Elastic Material Behavior Research Articles

Bending failure analysis and modeling of thin fiber reinforced shells

In this work, the impact of high stress gradients, found in bending of thin unidirectional fiber reinforced shells (~0.1 to 1 mm), on compressive micro-buckling failure, was analyzed. Such thin shells show increased resistance to compressive failure under high curvatures, which may even allow tensile fiber damage to drive ultimate failure for very low thickness (e.g. <0.5 mm). The main scope of this work is to analyze this increased resistance to compressive failure and propose a robust modeling scheme. The mechanical failure response was captured by a shell-buckling experimental campaign. The origins of the increased compressive failure resistance were initially attributed to the reduction of shear stresses acting on the most susceptible domain of a representative wavy fiber. This effect was effectively described by an analytically derived, stress-gradient-dependent parameter. The hypothesis for the establishment of this parameter was corroborated by a numerical micromechanical model adopting the embedded cell approach. This model also revealed important micromechanical interactions which were incorporated by simple stress and strain factors. The derived failure prediction scheme was further extended to include the non-negligible, non-linear elastic material behavior of carbon fibers by means of a numerical algorithm. The validity of the failure prediction model was demonstrated by the successful comparison with results acquired from the shell-buckling experiments on a unidirectional carbon-fiber reinforced epoxy system. To this end, the validity of the initial hypothesis of stress-gradient-dependence on compressive failure was corroborated. Major effect on the overall behavior modeling has carbon fiber's material non-linearity, as well as micromechanical interactions.

A modified bond model for describing isotropic linear elastic material behaviour with the discrete element method

Recently, the discrete element method is increasingly being used for describing the behaviour of isotropic linear elastic materials. However, the common bond models employed to describe the interaction between particles restrict the range of Poisson’s ratio that can be represented. In this paper, to overcome the restriction, a modified bond model that includes the coupling of shear strain energy of neighbouring bonds is proposed. The coupling is described by a multi-bond term that enables the model to distinguish between shear deformations and rigid-body rotations. The positive definiteness of the strain energy function of the modified bond model is verified. To validate the model, uniaxial tension, pure shear and pure bending tests are performed. Comparison of the particle displacements with continuum mechanics solution demonstrates the ability of the model to describe the behaviour of isotropic linear elastic material for values of Poisson’s ratio in the range 0 le nu < 0.5.

Anisotropic and age-dependent elastic material behavior of the human costal cartilage

Compared to articular cartilage, the biomechanical properties of costal cartilage have not yet been extensively explored. The research presented addresses this problem by studying for the first time the anisotropic elastic behavior of human costal cartilage. Samples were taken from 12 male and female cadavers and unconfined compression and indentation tests were performed in mediolateral and dorsoventral direction to determine Young’s Moduli EC for compression and Ei5%, Ei10% and Eimax at 5%, 10% and maximum strain for indentation. Furthermore, the crack direction of the unconfined compression samples was determined and histological samples of the cartilage tissue were examined with the picrosirius-polarization staining method. The tests revealed mean Young’s Moduli of EC = 32.9 ± 17.9 MPa (N = 10), Ei5% = 11.1 ± 5.6 MPa (N = 12), Ei10% = 13.3 ± 6.3 MPa (N = 12) and Eimax = 14.6 ± 6.6 MPa (N = 12). We found that the Young’s Moduli in the indentation test are clearly anisotropic with significant higher results in the mediolateral direction (all P = 0.002). In addition, a dependence of the crack direction of the compressed specimens on the load orientation was observed. Those findings were supported by the orientation of the structure of the collagen fibers determined in the histological examination. Also, a significant age-related elastic behavior of human costal cartilage could be shown with the unconfined compression test (P = 0.009) and the indentation test (P = 0.004), but no sex effect could be detected. Those results are helpful in the field of autologous grafts for rhinoplastic surgery and for the refinement of material parameters in Finite Element models e.g., for accident analyses with traumatic impact on the thorax.

