Elastic-plastic Constitutive Model Research Articles

Experimental Study on Stress Paths of Unsaturated Soils

The distribution of loess in China is concentrated in the Midwest, which is a typical structural soil. Its structure is extremely special, and its sensitivity to water is also unique. The strength and deformation characteristics of this kind of unsaturated soil have a great influence on the stress it bears. This study starts with the same stress ratio loading of loess with different moisture content and corresponding remolded loess, aiming at the changes of the structure of unsaturated soil under different stress ratios. Based on the comprehensive analysis of structural potential parameters of unsaturated soil under the condition of poor stress, the appropriate hardening parameters are constructed, and the corresponding elastic-plastic constitutive model is established. At first, the corresponding test scheme is designed, and then the test results are analyzed. Finally, the specific analysis is carried out from the constitutive model of stress elastic-plasticity of unsaturated soils.

Effect of feed condition on thrust force and torque during continuous and step-by-step drilling of cortical bone

Abstract Chip evacuation is one of the fundamental difficulties during continuous drilling of the cortical bone. As the drilling process progresses, discontinuous chips tend to cluster together and clog the drill flutes, which can result in increased temperature, poor hole quality, elevated thrust force and torque, and can even cause the drill bit to break. In this study, continuous and step-by-step drilling processes of the cortical bone were conducted to investigate the thrust force and torque using experimental and numerical modeling methods. By using the finite element method, an elastic–plastic constitutive model was employed to predict the thrust force and torque experienced during bone drilling, and a series of drilling tests was conducted. The experimental results showed a significant increase in the thrust force and torque owing to the chip clogging during the continuous drilling process while this increase was not observed in the simulations. It was shown that the step-by-step drilling method can reduce the increased thrust force and torque during the drilling of cortical bone, and the numerical results of this drilling process were demonstrated to be consistent with the experimental ones. The reduced thrust force and torque indicated that the chip clogging may be reduced by using the step-by-step drilling method, and the numerical results suggested that the finite element model can be used to assist surgeons in selecting drilling conditions to control the process in step-by-step drilling of the cortical bone.

Efficacy of elastic-plastic constitutive models in predicting the geo-mechanical response of gas hydrate sediments

Efficacy of elastic-plastic constitutive models in predicting the geo-mechanical response of gas hydrate sediments

Equivalent seismic coefficients for caisson foundations supporting bridge piers

Safety of a foundation under seismic loading is strongly dependent on the inertial forces transmitted by the superstructure, exchanged with the surrounding soil and acting into the foundation itself. The latter contribution, typically neglected for shallow and pile foundations, should be considered for caisson foundations, much more massive and rigid than the foundation soil. In this paper, the inertial forces acting in caisson foundations during seismic shaking are extracted from the results of a parametric study where different caissons supporting bridge piers are subjected to severe ground motions. The parametric study was carried out in the time domain via 3D Finite Element (FE) dynamic analyses performed in terms of effective stresses but assuming an undrained response of the foundation soil. Non-linear and inelastic soil behaviour was described in the analyses by an elastic-plastic constitutive model with isotropic hardening.In the framework of a pseudo-static approach, the caisson inertia is represented by equivalent horizontal and rotational seismic coefficients, kh eq and krot eq, relating the generalised inertial forces to the caisson weight. The coefficient kh eq turns out to be always remarkably smaller than the maximum value computed at ground surface in free-field conditions, kh max(g.s.). The equivalent seismic coefficients kh eq and krot eq are expressed via empirical relationships as a function of the dynamic properties of the whole system and the seismic input, through dimensionless parameters. Calculation examples are finally given, where safety assessment of bearing capacity is made for different systems using the pseudo-static approach, showing that use of the seismic coefficients computed by the proposed relationships yields results consistent with the ones obtained from the dynamic analyses.

