Linear Elastic Deformation Research Articles

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.

Study on the impact of the perforated floating breakwater on coastal bridge with box-girder superstructure under two-dimensional focused waves

The advantages of Floating Breakwater encompass its adaptability to varying water depths and tidal ranges, as well as its economic viability, mobility, and ease of installation. However, limited research has been conducted on the wave damping performance of floating breakwaters on the box-girder superstructure of coastal bridges during extreme wave conditions. In this study, a two-dimensional numerical model was established using the RANS equations and SST k-ω turbulence model in OpenFOAM. The breakwater was constrained by mooring forces, with linear elastic deformation, and underwent horizontal, vertical, and torsional movements under the action of ocean waves. The validity of the numerical model was confirmed by comparing it with existing numerical simulations and experimental data. The study examined influential factors, including the cross-sectional shape, submergence depth, and spacing of the floating breakwater, with a specific emphasis on the dimensions of the upper and lower openings for perforated breakwaters. Combined with attenuation rates and fluid-structure coupling analysis, the wave damping performance of the floating breakwater on the box-girder superstructure of coastal bridges under extreme wave conditions was evaluated. The research results demonstrate that the perforated floating breakwater, with Cs = 0.75, L = 10 m, and upper opening B1 = 0.1 B and lower opening B2 = 0.4 B, maximizes the wave damping performance on the box-girder superstructure of coastal bridges, which holds crucial significance for studying wave attenuation and disaster prevention on the box-girder superstructure of coastal bridges.

Fracture analysis in 2D plane strain problems for composite materials containing hard inclusions and voids using an extended consecutive-interpolation quadrilateral element

This paper investigates fracture mechanics in particle-reinforced composites by using the extended finite element method enhanced by the consecutive-interpolation quadrilateral element. These composite materials have discontinuous boundaries such as cracks, voids, holes, and soft inclusions. And the extended consecutive-interpolation quadrilateral element (XCQ4) is employed to model these boundaries in two-dimensional linear elastic deformation problems. XCQ4 combines the enrichment functions in the traditional extended finite element method with the consecutive interpolation on a 4-node quadrilateral element. This element uses both nodal values and averaged nodal gradients as interpolated conditions. In fracture analysis, the stress intensity factors (SIFs) are important parameters that must be defined. In this study, the values of SIFs at the crack tips are evaluated with the help of the interaction integrals approach. The obtained numerical results are compared with other reliable results showing high accuracy and convergence rate of the XCQ4 element.

Coupling of single-layer material point peridynamics and finite element method for analyzing the fracture behavior of composite laminates

In this paper a novel method, Single-Layer Material Point (SLMP) Peridynamics is proposed to simulate in-plane problems of composite laminates using a single layer of material points. Assuming that there is no relative displacement between the layers of laminates, the Single-Layer Material Point Peridynamics doesn’t need to create multi-layer material points. To further improve the calculation efficiency, a coupling model of single-layer material point Peridynamics and finite element method (FEM) is then developed to simulate the damage initiation and evolution of the composite laminates. Linear elastic deformation problems are studied with the SLMP Peridynamic model and the coupling model respectively, and the results are compared with those of FEM. Damage initiation and evolution problems are also analyzed by the coupling model and the results are compared with those of experiments. It is demonstrated that the presented method is of high accuracy.

Strength and microstructure characteristics of red-bed weathered residual soil stabilized by Titanium Gypsum-Cement

Due to its unfavorable engineering characteristics, the red-bed weathered residual soil (RBRS) frequently necessitates remedial measures to conform to design specifications. Solidification with the aid of binders stands out as a prevalent technique employed to enhance the engineering attributes of RBRS. This study investigates the characteristics of RBRS stabilized with Titanium Gypsum-Cement (TGC) by conducting unconfined compressive strength tests on solidified soil with varying contents and curing times. Additionally, SEM and MIP tests were conducted to analyze the internal structure change, reaction mechanism, and hydration characteristics of the TGC-stabilized soil. The experimental findings revealed that the stress-strain response of specimens with varying proportions and curing times exhibited four distinct phases, namely the compaction stage, linear elastic deformation stage, pre-peak failure stage, and post-peak stage. Increasing cement content led to greater ductility in the stress-strain curve, while a higher ratio of TG to cement in the admixture resulted in a milder trajectory with a gradual decline in unconfined compressive strength. The stabilized soil with TGC ratio 6:4 (10%) and 9:6 (15%) met the compressive strength requirement at curing times of 7, 14, and 28 days. Microscopic investigations revealed the formation of hydration products, including CSH, with the incorporation of TGC. The resulting three-dimensional network effectively enveloped soil particles, enhancing inter-particle bonding and permeating mesopores and macropores, leading to soil structure compaction.

