Elasto-plastic Response Research Articles

Finite element solution for static and dynamic interactions of cylindrical rigid objects and unsaturated granular soils

By employing a mortar-type contact algorithm, we develop a theoretical and numerical framework for elastoplastic interaction of unsaturated granular soils with a rigid cylindrical object in both static and dynamic analyses. The elastoplastic response is modelled with a constitutive model based on the effective stress concept for unsaturated soils. The constitutive model offers the ability to simulate the effect of stress-induced anisotropy on the plastic response. Several numerical examples are provided for verification purposes and sensitivity analysis, demonstrating the capabilities of the presented framework.

The in-plane elastic-plastic response of an incompressible, filled hexagonal honeycomb

Exact solutions are derived for the small-strain, in-plane, elasto-plastic response of a hexagonal honeycomb using slender beam theory; incompressibility of the honeycomb is enforced by filling its voids with an incompressible, inviscid fluid. The honeycomb has sides of equal length, but its inclined struts subtend an angle that can deviate from 120° with respect to the vertical side walls. The relative density is sufficiently small that the struts are slender and can be treated as Euler-Bernoulli beams. Exact solutions are obtained for the elastic moduli and macroscopic yield surface of the rigid, ideally plastic lattice under general in-plane loading: the solutions satisfy equilibrium, compatibility and the constitutive response of each elastic, ideally plastic beam. Prior to conducting an elastic analysis, and a rigid, ideally plastic analysis, initial insight is gained by exploring the vector space of inextensional collapse mechanisms of the pin-jointed, compressible version of the hexagonal truss. Two inextensional collapse mechanisms of the compressible honeycomb are identified from the null space of the kinematic matrix. The presence of an incompressible, inviscid fluid in the voids of the honeycomb locks-up one mechanism but the other mechanism survives and generates macroscopic shear strain. Consequently, the incompressible hexagonal honeycomb with rigid joints has a high shear compliance and a low shear strength, with values equal to that of the unfilled, compressible honeycomb. In contrast, macroscopic tensile straining of the incompressible honeycomb requires the stretching of bars in addition to bar-bending, and the tensile modulus and strength of the incompressible honeycomb are thereby elevated. Explicit analytical formulae are derived for the macroscopic tensile modulus and strength of the incompressible honeycomb.

Critical State Model of Sand-Tire Derived Aggregate Mixtures Based on Triaxial Tests

This study is part of an environmental experimental program on the use of scrap automobile tires for geotechnical applications. Different types of laboratory tests were conducted to determine the elastic, plastic, and creep parameters of tire derived aggregate (TDA)-sand granulated mixtures. However, this paper emphasizes the plasticity parameters via the development of a critical state model based on the results of triaxial tests. This was attained by considering loose sand specimens, at a predetermined TDA volumetric content, subject to three different confining pressures under a constant axial displacement rate. The calculated deviatoric stress versus axial strain curves, obtained via the modified Cam Clay model, captured the non-linear elastoplastic response obtained in the tests. Results indicated that the level of the shear strength is highly dependent on critical state friction angle which in turn depends on the TDA content. For the loose TDA-sand mixtures used in the present study, the effect of the TDA content demonstrates a reinforcement of the sand matrix. However this reinforcement diminishes as the TDA content increases.

A non-incremental numerical method for dynamic elastoplastic problems by the symplectic Brezis–Ekeland–Nayroles principle

The goal of the present work is the demonstration of the ability of the Symplectic Brezis–Ekeland–Nayroles (SBEN) principle for the numerical simulation of dynamic elastoplastic problems in small strains. This non-incremental approach is an alternative method to conventional step-by-step techniques, as it allows the computation of the whole evolution curve over the entire loading history. We show that the SBEN variational formulation yields to a constrained time–space minimization problem. The cost function depends on stress, displacements, and plastic multiplier fields, which, naturally, leads to a mixed finite element discretization. The details of the solution algorithm are illustrated through the numerical study of the elastoplastic response of the thin and thick pressurized tubes, including inertia effects. Moreover, the balance of momentum is handled using two approaches. Firstly, the Schaefer superposition technique is considered, where the balance of momentum is exactly satisfied. Secondly, the balance of momentum is considered as an optimization constraint and satisfied only at the Gauss integration point level of the finite element problem. The accuracy and efficiency of the SBEN principle are assessed by comparing the numerical results with the analytical solutions (for the thin tube) and the predictions derived by the conventional incremental finite element procedure.

