Elastic-plastic Constitutive Model Research Articles

Elastic–plastic model identification for rock surrounding an underground excavation based on immunized genetic algorithm

To compute the stability of underground engineering, a constitutive model of surrounding rock must be identified. Many constitutive models for rock mass have been proposed. In this model identification study, a generalized constitutive law for an elastic–plastic constitutive model is applied. Using the generalized constitutive law, the problem of model identification is transformed to a problem of parameter identification, which is a typical and complicated optimization. To improve the efficiency of the traditional optimization method, an immunized genetic algorithm that is proposed by the author is applied in this study. In this new algorithm, the principle of artificial immune algorithm is combined with the genetic algorithm. Therefore, the entire computation efficiency of model identification will be improved. Using this new model identification method, a numerical example and an engineering example are used to verify the computing ability of the algorithm. The results show that this new model identification algorithm can significantly improve the computation efficiency and the computation effect.

Numerical Modeling of the SR-18 Geogrid Reinforced Modular Block Retaining Walls

AbstractThe paper reports numerical model details and predictions of the end-of-construction performance for two instrumented and well-documented mechanically stabilized earth (MSE) walls. The walls were constructed as part of the highway SR-18 approach fills for a bridge near Seattle, Washington. The geogrid reinforced block face walls were modeled using a commercially available two-dimensional (2D) finite-difference program. The paper provides details on how material properties were selected from laboratory testing of wall components and how the computer modeling was carried out. The paper shows that predicted wall deformations and reinforcement strains were in reasonable agreement with measured data using both linear elastic-plastic and nonlinear elastic-plastic constitutive models for the soil. The geogrid reinforcement was simulated using a nonlinear load-strain-time secant stiffness model and cable elements. The paper compares numerical predictions of reinforcement loads at end of construction with ...

Elastic-Plastic Endochronic Constitutive Model of 0Crl7Ni4Cu4Nb Stainless Steels

We presented an elastic-plastic endochronic constitutive model of 0Crl7Ni4Cu4Nb stainless steel based on the plastic endochronic theory (which does not need the yield surface) and experimental stress-strain curves. The key feature of the model is that it can precisely describe the relation of stress and strain under various loading histories, including uniaxial tension, cyclic loading-unloading, cyclic asymmetric-stress axial tension and compression, and cyclic asymmetric-stress axial tension and compression. The effects of both mean stress and amplitude of stress on hysteresis loop based on the elastic-plastic endochronic constitutive model were investigated. Compared with the experimental and calculated results, it is demonstrated that there was a good agreement between the model and the experiments. Therefore, the elastic-plastic endochronic constitutive model provides a method for the accurate prediction of mechanical behaviors of 0Crl7Ni4Cu4Nb stainless steel subjected to various loadings.

Behaviour of Earth Dam under Seismic Load Considering Nonlinearity of the Soil

The stability and safety are very important issues for the dam structure which are built in seismic regions. The dam body consists of soil materials that behave nonlinearly modelled with finite elements. The numerical investigation employs a fully nonlinear finite element analysis considering linear and elastic-plastic constitutive model to describe the material properties of the soil. In this paper, seismic analysis of an earthen dam is carried out using Geo-Studio software based on finite element method. Initially, the in-situ stress state analysis has been done before the earthquake established, and then its results are used in the seismic analysis as a parent analysis. A complete parametric study is carried out to identify the effects of input motion characteristics, soil behaviour and strength of the shell and core materials on the dynamic response of earthen dams. The real earthquake record is used as input motions. The analysis gives the overall pattern of the dam behaviour in terms of contours of displacements and stresses.