Non-local criteria for the borehole problem: Gradient Elasticity versus Finite Fracture Mechanics

Two nonlocal approaches are applied to the borehole geometry, herein simply modelled as a circular hole in an infinite elastic medium, subjected to remote biaxial loading and/or internal pressure. The former approach lies within the framework of Gradient Elasticity (GE). Its characteristic is nonlocal in the elastic material behaviour and local in the failure criterion, hence simply related to the stress concentration factor. The latter approach is the Finite Fracture Mechanics (FFM), a well-consolidated model within the framework of brittle fracture. Its characteristic is local in the elastic material behaviour and non-local in the fracture criterion, since crack onset occurs when two (stress and energy) conditions in front of the stress concentration point are simultaneously met. Although the two approaches have a completely different origin, they present some similarities, both involving a characteristic length. Notably, they lead to almost identical critical load predictions as far as the two internal lengths are properly related. A comparison with experimental data available in the literature is also provided.

A Finite Element Method to Predict the Mechanical Behavior of a Pre-Structured Material Manufactured by Fused Filament Fabrication in 3D Printing

In this paper, a numerical method is proposed to simulate the mechanical behavior of a new polymeric pre-structured material manufactured by fused filament fabrication (FFF), where the filaments are oriented along the principal stress directions. The model implements optimized filament orientations, obtained from the G code by assigning materials references in mesh elements. The Gauss points are later configured with the physical behavior while considering a homogeneous solid structure. The objective of this study is to identify the elastoplastic behavior. Therefore, tensile tests were conducted with different filament orientations. The results show that using appropriate material constants is efficient in describing the built anisotropy and incorporating the air gap volume fraction. The suggested method is proved very efficient in implementing multiplex G code orientations. The elastic behavior of the pre-structured material is quasi-isotropic. However, the anisotropy was observed at the yield point and the ultimate stress. Using the Hill criterion coupled with an experimental tabular law of the plastic flow turns out to be suitable for predicting the response of various specimens.

Biaxial Loading Effects on Strain Energy Release Rate and Crack-Tip Strain Field in Elastic Hydrogels

We characterized the strain energy release rate and local crack-tip strain field for elastic hydrogels under several types of biaxial loading: planar, unequal biaxial, and equibiaxial extensions. The strain energy release rate (G) in each type of biaxial strain is characterized via two different approaches. One evaluates G from the change in strain energy with respect to the notch length (Xc) using single-edge notched specimens with various Xc values. The other estimates G from the difference in strain energy density between the two regions far behind and ahead of the crack tip. The excellent agreement between the G values obtained by the two methods demonstrated their reliability. We also revealed the features of the local crack-tip strain field in biaxial loading, including crack-tip opening displacement, strain field area, strain magnitude resulting from crack opening, and strain singularity exponent for strain growth near the crack tip. Importantly, these properties are governed exclusively by G, independent of the biaxial loading type. The results provide an important basis for a comprehensive understanding of the fracture behavior of elastic soft materials under complicated deformations.

Finite element formulations for constrained spatial nonlinear beam theories

A new director-based finite element formulation for geometrically exact beams is proposed by weak enforcement of the orthonormality constraints of the directors. In addition to an improved numerical performance, this formulation enables the development of two more beam theories by adding further constraints. Thus, the paper presents a complete intrinsic spatial nonlinear theory of three kinematically different beams which can undergo large displacements and which can have precurved reference configurations. Moreover, the hyperelastic constitutive laws allow for elastic finite strain material behavior of the beams. Furthermore, the numerical discretization using concepts of isogeometric analysis is highlighted in all clarity. Finally, all presented models are numerically validated using exclusive analytical solutions, existing finite element formulations, and a complex dynamical real-world example.

Design of Initial Shotcrete Lining for a Mine Shaft Using Two-Dimensional Finite Element Models Considering Excavation Advance Rate