Anti-Hertz bulging of actuated liquid crystal elastomers

We consider the ‘anti-Hertz’ elastic problem of inverse indentation, which happens when the surface of an elastic material is pressed down with a plate with a round hole to form a bulge. This classical problem takes on a new life when a polydomain nematic liquid crystal elastomer is used. In this case, the nematic director aligns with the leading principal direction of local stress distribution created by bulging. When the deformed material is crosslinked a second time, this alignment pattern and the resulting permanent protrusion are preserved as pressure is removed, creating a bulge that can be reversibly actuated from a flat surface upon cooling. Experimentally, we also observe a dimple ring around the bulge and a punt (indentation) underneath it at the bottom. Theoretically, we model the deformation by coupling linear elastic and anelastic deformations using non-monotonic nematic elasticity and the singular stress-order relation of the polydomain-monodomain transition. The theory is in excellent agreement with the experiments, and predicts the emergence of all observed features.

Study on the Characteristics of Granite in Different Stress Stages through a Cyclic Loading Experiment

The deformation and failure process of rocks is a gradual process. The purpose of this study was to examine the characteristics of rocks in different stages through a cyclic loading experiment. The experiment was carried out based on the MTS815 rock mechanics test system combined with acoustic emission monitoring equipment to study the typical characteristics of two kinds of granite in the stages of crack closure, linear elastic deformation, crack initiation and stable crack growth, along with crack damage and unstable crack growth. The results showed that there were significant differences in the characteristics of the strain response, energy evolution, and acoustic emission of the two granites in the different stages. Although the microstructure and mineral elements of the two granites are different, the characteristics of the two granites in the same stage were similar, indicating that the stage characteristics of brittle rocks in the failure process may be widespread and have significant similarities.

Bending of Plates with Complex Shape Made from Materials that Differently Resist to Tension and Compression

A new numerical-analytical method for solving physically nonlinear bending problems of thin plates with complex shape made from materials that differently resist to tension and compression is developed. The uninterrupted parameter continuation method is used to formulate and linearize the problem of physically nonlinear bending. For the linearized problem, a functional in the Lagrange form, given on the kinematically possible displacement rates, is constructed. The main unknown problems (displacements, strains, stresses) were found from the solution of the initial problem, which was solved by the Runge-Kutta-Merson method with automatic step selection, by the parameter related to the load. The initial conditions are found from the solution of the problem of linear elastic deformation. The right-hand sides of the differential equations at fixed values of the load parameter corresponding to the Runge-Kutta-Merson scheme are found from the solution of the variational problem for the functional in the Lagrange form. Variational problems are solved using the Ritz method in combination with the R-function method, which allows to submit an approximate solution in the form of a formula – a solution structure that exactly satisfies the boundary conditions and is invariant with respect to the shape of the domain where the approximate solution is sought. The test problem for the nonlinear elastic bending of a square hinged plate is solved. Satisfactory agreement with the three-dimensional solution is obtained. The bending problem of the plate of complex shape with combined fixation conditions is solved. The influence of the geometric shape and fixation conditions on the stress-strain state is studied. It is shown that failure to take into account the different behavior of the material under tensile and compression can lead to significant errors in the calculations of the stress-strain state parameters.

Study on the Bending Behaviors of a Novel Flexible Re-Entrant Honeycomb

Abstract In order to further improve the bending performance of the traditional re-entrant (RE) honeycomb, a novel auxetic honeycomb architecture, called RE-L honeycomb, was proposed by adding an additional link-wall structure to the RE cell. The bending behaviors of the novel RE-L honeycomb, including the properties under linear elastic deformation and the bending behaviors under large deformation, were comprehensively investigated by the analytical, numerical, and experimental models. Results show that the proposed RE-L honeycomb significantly improves the bending compliance in the x-direction due to the highly flexible performance of the additional structure, where the bending rigidity and the maximum bending force are only 23% and 29.4% of those of the RE honeycomb, respectively. Besides, the additional structure obviously improves the designability and orthotropic properties of the original auxetic honeycomb. In conclusion, the proposed RE-L shows improved bending performance, which deserves more attention in future research and related applications.