SHAKING TABLE TEST OF OFFSHORE WIND TURBINE SUPPORTING TOWER

At present, the wind power generation technology develops rapidly. As the main supporting structure of the wind turbine, the safety of the tower structure is very important under the action of earthquake. Since the behavior of this kind of tripod structure has not yet been investigated through shaking table test, a 1∶20 scaled model of offshore tripod supporting structure was tested through seismic shaking table. Subjected to a series of seismic ground motions with three peak acceleration levels of 0.3 g, 0.6 g and 0.9 g, the dynamic characteristics of the model structure and the seismic response were studied. Two support condition sceneries of the foundation for the test model were considered: with supports at 1.3 m high of each pile foundation, and removal of the supports (simulated pile foundation failure). Compared with the case with the foundation support, the dynamic acceleration response of the structure after the removal of the support was slightly reduced, and the decrease in the amplitude of peak acceleration in X and Y directions was 9.87% and 5.40%, respectively. In addition, finite element analysis by ABAQUS was performed to analyze the elastoplastic response of the structure, and the simulation results were compared with the test results. Good agreement was observed between the two results, which validates the results of both the finite element analysis and the shaking table test, and provides a reference for the elastoplastic time history analysis of the prototype structure.

Thermo-Mechanical Behavior of Poly(ether ether ketone): Experiments and Modeling.

Observations are reported on poly(ether ether ketone) (PEEK) in uniaxial tensile tests, relaxation tests and creep tests with various stresses in a wide interval of temperatures ranging from room temperature to 180 °C. Constitutive equations are developed for the thermo–mechanical behavior of PEEK under uniaxial deformation. Adjustable parameters in the governing equations are found by matching the experimental data. Good agreement is demonstrated between the observations and results of numerical simulation. It is shown that the activation energies for the elastoplastic, viscoelastic and viscoelastoplastic responses adopt similar values at temperatures above the glass transition point.

Effect of the mineralogical composition on the elastoplastic hydromechanical response of Opalinus Clay shale

Opalinus Clay is the shale currently under investigation as the host formation for geological radioactive waste disposal in Switzerland. Its hydromechanical response has been widely studied, and the experimental results show a range of values whose dispersion needs to be clarified.This work aims to explain the dispersion in the literature results by correlating the hydro-mechanical response to the mineralogical variability of the tested specimens.Based on published microstructural studies, the Opalinus Clay shale is herein schematised as a sequence of two kinds of layers: the shaly (high in clay-mineral content) and the sandy (low in clay-mineral content) layers. The mineralogical composition, porosity and hydromechanical parameters are assigned to each layer type. The one-dimensional compressibility and the elastic response of combinations of layers are derived adopting an analytical solution for the stratified, transversely isotropic medium. The drained elastic properties are used to calibrate the approach, and the undrained elastic properties are derived and compared to literature data. Empirical correlations between the layer composition and the geomaterial strength are also drawn.It is shown that by adopting a layered structure with an alternation of two kinds of layers, most of the variability in the studied geomechanical properties of Opalinus Clay can be captured.

Spectral phase-field model of deformation twinning and plastic deformation

Deformation twinning is critical to understanding and predicting the heterogenous deformation of many important material systems, e.g., hexagonal metals. In this work, we report a Fast-Fourier-Transform (FFT) based spectral phase-field method (PFM) model of deformation twinning and plasticity by directly incorporating the spectral FFT elasto-viscoplastic formulation, which allows two-way coupling between morphological evolution of deformation twinning and elastoplastic deformation. We verify the model by studying the twinning morphology evolution and plastic deformation of Mg single crystals and comparing the results with existing experimental measurements. We then apply the model to investigate heterogeneous twinning nucleation, growth and propagation behaviors, including twin-twin interactions, double twinning, and twin-grain boundary interactions. This work not only provides useful insights into the underlying deformation twinning mechanisms in hexagonal crystals but also presents an efficient PFM model of deformation twinning and plasticity which is generally applicable to modelling and predicting morphological evolution of deformation twinning and its effects on elasto-plastic responses of polycrystalline materials.