An analytical solution for circular tunnels excavated in rock masses exhibiting viscous elastic-plastic behavior

Investigating time-dependent behavior of tunnels driven in rocks has been the topic of interest for many years. The majority of researches were conducted with the assumption that the behavior of the surrounding rock masses is viscoelastic. In this paper, an analytical solution is proposed for circular tunnels under hydrostatic stress field, whose surrounding rock mass is isotropic, homogenous, obeying viscous elastic-plastic constitutive model. It is assumed that the rate of excavation is infinitely large. Therefore, the solution is proposed for unlined tunnels when the advance of tunnel face is halted, or after lining installation when the tunnel face is far from the studied section. The results were compared with those predicted by finite difference numerical model which exhibited a good agreement for both lined and unlined tunnels, except for large times where numerical model results slightly exceed the values predicted by the proposed solutions for lined tunnels.

Modeling the effects of loading scenario and thermal expansion coefficient on potential failure of cryo-compressed hydrogen vessels

A multiscale thermomechanical model for a simplified Type-3 cryogenic, compressed-hydrogen (H2) storage vessel is described in this paper. The model accounts for the temperature-dependent elastic-plastic behavior of the vessel's carbon/epoxy composite overwrap and aluminum alloy liner. The homogenized thermo-elastic-plastic behavior for the individual laminae of the vessel layup is obtained using an incremental Eshelby-Mori-Tanaka approach associated with a micromechanical failure criterion to predict laminar failure while a standard elastic-plastic constitutive model is used to describe the behavior of the typical aluminum alloy assumed for the liner. The vessel's response to external loadings is modeled using a finite element method. Four loading scenarios, representing four thermomechanical cycles applied to the vessel, are analyzed to evaluate constituent and laminar stresses as well as the associated failure criterion during the cycle according to these scenarios. The model can provide helpful guidance to mitigate thermal stresses by selecting a suitable loading scenario, optimizing the layup, and tailoring the thermomechanical properties of the resin matrix.

A damage constitutive model and its characterization parameters identification for elastic-plastic materials

This paper proposes a simple damage constitutive model for elastic-plastic materials on the basis of the classical elastic-plastic constitutive model and damage mechanics theory. Based on the simple damage constitutive model, ABAQUS built-in Python software was used to develop the virtual experimental platform, and the whole process simulation of the specimens stretching until the fracture was carried out. The correspondence between the damage characterization parameters and the performance indexes such as the fracture strain and the percentage reduction of area was studied. According to the comparison of the virtual/real test results of ZL114A, the situation shows that the simple damage constitutive model can realize the high fidelity simulation of the damage behavior of elastic-plastic materials. The relative accuracy of the important material property parameters such as the ultimate strength, the percentage total elongation at fracture and the percentage reduction of area reaches 5%.

A damage coupled elastic-plastic constitutive model and its application on low cycle fatigue life prediction of turbine blade

Based on continuum damage mechanics (CDM), a damage coupled elastic-plastic constitutive model combined with multilinear hardening relation is proposed and applied on low cycle fatigue (LCF) life prediction of turbine blade. The model has considered the local rigidity attenuation of structure caused by fatigue damage in elastic and plastic stage, and it is implemented combining with finite element method (FEM) to predict the crack initiation lives of turbine blades. Runge-Kutta (RK) method is employed in the solving process of damage accumulation. By conducting the calculation in several time step sizes, the convergence of the proposed model is examined. To validate the predicted results, groups of LCF experiments are conducted on full-scale turbine blades. The macroscopic fracture shows that the crack initiation region is in accordance with the predicted results. Compared with the experimental results, the predicted lives of the proposed model, an existing CDM model without coupling with constitutive relation and Morrow model are within factors of 2.31, 3.93 and 9.15 in scatter band respectively, indicating the high accuracy of the proposed model. Expect for turbine blades, the proposed model can be used to predict the LCF lives of other structures.

