional neural networks (CNNs), aiming at predicting cells’ elastic modulus and constitutive equations from their deformations while passing through micro-constriction channels. In the present study, the computational fluid dynamics technology is used to generate a dataset within the range of the cell elastic modulus, incorporating three widely-used constitutive models that characterize the cellular mechanical behavior, i.e., the Mooney-Rivlin (M-R), Neo-Hookean (N-H), and Kelvin-Voigt (K-V) models. Utilizing this dataset, a multi-input convolutional neural network (MI-CNN) algorithm is developed by incorporating cellular deformation data as well as the time and positional information. This approach accurately predicts the cell elastic modulus, with a coefficient of determination R2 of 0.999, a root mean square error of 0.218, and a mean absolute percentage error of 1.089%. The model consistently achieves high-precision predictions of the cellular elastic modulus with a maximum R2 of 0.99, even when the stochastic noise is added to the simulated data. One significant feature of the present model is that it has the ability to effectively classify the three types of constitutive equations we applied. The model accurately and reliably predicts single-cell mechanical properties, showcasing a robust ability to generalize. We demonstrate that incorporating deformation features at multiple time points can enhance the algorithm’s accuracy and generalization. This algorithm presents a possibility for high-throughput, highly automated, real-time, and precise characterization of single-cell mechanical properties.

Investigating the impact of nano copper on the electrical conductivity of aluminum: a comprehensive study utilizing genetic algorithms methods

Nanotechnology has emerged as a transformative field in material science, offering unprecedented opportunities to enhance the electrical properties of conventional materials through the incorporation of nano-sized particles. In this extensive study, we explore the effects of varying weight percentages (1%, 2%, and 3%) and lengths (30 nm, 60 nm, 150 nm, and 250 nm) of nano copper on the electrical conductivity of aluminum (Al) across different temperatures (20°C, 50°C, 80°C, and 100°C). Additionally, GA method and Numerical correction factor and constitutive equation using Zener –Holloman parameter were employed for modeling the rheological behavior of Al based on these parameters.

Driving response analysis of twisted and coiled polymer actuators by considering the viscoelastic behavior of their precursor fibers

Twisted and coiled polymer actuators (TCPA) represent a type of artificial muscle predominantly composed of viscoelastic polymers in their precursor fibers. An integral form of the viscoelastic constitutive model has been developed to predict the mechanical deformation of the precursor fibers. The model successfully accounts for the first-cycle effect and the creep deformation near the glass transition temperature of the precursor fibers. Combined with the multilayer model by Gao and Wang (2024 Smart Mater. Struct. 33 045031), which predicts the effective mechanical and thermal properties of TCPA, the proposed viscoelastic constitutive model accurately predicts the thermo-mechanical response of TCPA under the heating and cooling cycle and applied loads. It is noted that the driving strain of TCPA is sensitive to the heating and cooling cycles. When the cycle duration is short, the proposed viscoelastic model can be simplified to a linear elastic model. The numerical implementation of the viscoelastic constitutive model is detailed, with validation conducted on two polymer materials, polypropylene, and polyamide 66. The proposed constitutive model can effectively predict the driving response of TCPA under complex loading conditions.

Effects of Steel and Glass Fibers on the Compressive Behavior of Rubberized Concrete: An Experimental Study and Constitutive Modeling

Effects of Steel and Glass Fibers on the Compressive Behavior of Rubberized Concrete: An Experimental Study and Constitutive Modeling

An unresolved SPH-DEM model for simulation of ductile and brittle surface erosion by abrasive water-jet (AWJ) impact

The abrasive water-jet (AWJ) erosion process involves the complex interaction between fluid medium, abrasive particles and solid material, which brings great challenges to the establishment of numerical model. Because traditional grid-based methods are not suitable for the problems of local deformation and material removal, the meshfree method smoothed particle hydrodynamics (SPH), based on the unresolved coupling and the discrete element method (DEM), is adopted to establish the model for AWJ study. The fluid medium is treated as a weakly compressible viscous liquid, the solid material is treated as an elastic-plastic material, and the abrasives are treated as rigid bodies. The fluid and solid phases are discretized with SPH particles, and the abrasives are described with DEM particles. The Johnson-Cook (J-C) and Johnson-Holmquist-II (JH-2) constitutive models are used to describe the stress-strain behavior of ductile and brittle materials, respectively. The effectiveness of the numerical model is further verified by AWJ impact experiments. The plastic deformation and cumulative failure characteristics of ductile materials, and the crack formation and propagation characteristics of brittle materials are systematically analyzed. The results provide insight for the AWJ research and lay a foundation for investigation of other complex fluid-particle flow in a numerical way.