Constitutive modelling of high strength titanium alloy Ti-6Al-4 V for sheet forming applications at room temperature

• A rigours set of experiments were performed to measure the initial yield surface of Ti-6Al-4V at room temperature under different-stress states. • A constitutive equation based anisotropic hardening model (HAH) model combined with the new determined yield function was proposed and implemented into the FEA- Abaqus implicit solver. • The proposed model showed ability to accurately predict the cyclic hardening response of Ti-6Al-4V, and therefore presents a promising approach for the prediction of deformation behaviour of Ti-6Al-4V alloy in sheet metal forming processes. To enable the design and optimisation of forming processes at room temperature the material behaviour of Ti-6Al-4 V needs to be accurately represented in numerical analysis and this requires an advanced material model. In particular, an accurate representation of the shape and size of the yield locus as well as its evolution during forming is important. In this study a rigorous set of experiments on the quasi-static deformation behaviour of a Ti-6Al-4 V alloy sheet sample at room temperature was conducted for various loading conditions and a constitutive material model developed. To quantify the anisotropy and asymmetry properties, tensile and compression tests were carried out for different specimen orientations. To examine the Bauschinger effect and the transient hardening behaviour in – plane tensile – compression and compression – tensile tests were performed. Balanced biaxial and plane strain tension tests were conducted to construct and validate the yield surface of the Ti-6Al-4 V alloy sheet sample at room temperature. A recently proposed anisotropic elastic-plastic constitutive material model, so-called HAH, was employed to describe the behaviour, in particular for load reversals. The HAH yield surface is composed of a stable component, which includes plastic anisotropy and is distorted by a fluctuating component. The key of the formulation is the use of a suitable yield function that reproduces the experimental observations well for the stable component. Meanwhile, the rapid evolution of the material structure must be captured at the macro - scale level by the fluctuating component embedded in the HAH model. Compared to conventional hardening equations, the proposed model leads to higher accuracy in predicting the Bauschinger effect and the transient hardening behaviour for the Ti-6Al-4 V sheet sample tested at room temperature.

Evaluation of stress integration algorithms for elastic–plastic constitutive models based on associated and non-associated flow rules

This paper presents in-depth analyses of four stress integration algorithms for finite deformation elastic–plastic constitutive relations. In particular, the four integration schemes were developed for both non-Associated Flow Rule (non-AFR) and Associated Flow Rule (AFR) in the continuum level of plasticity theory. The four integration schemes are (1) fully implicit backward Euler, (2) semi explicit convex cutting plane, (3) fully explicit classical forward Euler and (4) fully explicit forward Euler named Next Increment Corrects Error (NICE-1), which were implemented into the user material subroutines of finite element software ABAQUS. Analysis on numerical accuracy was carried out by using uniaxial tensile simulations at various orientations and time increments. The same analysis was also conducted for uniaxial tension/compression tests to investigate the effect of time increment on the calculated hardening curve. Finally, cylindrical cup deep drawing (manufacturing process which stamps a cylindrical cup) simulations were performed to compare computation time and accuracy for both AFR and non-AFR schemes for the evaluation of more realistic forming application. From the systematic comparative analyses, the following conclusions are made; (1) Caution should be exercised when finding an optimum time increment for explicit integration schemes. (2) The computation time and accuracy for both AFR and non-AFR are not much different when identical integration scheme is used. (3) For the simulation of large scale sheet metal forming applications, the explicit type stress integration algorithm can be a more practical choice considering that it does not deteriorate the computational accuracy and efficiency compared to the fully implicit algorithm.

Simulation on the Supporting of Underground Storage Foundation Pit by Anchor and Soil Nail

At present, the composite supporting technology of prestressed anchor and soil nailing has been more and more widely used in the foundation pit engineering, but the related existing theory and method can not satisfy the engineering practice, so it is necessary to do the discussion of this technology. In this paper, the foundation pit of underground storage in Zheng Zhou City was chose as an example, the simulation model for composite supporting of anchor and soil nail was set by FLAC software, the ideal elastic-plastic constitutive model was selected for soil, the cable unit was selected for the prestressed anchor and soil nailing, based on the interaction between supporting system and soil, the dynamic process for the excavation and support of foundation pit was simulated. The law for the effect of the excavation on disturbance, soil changes in displacement and internal force distribution of soil nail and anchor was obtained in this study, the connection line of the maximum axial force of soil nail and anchor were actually the potential failure surface of soil foundation pit, the position change of maximum axial force reflected the trends of internal displacement of excavated soil. The related conclusions have certain reference significance for the composite anchor and soil nailing supporting design.

