Elastic-plastic Material Model Research Articles

CT-Based Micro-Mechanical Approach to Predict Response of Closed-Cell Porous Biomaterials to Low-Velocity Impact

In this study, a new numerical approach based on CT-scan images and finite element (FE) method has been used to predict the mechanical behavior of closed-cell foams under impact loading. Micro-structural FE models based on CT-scan images of foam specimens (elastic-plastic material model with material constants of bulk aluminum) and macro-mechanical FE models (with crushable foam material model with material constants of foams) were constructed. Several experimental tests were also conducted to see which of the two noted (micro- or macro-) mechanical FE models can better predict the deformation and force-displacement curves of foams. Compared to the macro-structural models, the results of the micro-structural models were much closer to the corresponding experimental results. This can be explained by the fact that the micro-structural models are able to take into account the interaction of stress waves with cell walls and the complex pathways the stress waves have to go through, while the macro-structural models do not have such capabilities. Despite their high demand for computational resources, using micro-scale FE models is very beneficial when one needs to understand the failure mechanisms acting in the micro-structure of a foam in order to modify or diminish them.

Determination of Mechanical Properties of Methyl Methacrylate Adhesive (MMA)

Abstract Experimental testing of epoxy adhesives, which are commonly used in civil engineering for the strengthening of existing structures with composite products have been a topic of limited studies. It was due to the damage which usually occurred not in the adhesive layer but in the strengthened material. Recent studies have shown that the choice of an adhesive significantly affects the load-bearing capacity of the entire joint. The paper presents the results of strength tests of a selected methyl methacrylate adhesive, carried out according to the standards EN ISO 527-1 and EN ISO 527-2. Comparing the results to the data provided by the manufacturer (tested in accordance with ASTM D638) discrepancies have been found in the normative assumptions and consequently differences in the results. Experiments on the adhesive showed clear dependency on the speed of testing which revealed through variable characteristics after the elastic limit. Numerical simulations were also carried out assuming the elastic-plastic material model. The analyses allowed to obtain the distribution of stresses and deformations along the length of the sample and allowed to verify the length of the extensometer used. Comparison of results obtained for different measuring lengths of chosen adhesive confirmed the need to use extensometers in the testing of mechanical properties.

Five node pyramid elements for explicit time integration in nonlinear solid dynamics

Pyramid finite elements have become increasingly popular to facilitate meshing due to their distinctive shape and innate ability to transition naturally between elements with quadrilateral and triangular faces. This is especially important for explicit time integration, as the alternative of constraints can be problematic for wave propagation applications frequently modeled by such methods. Although formulations to alleviate singularity problems near the apex node have existed for decades, pyramid elements are not available in typical explicit solid dynamics software. Several 5-node pyramid approaches are evaluated herein for suitability as transition elements in lumped mass explicit methods for nonlinear solid dynamics. Several typical pyramid elements generated from both hexahedral shape functions and with Bedrosian rabbit functions are extended to explicit temporal methods by the development of mass lumping and critical time increment estimation schemes. Standard and uniform strain hexahedrons are also degenerated into a pyramid by simple nodal duplication in the connectivity. A focus of the study is on the viability of using only existing hexahedron capabilities typically available in many explicit codes. Performance is assessed in standard benchmark problems and practical applications using various elastic and elastic-plastic material models and involving large strains/deformations, severe distortion, and contact-impact. Examples first evaluate the elements on their own and then for the principal case as transitions within a hexahedral-dominant model. Row-summation mass lumping is shown to be the best method for any pyramid element approach, which may require slight coding changes for degenerated hexahedrons. The results indicate that it may also be a good systematic method for mass lumping of general degenerate hexahedral types. The single quadrature point standard and Bedrosian pyramid elements are also found to be robust and the best performers, particularly requiring significantly fewer computations than the degenerated uniform strain hexahedron. If used properly, however, all element types are demonstrated to perform satisfactorily (and identically) and thus demonstrate their viability and benefits for practical applications using hexahedral-dominant meshing.