Dynamic Mechanical Properties and Constitutive Modeling of Polyurethane Microporous Elastomers.

The present study fabricated samples of polyurethane elastomers (PUEs) with three distinct densities and assessed their mechanical responses using split Hopkinson pressure bar (SHPB) tests. The findings reveal a significant increase in PUE stress with increasing strain rate and density. To further investigate the influence of strain rate sensitivity on PUEs, a strain rate sensitivity coefficient was employed to quantify the impact of strain rate on the mechanical properties of PUEs. Separate quantifications were performed for collapse stress, plateau stress, and densification strain as indicators of the strain rate sensitivity coefficient. The results demonstrate that the collapse stress sensitivity coefficient was notably affected by the applied strain rate. Additionally, both collapse and plateau stresses exhibited an increase with increasing density, which could be described by a power function relationship. Based on the theory of strain energy function, a constitutive model considering density and strain rate effects was developed to describe the stress-strain behavior of PUEs under various densities and strain rates. A comparison between this constitutive relationship and experimental results showed good agreement, highlighting its potential in describing dynamic mechanical behavior.

Mechanical Properties of 3D Printed PLA Scaffolds for Bone Regeneration

Abstract The growing interest in biodegradable scaffolds for bone regeneration created a need to investigate new materials suitable for scaffold formation. Poly(lactic acid) (PLA) is a polymer commonly used in biomedical engineering, e.g. in tissue engineering as a biodegradable material. However, the mechanical behavior of PLA along its degradation time is still not explored well. For this reason, the mechanical properties of PLA scaffolds affected by incubation in physiological medium needs to be investigated to show the potential of PLA to be used as a material for biodegradable scaffold formation. The purpose of this research is to determine the mechanical properties of PLA scaffolds before and after incubation, and to apply constitutive material models for further behavior prediction. Two sets of PLA scaffolds were printed by the 3D printer “Prusa i3 MK3S” and sterilized by ultraviolet light and ethanol solution. The first set of specimens was incubated in DMEM (Dulbecco’s Modified Eagle Medium) for 60, 120, and 180 days maintaining 36.5 °C temperature. The mechanical properties of the scaffolds were determined after performing the compression test in the “Mecmesin MultiTest 2.5-i” testing stand with a force applied at two different speed modes. The obtained data was curve fitted with the hyperelastic material models for a model suitability study. The second set of specimens was incubated in PBS (Phosphate Buffered Saline) for 20 weeks and used in a polymer degradation study. The obtained results show that the mechanical properties of PLA scaffolds do not decrease during incubation in physiological medium for a predicted new bone tissue formation period, though hydrolysis starts at the very beginning and increases with time. PLA as a material seems to be suitable for the use in bone tissue engineering as it allows to form biocompatible and biodegradable scaffolds with high mechanical strength, required for effective tissue formation.

Hysteretic Dynamic Modeling and Vibration Characteristics Analysis of Metal-Rubber Isolators

A novel hysteretic constitutive model (HCM) with four parameters was proposed to reproduce the nonlinear elasticity and dry friction characteristics of metal–rubber isolators (MRIs). The HCM accurately characterized the nonlinear hysteretic behavior due to its intrinsic relationship with the geometric properties of the hysteresis loop. A physics-based parameter estimation strategy was developed to provide reasonable initial iteration values. Three MRIs with different design stiffnesses were tested to investigate their hysteretic behavior under various excitation levels. The HCM accurately reproduced the entire experimental hysteresis loops using only a subset of the experimental data. This exhibited higher precision and scalability compared to the classical dynamic model. Friction damping forces were employed to distinguish the stick-slip states of the three MRIs. Additionally, the identified parameters were used to simulate the steady-state vibration response of a complex MRI system. The resulting frequency response functions (FRFs) agreed well with the experimental data. The proposed model can effectively capture the amplitude-dependent effects in MRI systems with various design stiffnesses, enabling more accurate predictions of vibration responses.