Experimental investigation and seismic response behavior of a self-centering precast concrete frame with hysteretic dampers

A new type of self-centering precast concrete (SCPC) frame with hysteretic dampers is developed to obtain sufficient self-recovering and energy consumption characteristics. The working principle of a novel connection is presented, and seven cyclic loading tests with different parameters on three full-sized novel beam-column joints are investigated. Adequate seismic performances were experimentally observed in cyclic loading tests. Numerical simulation of the novel connection was performed using the OpenSees software. The elaborate simulation results and test results were well matched, such as the hysteretic behaviors, prestressed tendons forces, energy consumption and self-recovering characteristics. Furthermore, a prototype structure was modeled, and the elastoplastic dynamic responses at the design-basis earthquake (DBE) and the maximum considered earthquake (MCE) levels were studied. The results showed that the peak and residual interstory drifts (θmax and θr,max) achieved desirable demands. The post-tensioned strands avoided excessive yielding at the MCE level, and the novel frame had an adequate energy consumption behavior. In addition, incremental dynamic analysis and vulnerability analysis were performed. The 50-year exceedance probabilities of the Immediate occupancy (IO) and Repairable (RE) limit states taking θmax and θr,max as the evaluation indicators were also calculated, respectively. The results demonstrate that the novel frame has adequate seismic performance, greater reliability and less damage potential than the traditional self-centering precast concrete (SCPC) frame without energy dissipation devices.

Seismic collapse resistance performance on out-jacketing frames with concrete-encased CFST columns for adding storeys

This research paper conducted a hysteretic behavior simulation on a single-span and single-storey frame composed of prestressed concrete-encased steel beams and concrete-encased concrete filled steel tube (CFST) columns. The hysteretic parameters of stiffness degradation, strength degradation and pinching behavior for members were suggested according to tested results. After that, an analytical model for corresponding out-jacketing frames with single-span and multi-storey was developed, and amounts of elastoplastic seismic response analysis were conducted for seismic fortification intensities 7 and 8 with various site-classes and design earthquake groups under rare earthquake. The results indicated that, the out-jacketing frames assigned to Intensity 7 with Site-classes I0 to III behaved perfectly in seismic collapse resistance performance, which could be designed as regular frames by using China's current codes; while referring to Intensity 8, a certain amount of out-jacketing frames assigned to Site-classes I0 to III had inter-storey collapse mechanism, and several design proposals were developed to prevent collapse failure by measurements of enhancing seismic grade.

Numerical Simulation of Some Steel Structural Elements with Uncertain Initial Porosity

The main research purpose of this work was to study the elasto-plastic responses of some fundamental steel structural elements exhibiting stochastic volumetric microvoids. The constitutive model of the steel material was consistent with the deterministic Gurson–Tvergaard–Needleman (GTN) porous plasticity model, where some of the microvoids parameters have additionally been defined as Gaussian random variables. The iterative stochastic finite element method implemented based on the-tenth order stochastic perturbation technique was utilized in numerical experiments. An interoperability of the computer algebra system MAPLE 2019 and the finite element method system ABAQUS was employed to study the influence of the initial microvoids f0 with uncertainty in the structural steel on the statistical scattering of the resulting stresses and deformations. The basic probabilistic characteristics of the structural response were computed and contrasted with statistical estimators inherent in the Monte–Carlo simulation and also with the results obtained from the semi-analytical probabilistic method. Reliability indices according to the first-order reliability method (FORM) were also calculated. Two numerical illustrations included the (i) tension test of the round cylindrical steel rebar and the (ii) bending test of the steel I-beam restrained at both its ends. Expectations and coefficients of variation of the structural responses confirmed here the importance of the microvoids for the stochastic elasto-plastic behavior of some basic engineering structures, where tensile stress plays an important role in designing procedures.

Dynamic ultimate bearing capacity of beam-plate coupled structures with deformable connection under uniaxial compression, compression-bending and compression–shear loadings

This paper presents a generalized constrained differential quadrature method to investigate the elastoplastic dynamic response and ultimate bearing capacity of beam-plate coupled structures under uniaxial compression, compression-bending and compression–shear loadings, considering the interaction between plates and beams. A beam-plate coupled structure is divided into some plate elements, considering the compatibility between contiguous plate elements using the penalty function method which can solve the problem of beam-plate deformable connection of different materials. Virtual work principle and generalized constrained differential quadrature method are used to derive the dynamic governing equations of the beam-plate in which the geometrical and material nonlinearity is considered in the paper. The iterative Newmark/Newton–Raphson method is used to solve the governing equations of the beam-plate. The verification analysis is carried out to demonstrate the accuracy of the proposed method by comparison with the results from FEM. Then, various effects of the rotational spring stiffness, width-to-thickness ratio, aspect ratio, impact time and coupling load on the elastoplastic dynamic response and ultimate bearing capacity of beam-plates are evaluated.