On catastrophic fracture of steel structures at temperatures lower than cold brittleness threshold

The paper considers crack propagation in elements of homogeneous steel structures and those with welded joints. For analysis of failure of the structures, diagrams of quasi-brittle fracture have been plotted. When constructing quasi-brittle fracture diagrams, the model of elastic-plastic material having an ultimate strain was used. The data report for quasi-brittle fracture diagrams of common elements of structures has been given. Analysis of parameters used in the proposed model was carried out for temperatures near or lower the brittleness threshold. Parameters of the model are selected from two laboratory experiments (critical stress intensity factor and classical stress-strain diagram) performed at appropriate temperatures. It has been established that weld structures with cracks in the vicinity of a welded joint exhibit decreased crack toughness. The effect of structure break under monotonic loading conditions is clearly visible inasmuch as ultimate loads essentially decrease with increasing a crack length. The attention is given to the parameter characterizing plastic material deformation and exhaustion of plasticity resource under preliminary plastic material deformation. After the plasticity resource is exhausted, the temperature of brittleness threshold approaches a room temperature.

Numerical studies of cavitation erosion on an elastic–plastic material caused by shock-induced bubble collapse

We present a study of shock-induced collapse of single bubbles near/attached to an elastic–plastic solid using the free-Lagrange method, which forms the latest part of our shock-induced collapse studies. We simulated the collapse of 40 μm radius single bubbles near/attached to rigid and aluminium walls by a 60 MPa lithotripter shock for various scenarios based on bubble–wall separations, and the collapse of a 255 μm radius bubble attached to aluminium foil with a 65 MPa lithotripter shock. The coupling of the multi-phases, compressibility, axisymmetric geometry and elastic–plastic material model within a single solver has enabled us to examine the impingement of high-speed liquid jets from the shock-induced collapsing bubbles, which imposes an extreme compression in the aluminium that leads to pitting and plastic deformation. For certain scenarios, instead of the high-speed jet, a radially inwards flow along the aluminium surface contracts the bubble to produce a ‘mushroom shape’. This work provides methods for quantifying which parameters (e.g. bubble sizes and separations from the solid) might promote or inhibit erosion on solid surfaces.

Theoretical prediction of the progressive buckling and energy absorption of the sinusoidal corrugated tube subjected to axial crushing

A theoretical study is conducted to predict the progressive buckling and energy absorption of the sinusoidal corrugated tube subjected to axial crushing. Based on the super folding element theory, the stationary plastic hinge mechanism is proposed. The theoretical prediction of the progressive buckling and energy absorption is proposed by taking the eccentricity factor and amplitude factor into account. In the theoretical analysis, the idealized elastic-plastic material model is adopted and strain hardening effect is employed. Also, the new lower bound and upper bound of the solutions for the mean crushing force are obtained. The theoretical result can predict the crushing behavior of the circular tube which produces the axisymmetric ring mode under axial crushing. The mean crushing force is related to the eccentricity factor and the amplitude factor, but the total energy is independent of the eccentricity factor. The theoretical results are compared well with the numerical and experimental results of previous studies. The theoretical predicts of corrugated tube produce excellent characteristics in term of force-consistent and low crushing force and provide a reference to the research of the progressive buckling and energy absorption of corrugated tube subjected to axial crushing.

Prediction of yield strength of MWCNT/PP nanocomposite considering the interphase and agglomeration

The yield strength of multi-walled carbon nanotube/polypropylene (MWCNT/PP) nanocomposite of 2wt% is predicted using a two-scale continuum model. In the nano-scale, FE models of representative unit cells (RUCs) consisting of MWCNT agglomerates, the surrounding PP matrix and the interphase between them are developed using TexGen software and ANSYS Workbench. The geometries of the agglomerates were determined from processing and analysis of scanning electron microscopy images of the MWCNT/PP material. The characteristics of the interphase were determined from atomic force microscopy images and nanoindentation tests conducted on MWCNT/PP specimens. The FE models of the RUCs were solved using the LS-DYNA explicit FE code. The non-linear behavior of the PP material was modeled using an elastic-plastic material model for which input data were obtained from uniaxial tension tests. The simulated behavior of the RUCs was assigned to the elements of the FE model of a tension specimen which was used to predict the yield strength of the MWCNT/PP material. The model predictions show a high sensitivity of yield strength with the characteristics of the MWCNT/PP interphase.

A Numerical Analysis of Selected Elastic-Plastic Fracture Parameters for DEN(T) Plates under Plane Strain Conditions

This paper provides a numerical analysis of selected parameters of fracture mechanics for double-edge notched specimens in tension, DEN(T), under plane strain conditions. The analysis was performed using the elastic-plastic material model. The study involved determining the stress distribution near the crack tip for both small and large deformations. The limit load solution was verified. The <i>J</i>-integral, the crack tip opening displacement, and the load line displacement were determined using the numerical method to propose the new hybrid solutions for calculating these parameters. The investigations also aimed to identify the influence of the plate geometry and the material characteristics on the parameters under consideration. This paper is a continuation of the author’s previous studies and simulations in the field of elastic-plastic fracture mechanics [4, 6, 16, 17, 31].

