Non-linear Elasto-plastic Model Research Articles

An elastoplastic damage ice material model based on modified Tsai-Wu yield criterion: Experiment, theory and numerical application

Ice, as a novel green and sustainable building material, has attracted more and more attention in building engineering. Appropriate ice material models are crucial for the performance analysis of the increasing ice structures. There is still challenging in modelling ice responses due to the complexity of ice. This study aims to present a nonlinear elastoplastic damage model for ice material. First, a triaxial compression test of artificial ice is conducted. Based on the test results, the modified Tsai-Wu failure criterion with better performance in the tensile zone and physical meaning for hydraulic strength is established. Then, combining plasticity theory with damage mechanics, an elastoplastic damage constitutive law considering the difference between tensile and compressive properties is proposed. The piecewise damage model and the Weibull exponential damage model are employed for compression and tension damage, respectively. Moreover, the numerical iterative algorithm is developed and a user-defined material subroutine (UMAT) is embedded in the finite element software ABAQUS to simulate the mechanical properties of ice. Furthermore, the constitutive model is verified by comparing the FEM results with the results of uniaxial compression, triaxial compression, and three-point bending tests. The results show that the constitutive model can well describe the stress-strain nonlinear behavior and capture the basic failure mode of ice materials. Finally, considering temperature affecting on the failure surface, a temperature dependent ice material model is developed. The current study would help in the design, operation and maintenance of ice structures.

Topology Optimization and Efficiency Evaluation of Short-Fiber-Reinforced Composite Structures Considering Anisotropy

The current study aims to develop a methodology for obtaining topology-optimal structures made of short fiber-reinforced polymers. Each iteration of topology optimization involves two consecutive steps: the first is a simulation of the injection molding process for obtaining the fiber orientation tensor, and the second is a structural analysis with anisotropic material properties. Accounting for the molding process during the internal iterations of topology optimization makes it possible to enhance the weight efficiency of structures—a crucial aspect, especially in aerospace. Anisotropy is considered through the fiber orientation tensor, which is modeled by solving the plastic molding equations for non-Newtonian fluids and then introduced as a variable in the stiffness matrix during the structural analysis. Structural analysis using a linear anisotropic material model was employed within the topology optimization. For verification, a non-linear elasto-plastic material model was used based on an exponential-and-linear hardening law. The evaluation of weight efficiency in structures composed of short-reinforced composite materials using a dimensionless criterion is addressed. Experimental verification was performed to confirm the validity of the developed methodology. The evidence illustrates that considering anisotropy leads to stiffer structures, and structural elements should be oriented in the direction of maximal stiffness. The load-carrying factor is expressed in terms of failure criteria. The presented multidisciplinary methodology can be used to improve the quality of the design of structures made of short fiber-reinforced composites (SFRC), where high stiffness, high strength, and minimum mass are the primary required structural characteristics.

HTS Tape Mechanical Behavior Sensitivity on Material Properties and Thickness of Material Layers

Multilayer 2G high-temperature superconductor (HTS) tapes undergo various mechanical loading steps as part of a superconducting magnet operation. The mechanical loading steps include cool-down to cryogenic temperatures and Lorentz forces when powering up the magnets. Studying the mechanical behavior of the constituent layers in a HTS tape can reveal the strain or stress level in each layer and help in predicting the probability of mechanical failure or critical current degradation. A detailed finite element method (FEM) -based simulation models enable us to estimate the mechanical behavior in each layer. However, defining the model parameters for material mechanical properties or thickness of each material layer can have consid-erable uncertainty due to variation in manufacturing processes and missing measurements of material properties within these tapes. The material properties in thin layers may not exactly comply with bulk materials of the same kind. In this paper we present a sensitivity analysis for mechanical behavior dependence on material properties variation in the constituent layers of a HTS tape. The results give important insight about the accuracy and reliability of mechanical simulation results and guide the priorities in future material characterization. In addition, we will investigate the effect of the thickness of Hastelloy layer on effective macroscopic mechanical behavior of the tape. A nonlinear elastoplastic FEM model is used for performing the simulations.