Time-dependent compaction of deep-water reservoirs: A study on the viscous behavior of unconsolidated sandstone

There have been many studies on reservoir compaction where different mechanisms being suggested as the reasons behind the changes of porosity, permeability, and integrity of reservoirs during production. The theory of poroelasticity is often used to evaluate the likelihood of reservoir compaction, however, it has failed to explain the time dependent viscous behavior of unconsolidated formations. In this study, attempts are made to have a closer look into the compaction mechanism of deep-water sandstone reservoirs by bringing a case study from a gas field in Australia. The results obtained indicated that depending on the type of clays presented in the rock matrix, confining pressure and the loading rate, unconsolidated/poorly consolidated sandstone may exhibit an elasto-plastic or viscoplastic behavior during compaction. It was also found that the deformations initiated during compaction is a time-dependent process and can be a function of clay type in the sandstone matrix. It appears that kaolinite pushes the sandstone to exhibit an elastoplastic behavior while sandstones with a huge amount (more than 45%) of illite/smectite show a viscous (time dependent) response to hydrostatic loading. It was also revealed that the viscous behavior is induced once the confining pressure reaches a certain threshold (above 10 MPa). It seems that as the loading rate increases from 0.5 MPa/min to 1 MPa/min, a viscoplastic deformation dominates but an elasto-plastic response is revealed once the loading rate reduces to 0.25 MPa/min. It was concluded that the type of clays and their contribution in the rock matrix should be analysed very carefully to determine the geomechanical responses of deep-water reservoirs under different in-situ stress conditions.

Anisotropic elastoplastic response of double-porosity media

We present a continuum framework to simulate fluid flow through anisotropic elastoplastic media with double porosity. Two effective stress measures σ′ and σ′′ emerge from the thermodynamic formulation, which are energy-conjugate to the elastic and plastic components of strain, respectively. Both effective stress measures can be expressed as a combination of the total Cauchy stress σ and the average pore pressure p¯ in the two pore scales. In the effective stress for elasticity, p¯ is scaled with a rank-2 Biot tensor, whereas the effective stress for plasticity follows the Terzaghi form in which p¯ is scaled by the Kronecker delta. The Biot tensor and storage coefficients are derived as functions of elasticity parameters and porosities. A mixed finite element formulation is introduced to discretize the domain and solve initial boundary-value problems. A stabilization scheme is employed on equal-order interpolation for both displacement and pressure fields throughout the entire range of drainage responses. Numerical simulations reproduce the hydromechanical response of Opalinus shale in one-dimensional consolidation tests throughout the range of primary and secondary consolidation under different external loads. Numerical simulations of the consolidation of a rectangular domain subjected to a strip load demonstrate the efficacy of the proposed stabilization scheme, as well as illustrate the impacts of stress history, mass transfer, and different pore systems on the hydromechanical response.

Irreversibility of soil skeletal deformations: The Pedagogical Limitations of Terzaghi’s celebrated model for soil consolidation

The paper examines the role of irreversibility of skeletal deformations of a consolidating soil and its role in the pedagogy for explaining the development of pore fluid pressures in saturated soils subjected to loading and unloading. The role of irreversibility is demonstrated through the consideration of a one-dimensional consolidation model with an elasto-plastic skeletal response.

A closed-form solution for temperature-dependent elastoplastic problems using the Prandtl operator approach

Finite element simulations of the temperature-dependent stress-strain response in the elastoplastic region of a material usually involve incremental procedures based on the Newton–Raphson iterative scheme. Although essential to obtaining the correct result, iterations inherently extend the computational time of the simulations. In order to increase the computational effectiveness of such finite element simulations, a novel solution technique is presented here, which introduces a closed-form determination of the elastoplastic stress-strain response using the Prandtl operator approach. Using this solution, the iterative procedure is no longer required. The positions of the tensile-compressive and shear meridians of the Haigh–Westergaard coordinate space are first conveniently modified, which then enables the configuration of coordinate-independent play operators. These play operators connect the stress and the strain tensors in a unique closed-form solution that significantly increases the computational power of the simulations, while retaining both the vigorous stability of the procedure and the high accuracy of the results. The method is successfully validated on several load cases, consisting of variable tensile, shear and combined thermomechanical load histories. Limitations of the current version of the approach, that are a part of on-going research, include extremely low values of the third deviatoric strain-invariant increments, in which the directions of movement of the yield surfaces can be changed. Furthermore, the discretisation of the cyclic stress-strain curves plays an important role. The optimal positions of the yield strains are hence another important issue for future studies. Additionally, the consistent material Jacobian results in an unsymmetric form in e.g. Abaqus when engineering shear strains are provided in the simulations and thus the computational power is not fully used. Nevertheless, the results using the Prandtl operator approach, when compared to the results obtained using the conventional, Besseling material model, show excellent agreement, while substantially reducing the computational time by up to 45%.