Investigation of the Influence of the Projectile Design on the Armor Penetration of Homogeneous Steel Barriers

Рассматриваются результаты математического моделирования процесса бронепробития однородной стальной преграды бронебойно-подкалиберным снарядом с учетом результатов моделирования внутренней и внешней баллистики. На основе модели упругопластичной среды решена задача проникания снаряда в преграду. Параметрические исследования показали, что для штатного заряда конечная скорость снаряда при подлете к цели и глубина пробития стальной преграды имеют немонотонный характер в зависимости от массы активной части снаряда и, соответственно, от диаметра бронебойного сердечника.

Too Sharp for its Own Good – Tool Edge Deformation Mechanisms in the Initial Stages of Metal Cutting

Metal cutting simulations have become an important part of cutting tool design and the research in the field in general. One of the most important aspects of modeling is the accuracy of the tool geometry. 3D microscopy is used for measuring the tool edge radius with good accuracy. However, especially with sharp tools, i.e. small tool edge radii, the measurements, no matter how accurate, are not much of a use, since the initial wear, or deformation is so fast in the first 1-30seconds into the cutting, that the tool geometry is significantly different than the one measured from the new tool. The average tool life is often set to 15minutes. Therefore, the cutting simulations that only predict the tool behavior in the first seconds of its lifetime are not very useful in predicting the process variables throughout the tool life. Simulations with creep and elastic-plastic material model however, can predict the initial deformation of the tool. This tool shape can be then used in rigid tool model to predict the process variables in the steady wear region of the tool life. This paper presents simulation model for predicting the initial tool edge deformation for WC-10%Co tool while machining AISI 304 stainless steel. The novelty in this approach is the simultaneous coupled calculation of contact surface temperature and stress and change of the tool shape.

Elasto-plastic Damage Analysis Based on Strain-space Plasticity

Continuum Damage Mechanics (CDM) is an evolving area of Solid Mechanics. CDM has been found to have great potential. Most of the plastic damage models attempt to bring together the theories of plasticity and CDM. In this paper, the strain-space plasticity theory is implemented for elastic-plastic damage material model in the framework of non-linear finite element analysis. In the stress space plasticity models the yield surface, loading and unloading criteria, flow rule, and often hardening rules are defined in stress space. The research paper presents a set of systematic formulations for the theory of isotropic elasto-plastic ductile damage. Lemaitre's model is considered for the damage evolution growth. The plastic flow and damage flow are coupled within the potential function. In order to verify the formulations presented, numerical results are compared with the results available in literature.

Investigation of a process simulation method for flexible clamping of sheet metal parts

Abstract Flexibility in the body-in-white shop can be increased with the use of a running clamping technology, which enables clamping with a welding robot during laser welding. Unlike common clamping fixtures, the running clamping technology is operated force controlled. A closed gap between flanges is necessary to achieve a proper weld seam. The objective of the presented FE-simulation method is to predict required clamping forces to close the gap between sheet metal part flanges with geometrical inaccuracies. For calibration of the simulation model, clamping experiments with simple geometry are used. Steel and aluminum L-specimens are manufactured using air bending and clamped with the running clamping technology. Clamping forces are measured precisely using a load cell, which has been integrated into the running clamping technology. In this contribution a FE-simulation method for process analysis of the flexible clamping process with the running clamping technology is investigated. For clamping simulation, specimens are generated by air bending simulation, as well as by optical measurement of experimentally manufactured specimens. Since specimens are bent during clamping process in the opposite direction of the previous bending process, influences of residual stresses and kinematic hardening on the required clamping forces are expected. Thus, in FE-simulation an elastic-plastic material model with kinematic hardening parameters is used. A mapping method with springback compensation is applied to obtain specimens with optically measured geometry including forming history data of bending simulation. Simulation setups are investigated regarding results of clamping forces. Simulation results are verified using the obtained experimental data.