Reliability based geometrically nonlinear bi-directional evolutionary structural optimization of elasto-plastic material

The aim of this paper is to integrate the reliability-based analysis into topology optimization problems. Consequently, reliability-based topology optimization (RBTO) of geometrically nonlinear elasto-plastic models is presented. For purpose of performing (RBTO), the volume fraction is considered reliable since that the application of (RBTO) gives different topology in comparison to the deterministic topology optimization. The effects of changing the prescribed total structural volume constraint for deterministic designs and changing the reliability index for probabilistic designs are considered. Reliability index works as a constraint which is related to reliability condition added into the volume fraction and it is calculated using the Monte-Carlo simulation approach in the case of probabilistic design. In addition, bi-directional evolutionary structural optimization (BESO) method is utilized to study the effect of geometrically nonlinear elasto-plastic design. The plastic behavior can be controlled by defining a limit on the plastic limit load multipliers. The suggested work's efficiency is demonstrated via a 2D benchmark problem. In case of elastic material, a 2D model of U-shape plate is used for probabilistic design of linear and geometrically nonlinear topology optimizations. Furthermore, a 2D elasto-plastic model is considered for reliability-based design to demonstrate that the suggested approach can determine the best topological solution.

Characterization and modeling of continuous carbon fiber-reinforced polycarbonate under multiaxial loads

The presented work considers the characterization of a continuous fiber-reinforced thermoplastic (FRTP) with unidirectional plies under quasi-static, multiaxial loading conditions and the modeling of the non-linear mechanical behavior. For the experimental investigation, hoop wound tubular specimens fabricated from carbon fiber-reinforced polycarbonate (CF-PC) tape were tested on an electromechanical static testing machine with an axial and torsional drive. The multiaxial material response was determined for an extensive set of tests performed at several load ratios of in-plane shear to transverse stress. For modeling the non-linear mechanical response, an elasto-plastic framework is used which is kept preferably simple in order to facilitate the application in numerical analysis. Based on the generated experimental data, suitable criteria for fracture and yielding are proposed. The defined yield criterion respects the special characteristics of a FRTP such as the different mechanical behavior under transverse tensile and compressive loading as well as a linear material response in the direction of the fiber reinforcement . Furthermore, the implementation of the proposed model as a user-defined material (UMAT) routine for implicit finite element analysis (FEA) using Abaqus /Standard is described and the calibration of the plasticity approach using only the data of the in-plane shear and transverse compression tests is discussed. The model predictions for multiaxial loads are validated using the determined biaxial material data. • Multiaxial experimental data for a continuous fiber-reinforced thermoplastic • Full dataset of the arithmetic mean stress–strain curves is provided • Selection of a suitable fracture criterion and definition of a yield criterion • Development and implementation of a non-linear elasto-plastic material model • Calibration and validation of the material model using the determined multiaxial data

2D and 3D simulations of static response of a geosynthetic reinforced soil bridge abutment

This paper presents two-dimensional (2D) and three-dimensional (3D) numerical simulations of a half-scale geosynthetic reinforced soil (GRS) bridge abutment during construction and bridge load application. The backfill soil was characterized using a nonlinear elastoplastic model that incorporates a hyperbolic stress–strain relationship and the Mohr–Coulomb failure criterion. Geogrid reinforcements were characterized using linearly elastic elements with orthotropic behavior. Various interfaces were included to simulate the interaction between the abutment components. Results from the 2D and 3D simulations were compared with physical model test measurements from the longitudinal and transverse sections of a GRS bridge abutment. Facing displacements and bridge seat settlements for the 2D and 3D simulations agree well with measured values, with the 2D-simulated values larger than the 3D-simulated values due to boundary condition effects. Results from the 3D simulation are in reasonable agreement with measurements from the longitudinal and transverse sections. The 2D simulation can also reasonably capture the static response of GRS bridge abutments and is generally more conservative than the 3D simulation.

Coupled crash mechanics and biomechanics of aircraft structures and passengers

The DYCAST (Dynamic Crash Analysis of Structures) experiments that started at NASA Langley Research Center during the late 1970s have greatly influenced the methodology and thinking of aircraft crashworthiness and survivability studies, and was continued and refined at other aerospace establishments. Nevertheless, so far most of the existing work has emphasized the impact damage to the aircraft section. Issues related to potential passenger injuries have not been properly addressed in the literature, to the best of our knowledge. Here, we study the DYCAST problem integrally by treating and combining impact damage and passenger injuries altogether. We develop the biomechanics by way of modal analysis of passenger dummy motions coupled with the vibration of aircraft structures in order to understand their basic interactions. Two types of mechanical dummies are used in this study. Such a modal analysis can help identify basic injury types, but is valid only in the constructed models, linear regime. However, we are able to extend the linear elastic model to a nonlinear elastoplastic computational model by using the versatile software LS-DYNA as the platform. Computer simulations are carried out on the supercomputer clusters and the numerical results are rendered into video animations for visualization and analysis. One can see, for example, how the passenger-dummy interactive motions with the fuselage and fixtures and the potential injuries caused in the event of general aircraft crashes on a fractal domain.