Mechanical property deterioration and a full-stage constitutive model of shale subject to water-softening effect

Mechanical property deterioration and a full-stage constitutive model of shale subject to water-softening effect

Fast simulation of coronary in‐stent restenosis: A non‐intrusive data‐driven reduced order surrogate model

AbstractModeling and simulation of coronary artery disease (CAD) is of great importance for supporting and predicting the outcome of percutaneous coronary intervention (PCI). However, an in silico model generally requires heavy computational resources. An effective reduced order surrogate model is indispensable in this context. This study aims to develop a non‐intrusive data‐driven reduced order surrogate model for coronary in‐stent restenosis (ISR) incorporating anti‐inflammatory drugs embedded in the drug‐eluting stents. The constitutive model includes a detailed multiphysics approach based on partial differential equations (PDEs), which include descriptions of platelet aggregation, growth‐factor release, cellular motility and drug deposition. Dimensionality reduction is carried out based on a 3D convolutional autoencoder, which comprises an encoder and decoder. The former condenses the full‐order solution into a lower‐dimensional latent space, while the latter recovers the full solution from the latent space. Special attention is paid to handle the multidimensional outputs and network architecture.

General solutions of the Maxwell’s equations for a mechano-driven media system (MEs-f-MDMS)

Abstract For engineering electromagnetism, media/objects have shapes and sizes and may move with accelerations along complex trajectories in reference to the observers in the Laboratory frame. To describe the electromagnetic behavior of a system that is made of multiple moving objects, we have developed the Maxwell’s equations for a mechano-driven media system (MEs-f-MDMS) under low-speed approximation (v << c) [Advances in Physics: X, 9 (2024) 2354767]. Through extensive studies, the MEs-f-MDMS are required for describing the electrodynamics inside a moving object, while the classical Maxwell’s equations are to describe the electrodynamics in the region that is at stationary with respect to the Laboratory frame. The full solutions of the two regions satisfy the boundary conditions. The accelerated movement of a medium is a source for generating electromagnetic wave at its vicinity, but this component was missed in classical Maxwell’s equations. In this paper, we present the strategies for solving the MEs-f-MDMS for a generate case with considering the dispersion of the medium and the related constitutive relations both in time and frequency spaces. The theory is rather general and will serve as general guidance for numerical calculations toward practical applications.

Wrinkling of compressible magnetic soft plates

This paper establishes an analytical method for the wrinkling of compressible magnetic soft (MS) plates subject to an in-plane biaxial stretching and an out-of-plane magnetic induction field. The bifurcation analysis is performed with external Maxwell stress considered by combining the surface impedance matrix method and the Stroh formulation in terms of true magnetic field variables. We decouple the resulting bifurcation equations into antisymmetric and symmetric modes and provide the explicit expressions within a neo-Hookean ideal magnetoelastic model. Numerical examples show that the antisymmetric wrinkling usually occurs prior to the symmetric one, unless the permeability of the plates μ is much smaller than that of the surroundings μ′, i.e., the normalized permeability μ/μ′→0. This observation is consistent with the previous studies on incompressible case. However, for nearly incompressible plates with μ/μ′>1, the compressible constitutive relation may impose an additional deformation constraint that noticeably limits the occurrence and extent of wrinkling in the plates. One intriguing observation in particular is that the critical stretches for the thin-plate instability exhibit a nonmonotonic character as the compressibility of plate varies. Release of compressibility plays a positive role on stabilizing the MS plates when 0<μ/μ′<1, yet a negative role when μ/μ′>1. This phenomenon may be attributed to the coupling effect between the compressibility and the normalized permeability μ/μ′, suggesting a potential way to regulate wrinkling behaviors of MS materials by tuning the surrounding permeability. The present work may serve as benchmark solutions for understanding structural failures in various related functional MS-based devices.