A methodology for control and design of required ground reinforcement measures regarding train-induced ground vibrations

A user-friendly methodology for efficient non-linear numerical calculations of train-induced ground vibrations in railway embankments has been developed. This was achieved by creating an input file for setting up the problem and a shell program that reads the input file, set-ups, and runs the model of the problem on commercial numerical software, and also extracts the results from the calculations to an output file. Through this, the calculations can be automated and thus become easy to use. In addition, much effort has been put into optimizing the calculations for the computational time while maintaining sufficient accuracy. A key part of the developed methodology is that it includes an efficient way to consider that the soil properties are shear strain dependent. This was achieved using the so-called equivalent linear method and by superposition of the calculated shear strain adjusted linear elastic deformations for a single moving load. The developed methodology has, with good agreement, been verified against a case history with vibrations measurements both before and after ground reinforcement measures consisting of lime-cement columns. The presented methodology, called base-model methodology, can identify the risk for large ground vibrations for planned new and existing railway embankments and design required ground reinforcement measures based on permissible vibration requirements.

Modeling material length-scale effect using the second-order peridynamic material correspondence model

In this paper, a study on modeling material length-scale effect using peridynamics via the second-order material correspondence formulation is presented. Connections of the second-order model with all three types of Mindlin first gradient theory are established. An implicit solution scheme based on the automatic differentiation technique for the construction of the stiffness matrix for linear elastic problems is developed. Numerical examples are used to examine the material stability of the model and verify its capability in modeling material length-scale effect for different length-scale parameters. From the wave dispersion analysis, it is found that the second-order model is stable as long as the material has nonzero length-scale parameter. In the linear elastic deformation study, great agreements between the model predictions and the analytical solutions for nonzero length-scale parameters are observed.

Deformation diagrams of amorphous polyimide (kapton H) in the state of moderate and deep cooling: Experiment and theory

A comprehensive experimental and theoretical study of the regularities of active deformation at a constant rate of an amorphous polymer at room temperature and the influence of moderate and deep cooling on them was performed. The samples of amorphous aromatic polyimide (an analogue of kapton H) that are randomly cut fragments of the industrially produced thermoplastic film with a thickness of 25 μm were the object of the experimental study. The σ–ε diagrams of the tensile test, where σ and ε=ε˙t are the tensile stress and the relative strain, respectively, were recorded for 32 samples at three rates ε˙ = 7⋅10–5, 7⋅10–4, 6⋅10–3 s–1 under three temperatures T = 293, 77, and 4.2 K. In the state of deep cooling at T = 4.2 K, several samples were deformed as brittle glassy bodies – rupture after short elastic deformation. But the majority of the samples at all values of the experimental parameters (T,ε˙) had the rheological properties of rubber-like highly elastic materials (elastomers) with traditional tensile test diagrams: initial stage I of linear elastic deformation σI=Meε with Young’s modulus Me=Me(T); stage III of linear highly elastic deformation σIII=σfe+Mheε with modulus Mhe=Mhe(T) and conditional limit of elasticity σfe=σfe(T,ε˙); intermediate stage II of the relaxation type σII(ε;T,ε˙) with a nonlinear stress-strain dependence. The σ–ɛ diagrams of the individual samples with sufficiently high accuracy coincide with the graph of the function σ(ε;T,ε˙) which is the solution of the previously derived nonlinear rheological equation (V. D. Natsik and H. V. Rusakova, Fiz. Nizk. Temp.48, 281 (2022) [Low Temp. Phys.48, 253 (2022)]; Fiz. Nyzk. Temp.49, 246 (2023) [Low Temp. Phys.49, 228 (2023)]). In its derivation, a molecular-kinetic model was used: an amorphous polymer is considered as a set of statistically independent kinetic units, namely, molecular segments, and the elementary act of deformation is caused by thermomechanical activation of nonlinear excitations of these segments called elastons. The elaston mechanism of transformation of the deformation diagrams of amorphous polyimide samples under their moderate and deep cooling is discussed in detail: the transition between deformation states of warm and frozen elastomer, low-temperature effects of structural-deformation glass transition and deformation melting. Comparing the results of experiments and theory made it possible to obtain the empirical estimates for the macromechanical characteristics of the studied samples and the microparameters of elaston excitations. A significant and unsystematic (random) scatter of the macro- and micromechanical characteristics of the samples was revealed, which indicates a significant and random heterogeneity of the macro- and microstructure of the polyimide film from which they were made.