On statistical strain and stress energy bounds from homogenization and virtual testing

Computational homogenization for quasistatic stress problems is considered, whereby the macroscale stress is obtained via averaging on Statistical Volume Elements (SVE:s). The variational workhorse for the subscale problem is derived from the presumption of weak micro-periodicity, which was proposed by Larsson et al. (2011). Continuum (visco)plasticity is adopted for the mesoscale constituents, whereby a pseudo-elastic, incremental strain energy serves as the potential for the updated stress in a given time-increment. Strict bounds on the incremental strain energy are derived from imposing Dirichlet and Neumann boundary conditions, which are defined as suitable restrictions of the proposed variational format. For this purpose, both the standard situation of complete macroscale strain control and the (less standard) situation of macroscale stress control are considered. Numerical results are obtained from virtual testing of SVE:s in terms of mean values and a given confidence interval, and it is shown how these properties converge with respect to the SVE-size for different prescribed macroscale deformation modes and different statistical properties of the random microstructure. In addition, the upper and lower bounds for a sequence of increasing strain levels, for a fixed SVE-size, are used as data for the calibration of a macroscopic elastic-plastic constitutive model.

Damage Mechanism Research of Yushu Airport Road Landslide No.3 Base on Elastoplastic Damage Constitutive Model

Due to the earthquake of Yushu in April 14, 2010, Airport Road landslide No.3 deformed cracking, resulting in lower stability of slope, triggering landslides and other diseases. Selecting the section 2-2 (mileage K823 + 809) of Airport Road landslide No.3 as the calculation section, we use the ABAQUS finite element program to establish landslide numerical mode. The slip mass of landslide was simulated by the elastic-plastic damage constitutive model, and the bedrock was analyzed as Mohr - Coulomb constitutive model. Landslide No3 is analyzed for example, and showed that earthquake triggering mechanism elastplastic damage constitutive model can describe the landslide very well.

복합재료 거동특성의 파괴해석 I - 이방성 소성 적합모델

A progressive failure analysis procedure for composite laminates is developed in here and in the companion paper. An anisotropic plastic constitutive model for fiber-reinforced composite material, is developed, which is simple and efficient to be implemented into computer program for a predictive analysis procedure of composites. In current development of the constitutive model, an incremental elastic-plastic constitutive model is adopted to represent progressively the nonlinear material behavior of composite materials until a material failure is predicted. An anisotropic initial yield criterion is established that includes the effects of different yield strengths in each material direction, and between tension and compression. Anisotropic work-hardening model and subsequent yield surface are developed to describe material behavior beyond the initial yield under the general loading condition. The current model is implemented into a computer code, which is Predictive Analysis for Composite Structures (PACS), and is presented in the companion paper. The accuracy and efficiency of the anisotropic plastic constitutive model are verified by solving a number of various fiber-reinforced composite laminates with and without geometric discontinuity. The comparisons of the numerical results to the experimental and other numerical results available in the literature indicate the validity and efficiency of the developed model.

Simulation of ionomer membrane fatigue under mechanical and hygrothermal loading conditions

Understanding the fatigue lifetime of common perfluorosulfonic acid (PFSA) ionomer membranes under fluctuating hygrothermal conditions is essential for the development of durable fuel cell technologies. For this purpose, a finite element based fatigue lifetime prediction model is developed based on an elastic–plastic constitutive model combined with a Smith-Watson-Topper (SWT) fatigue formulation. The model is validated against previously reported experimental results for a membrane under cyclic mechanical loadings. The validated model is then utilized to investigate the membrane fatigue lifetime in ex-situ applications under cyclic humidity and temperature conditions. The simulations suggest that the membrane fatigue lifetime is shorter under fluctuating humidity loadings than for temperature loadings. Additionally, the membrane fatigue lifetime is found to be more sensitive to the amplitude of the strain oscillations than to the mean strain under hygrothermal cycling. Most notably, the model predicts that simultaneous humidity and temperature cycling can exacerbate the fatigue process and reduce the fatigue lifetime by several orders of magnitude compared to isolated humidity or temperature cycling. The combination of measured mechanical fatigue data and the present numerical model provides a useful toolkit for analysis of membrane fatigue due to hygrothermal variations, which can be costly and time-consuming when addressed experimentally.