FE analysis of the residual stresses for the laser welded T-joint of Al-Li alloy under service loads

This paper attempts to reveal the evolution of welding residual stresses (WRS) in skin-stringer structure of Al-Li alloy exposed to service loads. 3D thermal-structural finite element (FE) formulation of the dual laser-beam bilateral synchronous welding process is first derived, and its accuracy is verified by experimental tests to acquire accurate WRS. FE numerical analyses incorporated with the elastic-plastic constitutive model, taking the WRS, strains distribution and total equivalent plastic strains as an initial condition, are next carried out to explore the residual stresses redistribution of the T-joint under service loads. The results unveil that longitudinal stress relaxation is pronounced (especially at the weld) in the skin after the end of the loads applying. However, the longitudinal stress in the middle of the stringer is not sensitive to the service loads. The extended high tensile stress concentration zone inside the joint in case 2 and case 4 may be the potential failure location after the progressive loading of the skin-stringer welding structure. Additionally, the weld toe, which is the obvious stress sudden change zone in the service process, is a non-negligible position for the improved failure estimation of the aerospace skin-stringer structure.

Flexural behavior of corroded HPS beams

Experimental research is conducted to investigate the flexural behavior of corroded High Performance Steel (HPS) beams. Four beams with various corrosion damage are designed and subjected to electrochemical accelerated corrosion process. 3D scanning technology is employed to analyze the geometric features affected by the corrosion damage. Flexural tests are carried out, and the impact of corrosion on the flexural response is discussed. Considering the randomness of corrosion pits in each area, predictive models are proposed for the flexural strength of corroded beams with an idealized elastic-plastic and linear-hardening constitutive relationship model. An analysis comparing the proposed models with Chinese and American codes is made. Results show that increasing the corrosion damage leads to a decrease of discreteness in the residual sectional area and causes a transformation in the compressed flange from noncompact to slender. A corrosion loss less than 10% leads to slight deterioration of both strength and stiffness degradation, while further corrosion damage results in a significant decrease. The depth and length of the buckling wavelength for corroded beams decreases gradually as the corrosion damage become more serious. The analytical models IEM and LHM or the GB50017-2017 may be suitable for predicting the lower and upper limit values of the ultimate flexural moment, respectively, and results predicted by AISC are conservative.

Characterisation and constitutive modelling of biaxially stretched poly(L-lactic acid) sheet for application in coronary stents

A poly(L-lactic acid) stent is exposed to a variety of processing techniques, temperatures and environmental conditions during its lifecycle, from the manufacturing process, to crimping through to deployment within the body. The effect of the biaxial stretching procedure and the effects of temperature and extension rate (post-processing) on the mechanical response of poly(L-lactic acid) are hereby investigated, and a constitutive model calibrated against experimental data is proposed. Dumb-bell specimens were punched from biaxially stretched sheets subjected to different processing histories, and tested under uniaxial tension at various temperatures (20, 37 and 55 °C) and extension rates (1, 5 and 10 mm/min). A Design of Experiments methodology was employed to identify the parameters that had the most significant effect on the mechanical response of the polymer. Results show that the elastic modulus and yield strength of the stretched sheets are strongly dependent on the aspect ratio of the biaxial deformation, along with the temperature during uniaxial deformation (post-processing). In contrast, these mechanical properties were not heavily dependent on extension rate (post-processing). A transversely isotropic, elastic-plastic constitutive model for finite element implementation is proposed, with the intention that it may be used as a design tool for developing high stiffness, thin-strut polymeric stents that contend with the performance of their metallic counterparts.