Numerical Study on the Development of Adiabatic Shear Bands During High Strain-Rate Compression of AISI 1045 Steel: A Comparative Analysis Between Plane-Strain and Axisymmetric Problems.

This work studies numerically the development of adiabatic shear banding (ASB) during high strain-rate compression of AISI 1045 steel. Plane strain and cylindrical axisymmetric compressions are simulated in LS-DYNA, considering rectangular and cylindrical steel samples, respectively. Also, a parametric analysis in height-to-base ratio is conducted in order to evaluate the effect of geometry and dimensional ratio of the sample on ASB formation. Doubly structural-thermal-damage coupled finite element models are developed for the numerical simulations, implementing the thermo-viscoplastic Modified Johnson-Cook constitutive relation and damage criterion, while further damage-equivalent stress and strain fields are introduced for the damage coupling. The simulations revealed that plane strain compression promotes more ASB formation, providing lower critical strain for ASB initiation and wider and stronger ASBs compared with axisymmetric compression. Further, X-shaped ASBs initially form during plane strain compression, while as deformation increases, they transform into S-shaped ASBs in contrast to axisymmetric compression, where parabolic ASBs are developed. Also, a lower height-to-base ratio leads to greater ASB propensity, reducing critical strain in axisymmetric compression. Finally, thermal softening is found to precede damage softening and dominate the ASB genesis and its early evolution, while in contrast damage softening drives later ASB evolution and its transition to fracture.

A constitutive model based on energy density for power-law variable thickness plates and its application

Variable thickness plates are relatively common structure in large-scale transportation equipment such as aerospace and ships. Due to their high running speed and large structural dimensions, such structures are usually induced high-frequency severe vibrations, which likely lead to structural damage. Therefore, it is crucial to accurately predict the high-frequency dynamic response characteristics during the structural design phase. The energy finite element method (EFEM) is a powerful tool for predicting high-frequency dynamic response. But, in recent EFEM for variable thickness plates, an approximate method (AEFEM) using a large number of constant thickness plate elements to approximate variable thickness plates is used. Due to that AEFEM is based on the constitutive equation for constant thickness plate, it will be imprecise and time-consuming. Aiming at power-law variable thickness plates, the constitutive equation based on energy density is derived and the finite element discrete scheme of the constitutive equation was studied. In this way, the precise new EFEM (NEFEM) for variable thickness plates was established. In addition, the dynamic response of a variable thickness plate was predicted by NEFEM presented and finite element method (FEM) respectively. The results are consistent. It is shown that the constitutive model presented is reliable and time-saving. Comparison of the results from AEFEM, the NEFEM can get more accurate results with fewer elements. The NEFEM based on the constitutive model presented can be used to predict precisely the high-frequency dynamic response for power-law variable thickness plates.

Study on Impact Resistance of Alkali-Activated Slag Cementitious Material with Steel Fiber

Alkali-activated slag cementitious materials (AASCMs) use alkaline activators to activate blast furnace slag and waste slag to replace traditional Portland cement, which can reduce CO2 emissions. An impact resistance test and scanning electron microscopy (SEM) microscopic performance analysis of alkali-activated slag cementitious material specimens with four different steel-fiber contents are performed. The effects of steel-fiber volume content and strain rate on the dynamic elastic modulus Ed, dynamic compressive strength σd, dynamic peak compressive strain εc, and energy absorption of the AASCM-SS are studied. The results indicate that the dynamic elastic modulus Ed, dynamic compressive strength σd, and energy absorption of the AASCM-SS increase with the increase of strain rate, and the dynamic peak compressive strain εc decreases with the increase of strain rate. The dynamic elastic modulus Ed, dynamic compressive strength σd, and dynamic peak compressive strain εc of the SS-AASCM increase first and then decrease with the increase of steel-fiber content. When the steel-fiber content is 0.5%, the σd and εc of the AASCM-SS are the highest, increased by 9.9% and 19.3%. The energy absorption of AASCM-SS increases with the increase of steel-fiber content. A dynamic constitutive model of the FR-AASCM considering the influence of damage, strain rate, and steel-fiber volume fraction is established. The proposed constitutive model is in acceptable agreement with the experimental AASCM-SS dynamic stress–strain curve, and the correlation coefficient is 0.91.