Experimental and parametric investigation on elastoplastic seismic response of CFST battened built-up columns

Previous studies have proven that CFST (concrete-filled steel tube) battened built-up columns (CFST-BBCs) exhibit good hysteresis energy dissipation capacity and deformation capacity under lateral cyclic repeated loading. To further understand the elastoplastic seismic response characteristics of such composite structures under strong earthquakes, two pseudo-dynamic tests of 1/8-scaled CFST-BBC pier specimens were first performed. The acceleration records obtained in the 1995 Kobe Earthquake and the 2008 Wenchuan Earthquake were used to investigate how ground motion intensity, ground motion characteristics, and aftershocks affect the seismic response of the CFST-BBC pier. Meanwhile, an extensive time-history analysis of 17 fiber-based finite element models (FFEMs) under 20 different ground motions was performed to reveal the influence of the ground motion intensity, the same-intensity aftershock, and the main structural parameters on the elastoplastic seismic response of the CFST-BBC pier. Finally, a two-stage checking method suitable for the seismic performance of the CFST-BBC pier under the E1-level frequent earthquake and the E2-level rare earthquake was proposed. Verified by experimental and FFEM analysis results, the proposed checking method can accurately and effectively evaluate the strength and deformation capacity of the CFST-BBC piers under strong earthquakes.

Development of surrogate predictive models for the nonlinear elasto-plastic response of medium density fibreboard-based sandwich structures

Medium-density fibreboard (MDF) belongs to a class of engineered wood products facilitating efficient use of wood wastes. For this class of materials, the development of predictive models is crucial for the simulation of their responses under mechanical loads. In this study, samples of sandwich structures based on MDF as the skins and a mushroom-based foam as the core are fabricated and tested under edgewise compression tests. Results from the tests support the idea that increasing the thickness of the skins strengthens the response of the sandwich structure against buckling failure, but also revealed that thicker skins are susceptible to complex failure modes. Towards data-driven constitutive modelling of the nonlinear elastic-plastic response of this bio-based structure, predictive models premised on feedforward backpropagation neural network (FFNN), cascade-forward backpropagation neural network (CFNN), and generalized regression neural network (GRNN) were developed. Performance of the models was assessed via error criteria that include the coefficient of determination (R2), root mean squared error (RMSE) and mean absolute error (MAE). Results from the models indicate that CFNN with 15 hidden neurons under the Levenberg-Marquardt backpropagation training algorithm outperformed FFNN and GRNN models, with R2=1.0, RMSE=0.0030 and MAE=0.0019.

Deep long short-term memory neural network for accelerated elastoplastic analysis of heterogeneous materials: An integrated data-driven surrogate approach

In this work, an integrated data-driven surrogate approach based on the finite-volume direct averaging micromechanics (FVDAM) and the long short-term memory (LSTM) neural network is explored to predict the elastoplastic response of composite materials. In particular, the FVDAM is first applied to generate the uniaxial and cyclic response of unidirectional composites with various off-axis orientations. Next, a two-layered neural network is trained to associate the applied strains to the corresponding stresses, which is subsequently evaluated using the separate, hold-out testing dataset. The LSTM-estimated stress–strain responses coincide with the FVDAM reference results for all the loading cases. The advantage of the LSTM to naturally capture the history-dependent stress–strain behavior over the fully connected neural network is presented, with the percentage prediction errors of the former approach an order of magnitude lower than the latter. Moreover, the robustness of the LSTM surrogate model is examined by analyzing the training data with white noise. The proposed framework offers a viable alternative for the determination of the history-dependent response of composites directly from data analysis without the need to understand the underlying deformation mechanism in the techniques of homogenization, as well as provides a foundation for efficient multiscale analysis of composite materials and structures.

Mechanical response of an high-strength automotive steel at different strain rates and evolution of damage-related parameters

The present work concerns a thin sheet high-strength steel of interest for automotive applications. The extended constitutive curves in static and dynamic conditions were determined by tensile tests on smooth specimens. Further tests carried out on notched specimens were simulated both to validate the elastoplastic response and to analyse the evolution of the relevant parameters related to ductile damage (triaxiality and Lode angle) in the critical areas of the specimens (diffuse and localized necking), studying the correlations between the trend of these quantities and the mode/location of the fracture initiation. The analysis of the images of the specimens acquired during the tests allowed to characterize in detail the behaviour of the material up to breakage, also providing different experimental references to validate the numerical simulations of the tests on the smooth and notched specimens.