Finite Element Simulation of Behaviour of Granular Materials under Low-Cyclic Loading

.Different continuous elastic-plastic constitutive models (Mohr-Coulomb model, modified Cam-Clay model, modified Drucker-Prager model) are analysed with respect to their ability to simulate hysteretic behaviour of granular materials under the low-cyclic kinematic loading. The analysis is done in the framework of the quasi-static infinitesimal deformations. In case of the Mohr-Coulomb constitutive model, hysteresis degeneration into the straight line is revealed. Energy loss due to the hysteretic behaviour is studied. It is shown that horizontal areas representing the elastic behaviour are significantly longer for the Mohr-Coulomb criterion.

A damage mechanics approach to fretting fatigue life prediction with consideration of elastic–plastic damage model and wear

In this investigation an approach to fretting fatigue life prediction is developed with consideration of damage-coupled elastic–plastic constitutive model and wear. Nonlinear kinematic hardening is employed in the analysis of elastic–plastic damage, and the total damage is divided into two parts, elastic damage and plastic damage, which are related to the cyclic stress and accumulated plastic strain, respectively. Wear is modeled by the energy wear law to simulate the evolution of contact geometry. A two dimensional plane strain finite element implementation is presented for fretting, including the case of partial slip and gross sliding. The progressive fatigue damage and wear is simulated and the results are compared with experimental data from the literature.

Constitutive model coupled with mechanical effect of volume change and transformation induced plasticity during solid phase transformation for TA15 alloy welding

In this paper, the elastic–plastic constitutive model for TA15 titanium alloy welding which describes the mechanical effect of volume change during diffusional solid phase transformation and transformation induced plasticity (Trp) during diffusionless solid phase transformation has been established. The model in combination of mixed strain hardening and mechanical effect of solid phase transformation is coupled in MSC. Marc software by secondary development and applied for finite element numerical simulation of the welding process. Firstly, the simulation results with and without consideration of Trp strain are compared. It is indicated that Trp strain can moderate the stress distribution, make the high tensile stress and high compressive stress converge to zero and finally lower the residual equivalent stress. Meanwhile, the simulation results with consideration of volume expansion and volume shrinkage are compared. Volume expansion produced in the cooling stage can offset the volume shrinkage due to temperature dropping that lower the residual equivalent stress. Volume expansion accompanied by phase transformation which proceeds at low temperature is better than that at high temperature, while volume shrinkage at high temperature is better than that at low temperature at lowering the residual equivalent stress. The influences of Trp strain and volume change strain are reasonable both in spatial distribution and histrionic evolution. Using the established constitutive model, welding residual stress and strain are in good agreement with the theoretical results.

Numerical Calculation of Micro-Plie in Slope Engineering

In order to conduct the numerical simulation of rock and soil slope strengthened by the micro-pile with reinforced bar, FEM strength reduction is combined with the program of FLAC which possesses the function of analyzing tensile and shear failure. The micro-pile is under plastic state due to its mechanic features. Solid element and ideal elastic-plastic constitutive model of Mohr-Coulomb are applied as the rock and soil mass and pile. The calculation model can work out the safety factor of slope, the dynamic changing process of pile deformation and failure, the failure mode of slope after strengthened by micro-pile. Then the structural element of pile is used to simulate piles, which can obtain the bending moment and shear force. The beam element is used to simulate the coupling beam. So the layout principle of inner force before the failure can be calculated.

Behavior Identification of a Multi-Layered Graded Stainless Steel Using an Inverse Method

The paper aimed at the behavior identification of a stainless steel sheet treated by surface mechanical attrition (SMAT). From tensile testing results on specimen after removing different depth of treated surface, a multi-layered model can be built. Therefore, the SMAT treated sheet is divided into five layers along thickness direction: the top and bottom hard layers of 0.15mm, the soft middle layer of 0.5mm, and two medium layers of 0.1mm in between. An elastic-plastic damageable constitutive model is adopted to describe the behavior of each layer. The parameters for each layer are identified using an inverse calculation technique. The three-dimensional ABAQUS/Explicit models with mass scaling are built for the SMAT treated tensile specimen with and without removed external harder layer. The best fit of parameters for each layer is obtained by minimizing the scatter between measured stress and calculated stress for the prescribed strain history. Finally, the identified material model is validated by the numerical simulation of a penetration test of SMAT treated sheet metal.