Deep-learning-based 3D fault detection for carbon capture and storage

Fault analysis plays an important role in determining the location of potential CO2 storage sites in which long-term storage feasibility is critical. The presence of faults and fracture zones can potentially lead to the gradual migration of CO2 from the storage reservoir to the atmosphere through the overburden strata. Traditional methods such as manual picking of faults are time-consuming and labor-intensive tasks, which can be costly for the CO2 storage site assessment process. To help address this concern, we develop a process for automating fault picking using deep neural networks. We implement two different deep neural networks based on the architectures of UNet and Deeplab v3+. We train the networks using synthetic data and labels and augment them using linear transformations and elastic deformations. We implement an ensemble-based approach to improve the generalization ability of our method. We also incorporate uncertainty estimation into the framework to aid in the risk management aspect of the decision-making process. We use data sets from different regions across the globe which help us to improve the methodology, with the ultimate aim to help 3D fault detection in the Smeaheia Field, a potential site for CO2 storage scale-up on the Horda Platform, offshore Norway.

Damage Evolution and Constitutive Model of Marble under Dynamic Loading

Through the application of SHPB (split Hopkinson pressure bar) test, the failure mode and dynamic stress-strain curves of marble samples were obtained. The dynamic constitutive model of marble was established with the fracture mechanical parameters (brittleness index), and the calculated curves were compared with the experimental curves. The evolution characteristic of damage variable D was analyzed. The results show that there are three main stages of marble deformation under dynamic impact load, which are linear elastic deformation stage, crack growth stage, and macroscopic failure stage. The sample shows obvious brittleness in the macroscopic failure stage. It is found that with the increase of strain rate, the degree of damage is getting worse. The stress-strain curves obtained based on the constitutive model are in good agreement with the experimental curves. The damage variable D can theoretically explain the evolution law of macroscopic failure of the sample. To some extent, there is a mechanism inside the rock to regulate the damage development of the rock, and the final failure degree of rock sample depends on △ σ BC and ε b .

An orthotropic peridynamic shell model for linear elastic deformation and crack propagation

Peridynamics is a non-local mechanics theory that can handle discontinuities such as cracks. This study presents an orthotropic peridynamic (PD) shell model based on the micro-beam bond. Under the homogenization assumption, eight PD material parameters expressed by four independent material constants are used to describe the axial, bending, and torsional deformations of the micro-beam bond. The eight PD material parameters can be derived by the rule of equating the strain energy density (SED) of the PD shell model and that of the classical continuum mechanics (CCM) shell model. To improve the computational efficiency and solve the surface effects of PD models, the morphing method is used to establish the PD-CCM shell coupling model. Several numerical examples of crack propagation in orthotropic materials are executed, and the results demonstrate the effectiveness of the proposed model.

Interfacial Nanoblisters Formed in Water Serving as Freestanding Platforms for Measuring Elastic Moduli of Polymeric Nanofilms.

Polymeric nanofilms have been widely utilized in diverse cutting-edge technologies, yet accurately determining their elastic moduli remains challenging. Here we demonstrate that interfacial nanoblisters, which are produced by simply immersing substrate-supported nanofilms in water, represent natural platforms for assessing the mechanical properties of polymeric nanofilms using the sophisticated nanoindentation method. Nevertheless, high-resolution, quantitative force spectroscopy studies reveal that the indentation test must be performed on an effective freestanding region around the nanoblister apex and meanwhile under an appropriate loading force, to obtain load-independent, linear elastic deformations. The nanoblister stiffness increases with either decreasing its size or increasing its covering film thickness, and such size effects can be adequately rationalized by an energy-based theoretical model. The proposed model also enables an exceptional determination of the film elastic modulus. Given that interfacial blistering is a frequently occurring phenomenon for polymeric nanofilms, we envision that the presented methodology would stimulate broad applications in relevant fields.