Electro-magneto-elastic analysis of a sandwich composite beam as diving board in swimming with composed of graphene origami metamaterials

A novel composite structure composed of graphene origami reinforcement integrated with piezoelectric/piezomagnetic layers is defined in this paper. The Material composition is assumed as steel novel metamaterials. The proposed model can be used as a diving board in swimming. The vibrational-based formulation is extended using an advanced higher-order thickness-stretchable model. The governing motion equations are derived using Hamilton’s principle through the computation of strain and kinetic energies as well as external work. The constitutive relations are extended for the composite core in terms of volume fraction, folding degree, and thermal load using some modifier functions using Halpin-Tsai micromechanical models for modulus of elasticity, Poisson’s ratio, thermal expansion coefficient, and density. The natural frequency responses are derived using the analytical method in terms of characteristics of graphene origami such as thermal load, foldability parameter, and amount of reinforcement. Furthermore, an investigation on the impact of initial electro-magneto-mechanical loads is studied on the responses.

Interpretation of mechanical properties gradient in laser-welded joints: Experiments and grain morphology-dependent crystal plasticity modeling

The grain size and morphology of laser welds show a gradient distribution, leading to variations in mechanical properties. This study proposes a microscopic crystal plasticity constitutive (CPC) model to examine the effect of ER4047 welding wire on the mechanical properties of laser-welded aluminum alloy joints. A finite element model updating strategy was used to fully invert the morphological mechanical parameters, marking a significant advancement. This study combines mesoscale electron backscatter diffraction (EBSD) observations with macroscopic uniaxial tensile tests to obtain crystal plasticity finite element analysis and strain field data from digital image correlation. The mechanical property gradient of the welded joints was systematically analyzed from a crystal perspective. The CPC parameters were inverted for different grain sizes and morphologies. The study found that using ER4047 welding wire significantly enhanced the mechanical properties of the welded joints, especially in the welding zone. As grain size increased, the yield strength of the material decreased, while the hardening modulus increased. Additionally, the cast characteristics of columnar crystal morphology reduced both yield strength and hardening modulus.

A block-based numerical strategy for modeling the dynamic out-of-plane behavior of unreinforced brick masonry walls

AbstractIn this paper, a numerical procedure is proposed to simulate the dynamic out-of-plane response of unreinforced masonry (URM) walls. A state-of-the-art damaging block-based model, originally developed for quasi-static simulations, is extended for the first time in a dynamic regime. The blocks are represented using solid 3D finite elements governed by a plastic-damage constitutive law for both tension and compression. A cohesive-frictional contact-based formulation is used to account for interactions between the blocks. A simplified mechanical characterization is formulated to improve efficiency in wall-level analyses. Dynamic simulation is performed using a generalized HHT-$$\alpha$$ α direct integration implicit solver and by implementing Rayleigh damping in the bulk. Such consideration allows the use of both mass and stiffness proportional terms of the Rayleigh damping without compromising efficiency. The strategy is applied to simulate incremental dynamic experiments performed on full-scale walls, showing good agreement between numerical and experimental results. The calibrated numerical model is then optimized to reduce computational effort while maintaining accuracy. The optimized model is used to investigate the effect of relative support motion on the one-way bending out-of-plane seismic response of URM walls, demonstrating the potential of the modeling strategy to explore the effect of boundary conditions that occur in real buildings but are often overlooked in laboratory experiments. This investigation also explores the adequacy of simplifications in capturing the effect of relative support motion, which can be adopted for simple modeling strategies commonly used in standard engineering practice.

Research and Development of Laboratory Experiments on the Static Characteristics of Pile-Soil Contact Surfaces

This paper systematically investigates the mechanical properties of contact surfaces between soil and piles under static loading conditions across various scenarios through comprehensive laboratory experiments. The study offers an overview of current experimental equipment and testing protocols, succinctly describes the mechanical characteristics of pile-soil contact surfaces influenced by multiple factors, and summarizes existing constitutive models related to these interfaces. The objective of this research is to provide a more accurate and reliable laboratory methodology for analyzing the static mechanical properties of pile-soil contact surfaces, thereby fostering innovative advancements in the safety of pile foundations.