Thermo-mechanical behavior of polyethylene under mechanical loads at cryogenic and elevated temperatures

For the design of a polymer liner in a high-pressure vessel, experimental and numerical analyses of high-density polyethylene (HDPE) are conducted under tensile and compressive loads. The effect of temperature on the mechanical behavior of the HDPE is investigated experimentally in a range of 223K to 373K. For tensile and compression tests, specimens are cut out of a prototype polymer liner, which is to be developed for automobile high-pressure hydrogen tanks. The specimens include manufacturing influences of the future used liner. Investigating the effect of temperature numerically in a finite element analysis, two different material models are taken into consideration to represent the thermo-mechanical behavior of the HDPE: an elastic-plastic material model with isotropic hardening and a hyperelastic material model. The results of the finite element analyses are compared with the experimental results in the entire temperature range. Temperature-dependent impacts of the tension-compression asymmetry are quantified experimentally and numerically for the mechanical behavior of polyethylene.

Finite element modeling of superplastic co-doped yttria-stabilized tetragonal-zirconia polycrystals

Yttria-stabilized tetragonal-zirconia polycrystals (Y-TZP) have been shown to have superplastic properties at high temperatures, opening a way for the manufacture of complex pieces for industrial applications by a variety of techniques. However, before that is possible, it is important to analyze the deformation and fracture mechanisms at a macroscopic level based on continuum theory. In this paper, an elastic-plastic material model with a theoretical large deformation is constructed to simulate the true stress-true strain relationships of superplastic ceramics. The simplified constitutive law used for the numerical simulations is based on piecewise linear connections at the turning points of different deformation stages on the experimental stress-strain curves. The finite element model (FEM) is applied to selected tensile tests on 3-mol%-Y-TZP (3Y-TZP) co-doped with germanium oxide and other oxides (titanium, magnesium, and calcium) to verify its applicability. The results show that the stress-strain characteristics and the final deformed shapes in the finite element analysis (FEA) agree well with the tensile test experiments. It can be seen that the FEM presented can simulate the mechanical behavior of superplastic co-doped 3Y-TZP ceramics and that it offers a selective numerical simulation method for advanced development of superplastic ceramics.

Revealing complex aspects of compressive failure of polymer composites – Part II: Failure interactions in multidirectional laminates and validation

The compressive failure of multidirectional laminates can be considered as an interaction of four failure mechanisms: fiber kinking, fiber splitting, matrix cracking and delamination. The interaction of these four failure mechanisms is responsible for the macroscopically observed nonlinear behavior and ultimate failure of the structure.In this paper, a numerically efficient 3D Finite Element modeling approach is presented combining the benefits of homogenizing material models and micromechanical modeling strategies. The micro model is used to resolve the regions which are prone to fiber kinking. In all other regions, a single UD ply is considered as a continuum (i.e. in a homogenized way) and the material properties are represented using a transversely-isotropic constitutive model. At both scales, fully 3D elastic–plastic material models regarding nonlinearities and failure under multiaxial loading conditions are used.With this approach, the progressive failure of multidirectional laminates under compressive loading can be simulated in detail considering the complete kinking process and the progression of kink bands. The sequence and interaction of the different failure mechanisms is studied and discussed. In order to validate the numerical results, the nonlinear stress–strain response and ultimate failure stress of selected carbon epoxy laminate layups is predicted and compared with experimental results.

Validation of a temperature-gradient-dependent elastic-plastic material model of ice with finite element simulations

A temperature-gradient-dependent elastic-plastic material model of ice is proposed for the numerical study of the influence of temperature-gradient on impact force in ship-iceberg collisions. The model is based on the ‘Tsai-Wu’-type yield surface, and an empirical failure criterion is adopted. A series of yield surfaces with different sizes but the same shape are obtained from the linear interpolation of test results to represent the continuous temperature range in an iceberg. Temperature dependence is defined as the change in ice properties due to the temperature gradient as a function of depth of the iceberg. Based on field test data, three types of iceberg temperature profiles are assumed. The ice model is implemented as a user-defined subroutine in the commercial explicit finite element code LS-DYNA. Collisions between a rigid plate and different geometric iceberg shapes are simulated to analyse the influence of iceberg geometry and ice model temperature. The calculated contact area-pressure curves are compared with design laws to further calibrate the proposed ice model. Both a sharp temperature profile and low temperature range can increase the local contact pressure and global contact force as the penetration increases. The simulation results show that the ice model can capture and be used to demonstrate the influence of temperature-gradient on contact force in ship-iceberg collisions.