Stability Evaluation of Sliding-Type Perilous Rock in Huangzangsi Hydrojunction Project Based on Natural Vibration Frequency

The instability of perilous rock is mostly manifested as sudden collapse and failure without obvious displacement characteristics. Therefore, it is difficult to achieve the purpose of monitoring and early warning by conventional displacement monitoring. But the existing stability monitoring indicators are mostly deformation, stress, and strain. There is a problem that the stability evaluation parameters are inconsistent with the monitoring parameters. Taking sliding-type perilous rock as the research object, the structural plane is assumed to be homogeneous and isotropic, and linear elastic deformation in the amplitude range. Based on the dynamic theory and limit equilibrium model, the quantitative relationship model can be established involving safety factors, natural vibration frequency, structural surface bonding area, elastic modulus, and mass. The remote laser vibrometer is used to monitor the natural vibration frequency of the sliding-type perilous rock on the slope of the Huangzangsi Hydrojunction, and the stability evaluation of the perilous rock is achieved based on the quantitative relationship model between the safety factor and the natural vibration frequency. In this way, the frequency of slipping perilous rock stability evaluation and safety factor can be monitored. The results are basically the same with the safety factor calculated by the limit equilibrium method, indicating that the method is correct and feasible. The research has high theoretical significance and practical value for the safety monitoring and advanced warning of sliding perilous rock.

Review and Stress Analysis on the Lithiation Onset of Amorphous Silicon Films

This work aims to review and understand the behavior of the electrochemical lithiation onset of amorphous silicon (a-Si) films as electrochemically active material for new generation lithium-ion batteries. The article includes (i) a review on the lithiation onset of silicon films and (ii) a mechanochemical model with numerical results on the depth-resolved mechanical stress during the lithiation onset of silicon films. Recent experimental studies have revealed that the electrochemical lithiation onset of a-Si films involves the formation of a Li-poor phase (Li0.3Si alloy) and the propagation of a reaction front in the films. The literature review performed reveals peculiarities in the lithiation onset of a-Si films, such as (i) the build-up of the highest mechanical stress (up to 1.2 GPa) during lithiation, (ii) a linear increase in the mechanical stress with lithiation which mimics the characteristics of linear elastic deformation, (iii) only a minute volume increase during Li incorporation, which is lower than expected from the number of Li ions entering the silicon electrode, (iv) the largest heat generation appearing during cycling with only a minor degree of parasitic heat contribution, and (v) an unexpected enhanced brittleness. The literature review points to the important role of mechanical stresses in the formation of the Li-poor phase and the propagation of the reaction front. Consequently, a mechanochemical model consisting of two stages for the lithiation onset of a-Si film is developed. The numerical results calculated from the mechanochemical model are in good accord with the corresponding experimental data for the variations in the volumetric change with state of charge and for the moving speed of the reaction front for the lithiation of an a-Si film of 230 nm thickness under a total C-rate of C/18. An increase in the total C-rate increases the moving speed of the reaction front, and a Li-rich phase is likely formed prior to the end of the growth of the Li-poor phase at a high total C-rate. The stress-induced phase formation of the Li-poor phase likely occurs during the lithiation onset of silicon electrodes in lithium-ion battery.

Using penalty function method in identification stiffness of elastic spring of the underground structure

This paper studies a method to identify the spring stiffness of the frame - soil structure. The model of the problem is a two-dimensional structure, linear elastic deformation, model of soil using the Winkler model (with normal, tangential spring). The problem will be solved by the penalty function method - the minimum of the objective function - combined with the finite element method. The numerical calculations show that the model, algorithm and calculation program are reliable. The program can be used to identify the spring stiffness of the frame - soil structure in two dimensions, serving to determine the actual working state of the structure, to propose solutions for reinforcement, repairing, improving bearing capacity, prolonging the life of the structure.

Using penalty method in identification of elastic fixed stiffness of frame structure

This paper studies a method to identify the elastic fixed stiffness of the frame structure. The model of the problem is three dimensional structure, linear elastic deformation, pile - soil link is replaced by elastic fixed with stiffness. The problem will be solve by the penalty function method - the minimum of the objective function (which is the total squared error between the measured value and the calculated values particular) - combined with the finite element method. The numerical calculations show that the model, algorithm and calculation program are reliable. The program can be used to identify the elastic fixed stiffness of the frame structure in three dimension, serving to determine the actual working state of the structure, to propose solutions for reinforcement, repairing, improving bearing capacity, prolonging the life of the structure.