Performance Evaluation of Buried Concrete Pipe Considering Soil Pressure and Crack Propagation Using 3D Finite Element Analysis

Numerous factors affect the soil pressure distributions around buried pipes, including the shape, size, and stiffness of the pipe, burial depth, and the stiffness of the surrounding soil. Additionally, to some extent, a pipe can benefit from the soil arching effect, where the overburden and surcharge pressure at the crown can be supported by the adjacent soil. As a result, a buried pipe only needs to support the portion of the load that is not transferred to the adjacent soil. This paper presents numerical investigations of the soil pressure distributions around buried concrete pipes and crack propagation under different environmental conditions, such as loading, saturation level, and the presence of voids. To this end, a nonlinear elastoplastic model for backfill materials was implemented using finite element software and a user-defined subroutine. Three different backfill materials and two different native soils were selected to examine the material-specific behaviors of concrete pipes, including soil pressure distributions and crack propagation. For each backfill material, the effects of the loading type, groundwater, and voids were investigated. These simulation results provide helpful information regarding pressure redistribution and buried concrete pipe behavior under various environmental conditions.

A nonlinear elasto-plastic bond model for the discrete element modeling of woody biomass particles

This work presents an experiment-informed, semi-empirical, elasto-plastic bond model for the discrete element modeling of woody biomass particles. The model renders nonlinear plastic deformation of materials when subjected to compression/tension, bending, and twisting, essential for accurately simulating the behavior of biomass in comminution. The model is implemented in an open-source DEM package LIGGGHTS and is assessed in a number of verification tests. The model is applied to simulate the fracturing test of notched loblolly pine blocks. Reduced bond strength is prescribed to the weak planes along the growth rings. It is found that the square-root formulation for describing the elasto-plastic normal bond contact delivers the best agreement with the experimental data over its linear and quadratic counterparts. Furthermore, the model predicts a strong anisotropic behavior of wood blocks with regard to the grain orientations, indicating that the cutting angle should be an important attribute for the optimization of biomass comminution.

Implicit numerical integration of highly nonlinear plasticity models

When using an implicit numerical integration algorithm to implement a highly nonlinear elasto-plastic constitutive models in FEM simulations, some difficulties would encounter including Jacobian matrix singularity and non-convergence. Based on the composition of the elastoplastic constitutive model and the characteristics of the traditional implicit algorithms, this paper proposes three improved implicit algorithms, namely the Homotopy-Newton-CPPM algorithm, the CG-Newton-CPPM algorithm and the two-stage algorithm, which would contribute to improve the convergence and deal with singularity of the Jacobian matrix. Besides, the convergence and the computational efficiency as well as the accuracy of five algorithms, including a conventional explicit algorithm, a conventional implicit algorithm and three improved implicit algorithms, are compared with reference to numerical simulations of single element tests and multi-element analysis.

Flexural behaviour of back-to-back built-up cold-formed steel channel beams: Experiments and finite element modelling

In cold-formed steel (CFS) structures, the application of back-to-back built-up channel beams is increasing steadily. The increasing demand of CFS sections as a cost-effective design solution has led to the development of CFS built-up sections. These sections take advantage of higher load-carrying capacities and may be used for longer beam spans. Applications include beam members in CFS wall studs, truss members and floor joists. In such an arrangement, the intermediate screw fasteners at discrete points along the length prevent the individual channel sections from buckling independently. However, limited experimental or finite element (FE) analyses have been reported in the literature for back-to-back built-up channel sections under four-point bending. Furthermore, there is limited investigation of the effect of screw spacing for flexural strength. This paper addressees this issue with 12 experimental test results. Two different cross-sections, referred to as BU75 and BU90, were considered with different screw spacings of 1900 mm, 950 mm and 475 mm. Initial geometric imperfections were measured prior to the bending tests. A nonlinear elasto-plastic FE model was then developed, the results of which showed good agreement against the experimental test results. Using the validated FE model, an extensive parametric study was conducted to investigate the effect of screw spacing on flexural strength of such back-to-back built-up CFS channel beams. In total, the results of 108 parametric analyses are reported. Both the experimental and FE results were compared against the design strengths calculated in accordance with the American Iron and Steel Institute (AISI) and Australian and New Zealand Standards (AS/NZS).