Shotcrete is widely used as a temporary support element in the construction of underground mine excavations, tunnels, and shafts. It is sprayed on the excavation walls to provide safe working conditions for mine personnel and equipment until the permanent support is installed. Therefore, the ability of the shotcrete liner to resists falls of ground is of paramount importance. In this paper, a two-dimensional finite element program is used to simulate a three-dimensional excavation advance and a shotcrete liner that is used as temporary support in a mine shaft. The mechanical properties of the shotcrete are determined based on existing empirical equations by considering the shaft advance rate. The study uses three methods to analyze the stability of the initial shotcrete liner. The first method pertains to the calculation of the load factor of safety based on the convergence confinement method. In the second method, the shotcrete liner is simulated using a structural element with elastic properties, and its stability is analyzed using support capacity diagrams. In the third method, a material model is used to explicitly simulate the shotcrete liner with elastic perfectly-plastic material behavior. This method allows for capturing the progressive yielding of the shotcrete liner during the excavation advance. The results of numerical simulations are then used to calculate a strain factor of safety for the shotcrete liner by dividing the lateral strain capacity of the shotcrete by the radial strain of the liner due to the shaft convergence. The study infers that the strain factor of safety for the 100 mm shotcrete liner is greater than unity although its load factor of safety is less than unity. Therefore, it is concluded that the 100 mm shotcrete liner can be used as temporary support until the installation of the final concrete liner.

Eliminating plasticity effects in the measurement of residual stress by using the hole-drilling method

Abstract When the hole-drilling method is used to measure residual stress, plasticity effects occur if the residual stress exceeds 60 % of the yield stress. Plasticity effects result in an overestimation of the residual stress as the hole-drilling method is based on the linear elastic behavior of materials. To overcome this problem, a simplified iterative method based on an existing iterative method and using the optimizer tools of the ANSYS program is proposed in this paper. The proposed method is verified through numerical and experimental studies. The numerical case study reveals that, for the case studied, the proposed method can achieve the same accuracy as the original iterative method and has a higher convergence ability. The experimental study demonstrates that the values of the maximum principal stress calculated using the American Society of Testing Materials standard is generally greater than the true values and that the error magnitude increases with an increase in stress levels. Using the proposed method, errors are reduced for the maximum principal stress while increasing slightly for the minimum principal stress. The proposed method has a high convergence ability; for the case studied, only two or three iterations are needed to achieve acceptable accuracy.

A transversely hyperelastic constitutive model of flexible film composite

This paper presents a transversely hyperelastic constitutive model for predicting mechanical properties of flexible composites under unidirectional tension. A strain energy function which reflects the behavior of anisotropic elastic material is decomposed into three parts: matrix, fiber and fiber-matrix interaction. The fiber-matrix interaction was decomposed into in-plane shear stresses and out-of-plane shear stress, the in-plane shear stresses were related to the fiber elongation invariants, and the out-of-plane shear stress was related to the fiber elongation invariants and the matrix invariants. The fiber-matrix interaction considering shear factor was established. Based on fiber reinforced continuum mechanics, a transverse hyperelastic constitutive model including fiber, matrix and their interaction is developed. The transversely hyperelastic constitutive model is verified by the uniaxial tension tests. The constitutive model can be used to design the flexible structure of stratospheric airship.

Quasi-Linear Viscoelastic Characterization of Soft Tissue-Mimicking Materials.

We present a novel method based on the quasi-linear viscoelastic (QLV) theory to describe the time-dependent behavior of soft materials. Unlike previous methods for deriving QLV parameters, we characterize the elastic and viscous behavior of materials separately by using two different sets of experiments. To model the nonlinear elastic behavior, we fit the elastic stress response with a one-term Ogden model. Then, we model the relaxation behavior with a Prony series to compare the stress relaxation of the material at different timescales. This new method allows us to characterize materials with narrow confidence intervals (high accuracy), independently from the loading conditions. We validate our model using samples made of phantom materials that mimic normal and cancerous prostate tissues in terms of Young's modulus. Our model is shown to distinguish materials with similar elastic (viscous) properties but different viscous (elastic) properties. Drawing a precise distinction between the phantoms, this method could be useful for prostate cancer (PCa) diagnosis; but significant clinical studies will be needed in the future.

Подходы к уточнению расчетных моделей для оценки напряженно-деформированного состояния конструкции на основе анализа данных систем мониторинга

Object and purpose of research. This paper discusses numerical simulation possibilities in terms of stress-strain monitoring for marine engineering structures. This approach can simulate the behavior of strain gauges for both elastic and plastic material behavior. Materials and methods. FEM-based simulation of strain gauge operation process taking into account geometric and physical non-linearity. Main results. Development of refined FE models for sensor installation area of stress-strain monitoring system. Numerical simulation of uniaxial and triaxial strain gauge operation. Time histories of strain gauge readings for linear and non-linear behavior of material. Sensitivity analysis of strain gauges in terms of various strain types. Update of strain gauge arrangement for the best description of structural strains. Conclusion. These results demonstrate and confirm a strong potential of numerical models in development of stress-strain monitoring systems for engineering structures. Simulating strain gauge operation, these models make it possible to determine global strained state of given structure as per strain gauging data for some of its areas.