A three-dimensional elastoplastic constitutive model for concrete

Strength of concrete materials can be described by the theory of nonlinear unified strength criterion with four independent parameters. The failure surface of the strength criterion in the principal-stress space is smooth, and therefore it has continuous partial derivatives. The theory of nonlinear unified strength criterion is applied as a yield function, plastic shear strain is used as the hardening and softening parameters, and the hardening and softening laws are given by the stress-strain relationship under uniaxial compression. Then a three-dimensional elastic-plastic constitutive model for concrete is established. A user-defined material mechanical behavior (UMAT) is developed based on the finite element analysis software ABAQUS. The load resistance and the deformation capacity of a reinforced concrete column under eccentric compression are simulated using the present model. The present theoretical results are comparable to the available material-test data, and the numerical results have a good agreement with the experimental observations of the concrete column. This indicates that the developed constitutive model is capable of describing the strength and deformation behaviors, and representing the strain softening behavior of concrete under three-dimensional stress state. Furthermore, the model has high efficiency and accuracy in the numerical analysis.

An elastic–plastic constitutive model for ceramic composite laminates

Existing phenomenological constitutive models are unable to capture the full range of behaviors of ceramic composite laminates. To ameliorate this deficiency, we propose a new model based on the deformation theory of plasticity. The predictive capabilities of the model are assessed through comparisons of computed and measured strain and displacement fields in open-hole tension tests. The agreements in the magnitude of strains and in the size and shape of shear bands that develop around a hole are very good over most of the loading history. Some discrepancies are obtained at high stresses. These are tentatively attributed to non-proportional stressing of some material elements: a feature not captured by the present model.

State update algorithm for associative elastic-plastic pressure-insensitive materials by incremental energy minimization

This work presents a new state update algorithm for small-strain associative elastic-plastic constitutive models, treating in a unified manner a wide class of deviatoric yield functions with linear or nonlinear strain-hardening. The algorithm is based on an incremental energy minimization approach, in the framework of generalized standard materials with convex free energy and dissipation potential. An efficient method for the computation of the latter, its gradient and its Hessian is provided, using Haigh-Westergaard stress invariants. Numerical results on a single material point loading history and finite element simulations are reported to prove the effectiveness and the versatility of the method. Its merit turns out to be complementary to the classical return map strategy, because no convergence difficulties arise if the stress is close to high curvature points of the yield surface.

The role of epistemic uncertainty of contact models in the design and optimization of mechanical systems with aleatoric uncertainty

Epistemic uncertainty, the uncertainty in the physical model used to represent a phenomenon, has a significant effect on the predictions of simulations of mechanical systems, particularly in systems with impact events. Impact dynamics can have a significant effect on a system’s functionality, stability, wear, and failure. Because high-fidelity models of systems with impacts often are too computationally intensive to be useful as design tools, rigid body dynamics and reduced order model simulations are used often, with the impact events modeled by ad hoc methods such as a constant coefficient of restitution or penalty stiffness. The choice of impact model, though, can have significant ramifications on design predictions. The effects of both epistemic and aleatoric (parametric) uncertainty in the choice of contact model are investigated in this paper for a representative multiple-degree of freedom mechanical system. Six contact models are considered in the analysis: two different constant coefficient of restitution models, a piecewise-linear stiffness and damping (i.e., Kelvin–Voight) model, two similar elastic-plastic constitutive models, and one dissimilar elastic-plastic constitutive model. Results show that the optimal mechanism design for each contact model appears extremely different. Further, the effects due to epistemic uncertainty are differentiated clearly in the response from the effects due to aleatoric uncertainty. Lastly, when the mechanisms are optimized to be robust against aleatoric uncertainty, the resulting designs show some robustness against epistemic uncertainty.