Finite element modelling for as-laid embedment of pipeline in clayey sediments

A numerical modelling technique for the estimation of as-laid pipeline embedment in clayey sediments is introduced in the paper. The process of pipe-laying is modelled numerically with the pipe-soil interaction defined using a nonlinear elasto-plastic model, therefore the soil resistance contributed by soil buoyancy can be well considered in the evaluation of as-laid pipeline embedment. The impact of the soil buoyancy in the estimate of as-laid embedment is then quantitatively assessed using the proposed numerical modelling technique, and the results show that the as-laid pipeline embedment can be significantly overestimated if the soil buoyancy is ignored in the analysis.

Numerical investigation of seismic performance of high modulus columns under earthquake loading

This paper presents the result of two-dimensional finite element modeling studies in order to investigate the seismic behavior of high modulus columns in liquefiable soil. Particular attention was paid to the shear stress reduction mechanism of the high modulus columns and the shear strain distribution between soil and columns during earthquake motion. Numerical analyses were performed using a nonlinear elasto-plastic model in Plaxis 2016. The reliability of the numerical simulations was verified through the results of a centrifuge test model designed to investigate the contribution of high modulus columns in liquefaction mitigation. The capability of numerical simulations was assessed primarily through comparison of predicted acceleration-time histories, pore water pressures, and displacements with the measured counterparts. The results of the numerical analysis showed that the presence of the columns did not reduce seismic shear stresses in the soil when compared to the unimproved soil condition and pure shear behavior between soil and column did not develop as expected in the current design methodology.

Fatigue sensitivity to foundation modelling in different operational states for the DTU 10MW monopile-based offshore wind turbine

The importance of foundation modelling for the support-structure fatigue damage estimation of a 10 MW monopile based offshore wind turbine is investigated in different operational states and wind-wave misalignment conditions. Three different models are used: (1) a non-linear elasto-plastic model including hysteretic behaviour effects, (2) a linear elastic model and (3) a non-linear elastic model, using numerical simulations with an aero-hydro-servo-elastic computational tool. Depending on the environmental condition, different dynamic processes dominate the responses. For parked states, deviations between models up to 160% were found. For wind wave-misalignment over 30° in operational cases, differences up to 180% were found for low sea states and 119% for high sea sates. Both nonlinear foundation damping and stiffness formulation have considerable effect on the responses, with hysteretic effects becoming crucial when aerodynamic damping is negligible in the direction of the response. Attention is required when comparing the fatigue damage only at the mudline, as larger variations between the models may occur in the embedded part of the monopile, where the absolute maximum is found.

Impact behavior analysis of carbon fiber reinforced aluminum laminates based on a micro-mechanical damage model

A micro-mechanical damage model is proposed to investigate the low-velocity impact behavior of carbon fiber reinforced aluminum laminates (CARALL). This proposed method is able to study the failure mechanisms of fiber and matrix based on their individual micro stresses, which is more precise than other macro stress damage models. Stress amplification factors are adopted to realize the rapid micro stress calculation of key points in fiber and matrix, and combined with physical failure criteria the progressive degradation of composite stiffness is realized. A nonlinear elasto-plastic model is adopted to study the deformation and fracture of aluminum sheet. The cohesive zone model with a bilinear traction-separation relation is adopted to study the delamination initiation and propagation. The finite element model of impacted CARALL is established on ABAQUS/Explicit platform, and a user-defined material subroutine (VUMAT) is written to implement this proposed model. The predicted structure responses and damage mechanisms show good agreements with experimental results, which helps to obtain the profound understanding of this new kind of hybrid material.

Influence of Porosity on the Mechanical Behavior during Uniaxial Compressive Testing on Voronoi-Based Open-Cell Aluminium Foam.