Excavation of artificial caverns inside asteroids by leveraging rotational self-energy

Future space ventures will likely require exploitation of near-Earth asteroid resources. Moreover, it can be envisaged that asteroids may host habitats in their interiors. In fact, a cavern inside an asteroid would be a natural radiation shield against cosmic radiation and may also serve as a confined environment for storage of mined material such as water ice or other processed volatiles such as propellants. To this end, this paper proposes to leverage the asteroid rotational self-energy to remove material from the asteroid interiors and create a spherical cavern, by means of the orbital siphon concept. The siphon is a chain of tether-connected payload masses (the asteroid material), which exploits the rotation of the asteroid for the delivery of mass from the asteroid to escape. Under certain conditions the siphon can be initiated to ensure self-sustained flow of mass from the asteroid to escape. A net orbital siphon effect is generated by connecting new payloads at the bottom of the chain while releasing the upper payloads. Key parameters are discussed, such as the required siphon dimension and the maximum size of the internal cavity that can be excavated, as a function of the asteroid rotational period. Moreover, assuming elastic material behaviour, a closed-form expression for the stress tensor is found and a failure criterion is used to identify regions in the asteroid interiors subjected to the larger stresses. It is shown that the conditions for failure are relaxed as the radius of the internal void increases.

Effect of cell structure on the uniaxial compression properties of closed-cell foam materials

In this study, the effect of cell structure on the uniaxial elastic and plastic properties of closed-cell foam materials are investigated numerically. 76 closed-cell foam models with different cell size distributions and cell shapes are established in this study. And two structural parameters defined in our previous studies are used to characterize the morphological features of foam models. Then, the uniaxial compression simulations are proposed in this study to simulate the elastic and plastic behavior of closed-cell foam materials at the beginning loading stage. The results indicate that the relative Young’s modulus and relative yield strength decrease with the increasing characteristic diameter Dch and characteristic shape anisotropy αch. Finally, the stress and strain distributions obtained from numerical simulations are analyzed to explain why the foams with regular cell structures are inclined to have a better performance in load-bearing.

Structure-property relationship of a nickel-based honeycomb sealing composite

Since brittle intermetallic compounds can form during soldering of nickel-based alloys, the microhardness in the area of the solder material is increased. This can be observed when joining thin-walled honeycomb structures. They are used as stationary component in sealing systems of gas turbine engines. Both the increase in the microhardness and the volume fraction of the solder material are assumed to threaten the integrity of the rotating sealing component if contact (rubbing) between the two components occurs during engine operation. To predict the impact of the solder material on the structure-property relationship of the nickel-based honeycomb structure, a micromechanical modelling approach is presented in this work. The three-dimensional micromechanical modelling approach comprises a composite of two distinct materials, the cell-wall and the solder material. The constitutive behaviour of the ductile cell-wall material is modelled with a crystal plasticity approach. A purely elastic material behaviour is assumed for the brittle solder material. For an efficient simulation, the investigated domain is restricted to the unit cell of the honeycomb composite. The studies show that with increasing volume fraction of the solder material, both thermal and mechanical loads of the honeycomb composite increase significantly, raising the likelihood of damage to the material of the rotating sealing component.

Relaxation effects on thermoelastic interactions for time-dependent moving heat source under a recent model of thermoelasticity

In the present article, we investigate the thermal and elastic behaviour of an infinite thermoelastic material with a cylindrical cavity caused by a time-dependent moving heat source. The cavity surface is assumed to be subjected to a thermal shock. The formulation of the problem is applied for the recently proposed generalized thermoelastic model [Modified Green–Lindsay (MGL)] that takes into account the strain and temperature rates in the constitutive relations. We derive the governing equations in the present context along with the other two models, namely Lord–Shulman model and Green–Lindsay, by unifying governing equations under all these three models. The solutions are obtained for all three models in the Laplace transform domain, which are represented by unified expressions. The numerical computations for temperature, displacement and thermal stresses are carried out and depicted graphically. A detailed comparison is made amongst the results predicted by three models to highlight the effects of velocity of heat source and strain, temperature rate terms involved in the MGL model.