A new method of developing elastic-plastic-viscous constitutive model for clays

A new method is presented to develop the existing elastic-plastic constitutive model into an elastic-plastic-viscous one for clays. The actual loading process is divided into an instant process and a delayed process denoting the elastic-plastic strain and viscous strain, respectively. The elastic-plastic strain is determined by either an elastic-plastic model for overconsolidated clays or an improved model based on the elastic-plastic model for normally consolidated clays. In order to calculate viscous strain, a reference state line is defined based on the actual loading path. Combining the reference state line, an existing elastic-plastic model can be conveniently developed into an elastic-plastic-viscous model. Furthermore, using the proposed method, the modified cam clay model is extended into an elastic-plastic-viscous model. Comparisons with test results demonstrate that the extended model can capture the main time-dependent behaviours of clays, including creep, stress relaxation and strain rate effects.

An Elastic-plastic Constitutive Model of Concrete Based on Thermodynamic Principles and Its Application in Arch Dam Design

An Elastic-plastic Constitutive Model of Concrete Based on Thermodynamic Principles and Its Application in Arch Dam Design

Analysis of the fatigue crack initiation of a wind turbine gear considering load sequence effect

Under the action of the wind, wind turbine gears experience complex loading histories in which the amplitude of the load is varying. The variable load conditions make the load sequence and the load amplitude inverse number as important factors to be considered for gear fatigue analysis. In the present work, a damage-coupled elastic-plastic constitutive model based on the continuous damage mechanics (CDM) is established to analyze the influence of load sequence on rolling contact fatigue (RCF) crack initiation of a wind turbine gear. The crack initiation is indicated by reaching the critical threshold of the defined damage variable related to the shear stress range and the plastic strain. During repeated loading cycles, the deterioration of material is reflected by gradually reducing mechanical properties. The numerical simulation is carried out in the frame of ABAQUS using the subroutine of user defined material subroutine (UMAT). The two-level load conditions are selected and results of which are compared with those of constant amplitude load conditions. Different inverse numbers are utilized to investigate the influence of load amplitude inverse number on crack initiation life. Simulation results are compared with existing damage accumulation criteria. The results indicate that when the first crack initiates, the sum of lifetime ratio is greater than unity for the low-high load sequence, while this value is less than unity for the high-low load sequence. Furthermore, the increase of the load amplitude inverse number will weaken the influence of the load sequence with regard to the crack initiation life. The highly nonlinear characteristic of damage accumulation during fatigue process under variable loading histories is captured by the proposed method. This method provides a new way to reveal the contact fatigue process of gears under variable loading histories and lay a foundation for predicting the accurate fatigue life under the real, complex loading condition of a gear.

A finite-strain phase-field approach to ductile failure of frictional materials

This work presents a modeling framework for the ductile failure of frictional materials undergoing large deformations with a focus on soil mechanics. Crack formation and propagation in soil can be modeled in a convenient way by the recently developed continuum phase-field approach to fracture. Within this approach sharp crack discontinuities are regularized. It allows the use of standard discretization methods for crack discontinuities and is able to account for complex crack paths. In the present contribution, we develop a computational modeling framework for the phase-field approach to ductile fracture in frictional materials. It combines a non-associative Drucker–Prager-type elastic-plastic constitutive model with an evolution equation for the crack phase field in terms of an elastic-plastic energy density. An important aspect is the development of an isotropic hardening mechanism that accounts for both friction and cohesion hardening. In order to guarantee a locking- and hourglass-free response, a modified enhanced element formulation, namely the consistent-gradient formulation, is employed as a key feature of the finite-element implementation. The performance of the formulation is demonstrated by means of representative numerical examples that describe soil crack formation rooted in elastic-plastic fracture mechanics.

The elastic-plastic delamination analysis of layered beam configurations

The elastic-plastic delamination fracture in layered beams was studied theoretically. Two Four Point Bend (FPB) beam configurations (the Double Leg Four Point Bend (DLFPB) and the Single Leg Four Point Bend (SLFPB)) were analyzed. An elastic-plastic constitutive model with power law hardening was used in the analysis. Fracture behavior was studied by applying the J-integral approach. The analytical solutions of the J-integral were obtained at characteristic levels of the external load. The solutions obtained were verified by analyzing the strain energy release rate with taking into account the material non-linearity. The variation of J-integral value in a function of crack location along the beam dept was investigated. The effect of material non-linearity on the fracture was evaluated. The analysis revealed that the J-integral value decreased with increasing the lower crack arm thickness. It was also found that the material non-linearity has to be taken into account in fracture mechanics based safety design of structural members and components made of layered materials. The analytical solutions obtained are very useful for non-linear investigations, since the simple formulae derived capture the essentials of non-linear fracture in the layered beams under consideration.