We have studied an application of the Voronoi tessellation method in the modeling of open-cell aluminium foam under uniaxial compressive loading. The Voronoi code was merged with computer-aided design (CAD) for converting the polyhedral model into an irregular open-cell cellular structure to create porous samples for compression testing simulations. Numerical simulations of the uniaxial compression uniformly over the upper surface of the sample in the z-axis direction at a constant 20 N load was realised. Samples with three different porosities (30%, 60% and 80%) were studied. A nonlinear elasto-plastic material model with perfect plasticity, without hardening, based on the von Mises yield criterion was applied below 10% strain. Corresponding stress–strain curves were observed and the influence of porosity on deformation mechanism was discussed. Samples with higher porosity exhibited significantly higher normal stress under the same load, and increased stress plateaus. An increase of porosity produced an increase of both compressive and tensile stresses and struts exhibited complex stress fields. Voronoi-based modeling was in accordance with experimental results in the literature in the case of the quasi-static condition and linear elastic region (below 1% strain). Further study is necessary to enable the simulation of real dynamic behaviour under all deformation regimes by using the Voronoi tessellation method.

Extended Iwan-Iai (3DXii) constitutive model for 1-directional 3-component seismic waves in liquefiable soils: applicationto the Kushiro site (Japan)

The influence of pore water pressure has to be taken into account when the propagation of seismic waves in saturated soils is simulated, because it controls the strength decrease during the dynamic process and can induce phenomena such as cyclic mobility and liquefaction. The decrease of effective stresses leads to permanent deformation in the soil and damages to the surface structures. This research aims at validating a 1-directional propagation model of 3-component seismic waves (1D-3C) in a horizontally layered soil, in the case of saturated soil. A 3-D non-linear elasto-plastic model for soils is used and the variation of the shear modulus reduction curve with the pore water pressure is taken into account during the seismic event. In the case of multiaxial stress states induced by a 3C seismic motion, if no additional information is available, the modulus reduction curves in shear and compression, normalized with respect to the elastic moduli, are assumed identical, since the Poisson's ratio is supposed to be constant during the process. The multiaxial stress state in saturated soils induced by a 3C seismic motion is analysed for various stress paths. The 1D-3C wave propagation model is used to compute the seismic response of the Kushiro soil profile (Japan). The stratigraphy and geotechnical properties are deduced from in situ and laboratory tests provided by the PRENOLIN benchmark. Numerical results are in correct agreement with the records at the surface in terms of acceleration envelope

Modeling Features of Both the Rupture Process and the Local Tsunami Wave Field from the 2011 Tohoku Earthquake

This paper presents the numerical simulation of the displacement distribution in the source of the 2011 Tohoku earthquake, based on the following assumptions on the geometry and mechanics of the source, and features of the subduction zone structure: displacement in the source is determined by specifying a reduced friction coefficient on the plate interface, considering heterogeneous initial stress state of the medium; source is considered in the framework of the Lay–Kanamori model as two consecutive subsources with deep and shallow location; a nonlinear elasto-plastic model of behavior of the medium under the Mohr–Coulomb yield criterion is applied. For the numerical modeling, a program code FLAC 3D implementing an explicit finite-difference scheme solution is used. The resulting lithosphere displacement distribution was used for computation of the tsunami source for given earthquake. The numerical simulation of the corresponding tsunami wave field was performed.

Stress Distribution of Buried Concrete Pipe Under Various Environmental Conditions

There are numerous factors that affect stress distribution in a buried pipe, such as the shape, size, and stiffness of the pipe, its burial depth, and the stiffness of the surrounding soil. In addition, the pipe can benefit from the soil arching effect to some extent, through which the overburden and surcharge pressure at the crown can be carried by the adjacent soil. As a result, the buried pipe needs to support only a portion of the load that is not transferred to the adjacent soil. This paper presents numerical efforts to investigate the stress distribution in the buried concrete pipe under various environmental conditions. To that end, a nonlinear elasto-plastic model for backfill materials was implemented into finite element software by a user-defined subroutine (user material, or UMAT) to more precisely analyze the soil behavior surrounding a buried concrete pipe subjected to surface loading. In addition, three different backfill materials with a native soil were selected to examine the material-specific stress distribution in pipe. The environmental conditions considering in this study the loading effect and void effects were investigated using finite element method. The simulation results provide information on how the pressures are redistributed, and how the buried concrete pipe behaves under various environmental conditions.

Нелинейная упругопластическая модель коллинеарного удара

Нелинейная упругопластическая модель коллинеарного удара