Poisson's ratio bounds in orthotropic materials. Application to natural composites: wood, bamboo and Arundo donax

The paper discusses the restrictions the positive definite character of the strain energy imposes to the values of the Poisson's ratios in a linear elastic orthotropic constitutive law. By exploiting the reciprocity principle and the conservation of energy, non-trivial constraints arise, leading to a particularly expressive form of the domain of existence, named Tetrahedron-Ellipsoid locus, in the space of three independent Poisson's ratios.The presented analysis establishes several notable restrictions for the elastic behavior of orthotropic composite materials, in all the cases in which there are great differences in the Young's moduli. For instance, near the edge of this locus, some Poisson ratios may belong to an interval not including the zero value; a very interesting peculiarity, perhaps not yet figured out in literature. In order to assess the coerciveness of the formulation, the results are applied to common wood essences, to several Italian growing species of bamboo and Arundo donax, natural composite functionally graded orthotropic materials. In the latter cases, an extensive experimental investigation is carried out to detect several Poisson's ratios, not studied in literature. Poisson ratios are obtained directly by strains measured by means of both physical strain gauges and Digital Image Correlation (DIC).

Numerical study of visco-hyperelastic damper with high axial damping rubber subjected to harmonic loading

Structural control prevents structural damage and provides the desirable performance level through the ductility of components and using passive energy dissipation systems. In this paper, the performance of a recently introduced passive control device called Visco-Hyperelastic Damper (VHD) is investigated by ABAQUS FEM software. This device has the properties of both velocity-dependent and displacement-dependent dampers and provides additional energy dissipation for structures. This device consists of a viscoelastic material sandwiched between two metal rings dissipating energy through a combination of the elastic behavior of the viscoelastic material and the plastic deformation of the steel parts. In order to validate the numerical model, after separately testing the steel and rubber parts, their results are used in damper modeling. VHD performs desirably under different levels of excitation such that 82% to 99% of energy dissipation, depending on the type of loading, is observed by this device. The dynamic behavior of VHD can be further improved by modifying variable parameters such as dimensions and type of materials of the device.

Influence of compressed hydrogen on the fatigue behavior of a ferritic stainless steel

Metallic materials, e.g. used for fuel cell components, have to show a high corrosion fatigue resistance against gaseous hydrogen in context of hydrogen susceptibility. This work shows the influence of gaseous hydrogen on the fatigue behavior of a ferritic stainless steel in the low cycle (LCF) and the high cycle fatigue regime. Therefore, strain-controlled and load-controlled fatigue tests are conducted in gaseous hydrogen under pressure and as a reference in ambient air.The evaluation of the test results focuses on the determination of the stress-strain behavior and the cyclic softening and hardening behavior. Based on this evaluation the investigated ferritic stainless steel shows a strong reduction in lifetime at high strain amplitudes under gaseous hydrogen compared to the reference investigations in air. The evaluation of the stress-strain behavior in form of the cyclic stress-strain curve and the cyclic deformation curves showed no significant difference, instead. However, a lifetime reducing effect of the hydrogen can be observed.On the other hand, it can be shown by the help of the load-controlled fatigue tests that the damaging influence of the hydrogen decreases with the reduction of the load level. If the local stress or strain falls below a level where only elastic material behavior can be assumed, the determined fatigue strength under air and hydrogen coincide. In this case, the generation of dislocation is drastically reduced, lowering the damaging influence of on the investigated material.

Dynamical behavior of the orthotropic elastic material using an analytical solution

In this work, an analytical solution is provided for the dynamical response of an orthotropic non-homogeneous elastic material. The present study has engineering applications in the fields of geophysical physics, structural elements, plasma physics, and the corresponding measurement techniques of magneto-elasticity. The analytical performances for the elastodynamic equations has been solved regarding displacements. The influences of the rotation, the magnetic field, the non-homogeneity based radial displacement and the corresponding stresses in an orthotropic material are investigated. The variations of the stresses, the displacement, and the perturbation magnetic field have been illustrated. The comparisons is performed using the previous solutions in the magnetic field absence, the non-homogeneity and the rotation.