Development of a framework to combine an elastic-plastic constitutive model and a creep constitutive model

Development of a framework to combine an elastic-plastic constitutive model and a creep constitutive model

A comparative Study on the Analysis of Elastic Plastic and Viscoelastic Constitutive Model in Soft Rock large Deformation Tunnel

With the construction of large highway engineering, large section soft rock highway tunnel is more and more. In the process of excavation, large section highway tunnel, soft surrounding rock and complex stress, during the excavation process prone to large deformation. Reasonable determination of the deformation of the large section soft rock highway tunnel is particularly important. According to the geological conditions and the mechanical characteristics of surrounding rock, using elastic-plastic and visco elastic constitutive model for deformation of the same level under different embedding rock by numerical analysis, the same rock using different constitutive relations, area difference, measured data through the laying on the site to provide the comparative analysis by the viscoelastic constitutive relation constitutive model is closer to the actual site, which is due to the large section soft rock tunnel has obvious time effect in the process of excavation, therefore in the process of excavation for large deformation of soft rock tunnel is more close to the actual rheological constitutive model considering the effect of amount.

Identification of mechanical parameters of urea-formaldehyde microcapsules using finite-element method

To obtain the mechanical parameters for a microcapsule, such as the Young's modulus, yield stress, and hardening coefficients using different mechanical constitutive models, parameter identification must be implemented using inverse analysis. In the present study, a new approach combining the finite-element method and an optimisation procedure is proposed for determining the constitutive parameters of urea-formaldehyde microcapsules, in which three types of elastic-plastic constitutive models are considered: the power-law hardening model, the elastic-perfectly plastic model, and the elastic-perfectly plastic model with linear hardening. A nonlinear optimisation procedure is applied to determine the minimum of the multivariable objective function, which is defined as the norm of the difference between the numerical and experimental results. The efficiency and robustness of the proposed method are verified with different initial values and numbers of elements. The force-displacement curves from a numerical simulation show good agreement with the experimental data, indicating that the proposed approach and the mechanical parameters determined are reliable.

Importance of asymmetry and anisotropy in predicting cortical bone response and fracture using human body model femur in three-point bending and axial rotation.

Modeling of cortical bone response and failure is critical for the prediction of Crash Induced Injuries (CII) using advanced finite element (FE) Human Body Models (HBM). Although cortical bone is anisotropic and asymmetric in tension and compression, current HBM often utilize simple isotropic, symmetric, elastic-plastic constitutive models. In this study, a 50th percentile male femur FE model was used to quantify the effect of asymmetry and anisotropy in three-point bending and axial torsion. A complete set of cortical bone mechanical properties was identified from a literature review, and the femur model was used to investigate the importance of material asymmetry and anisotropy on the failure load/moment, failure displacement/rotation and fracture pattern. All models were able to predict failure load in bending, since this was dominated by the cortical bone material tensile response. However, only the orthotropic model was able to predict the torsional response and failure moment. Only the orthotropic model predicted the fracture initiation location and fracture pattern in bending, and the fracture initiation location in torsion; however, the anticipated spiral fracture pattern was not predicted by the models for torsional loading. The results demonstrated that asymmetry did not significantly improve the prediction capability, and that orthotropic material model with the identified material properties was able to predict the kinetics and kinematics for both three-point bending and axial torsion. This will help to provide an improved method for modeling hard tissue response and failure in full HBM.