An elastic-plastic iceberg material model considering temperature gradient effects and its application to numerical study

To simulate the FPSO-iceberg collision process more accurately, an elastic-plastic iceberg material model considering temperature gradient effects is proposed and applied. The model behaves linearly elastic until it reaches the ‘Tsai-Wu’ yield surfaces, which are a series of concentric elliptical curves of different sizes. Decreasing temperature results in a large yield surface. Failure criteria, based on the influence of accumulated plastic strain and hydrostatic pressure, are built into the model. Based on published experimental data on the relationship between depth and temperature in icebergs, three typical iceberg temperature profiles are proposed. According to these, ice elements located at different depths have different temperatures. The model is incorporated into LS-DYNA using a user-defined subroutine and applied to a simulation of FPSO collisions with different types of iceberg. Simulated area-pressure curves are compared with design codes to validate the iceberg model. The influence of iceberg shape and temperature on the collision process is analyzed. It is indicated that FPSO structural damage not only depends on the relative strength between the iceberg and the structure, but also depends on the local shape of the iceberg.

Discretization effects in the finite element simulation of seismic waves in elastic and elastic-plastic media

Presented here is a numerical investigation that (re-)appraises standard rules for space/time discretization in seismic wave propagation analyses. Although the issue is almost off the table of research, situations are often encountered where (established) discretization criteria are not observed and inaccurate results possibly obtained. In particular, a detailed analysis of discretization criteria is carried out for wave propagation through elastic and elastic-plastic media. The establishment of such criteria is especially important when accurate prediction of high-frequency motion is needed and/or in the presence of highly non-linear material models. Current discretization rules for wave problems in solids are critically assessed as a conditio sine qua non for improving verification/validation procedures in applied seismology and earthquake engineering. For this purpose, the propagation of shear waves through a 1D stack of 3D finite elements is considered, including the use of wide-band input motions in combination with both linear elastic and non-linear elastic-plastic material models. The blind use of usual rules of thumb is shown to be sometimes debatable, and an effort is made to provide improved discretization criteria. Possible pitfalls of wave simulations are pointed out by highlighting the dependence of discretization effects on time duration, spatial location, material model and specific output variable considered.

Advanced analysis of crack tip plastic zone under cyclic loading

The different types of plastic zones found at a crack tip under cyclic loading of a commercially available aluminium alloy are studied based on 3-dimensional finite element simulations and mechanical testing. During the experiments, the local strain field at the crack tip is computed based on digital image correlation analysis of the specimen’s surface under different load levels. The simulations with an elastic-plastic material model (bilinear isotropic hardening) predict the experimental surface strain field at the crack tip pretty well. The combination of experimental results and finite element analysis allows for the accurate distinction into monotonic and cyclic plastic zone, and moreover, into backward cyclic plastic zone and forward cyclic plastic zone. Furthermore, it is possible to calculate the energy accumulation ahead of the crack tip which represents a very useful quantitative measure for the analysis of local fatigue damage accumulation inside the plastic zone ahead of a crack tip.

Second-order finite elements for Hex-Dominant explicit methods in nonlinear solid dynamics

Hexahedral-dominant modeling approaches strike a balance of meshing ease and accuracy/efficiency by exploiting wedge (and/or pyramid) elements to transition from hexahedral elements to volumes filled by other types. Unfortunately, first-order wedges are frequently very poor performers and are the only ones typically contained in explicit solid dynamic programs. The historic preference of first-order elements with explicit methods has frequently been for simplicity and cost, but has also been from the lack of both a satisfactory consistent nodal loading distribution and an acceptable mass lumping technique for serendipity elements. Row summation lumping, for example, produces negative and zero vertex node masses for the popular fifteen and eighteen node wedges, respectively, and zero vertex nodal loads from a uniform traction on the triangular faces. The paper first presents twenty-one node wedge element formulations that produce all positive nodal loads from uniform tractions and row summation mass lumping for this element is shown to produce all positive nodal masses. In addition, they are compatible with other second-order elements applicable to lumped mass explicit methods. Performance is assessed in standard benchmark problems and practical applications using various elastic and elastic-plastic material models and involving very large strains/deformations, severe distortions, and contact-impact. These wedge elements are evaluated on their own as well as part of hexahedral-dominant meshes that use wedges for fill regions and transition from hexahedral to tetrahedral elements. In all cases, these elements performed satisfactorily and thus demonstrate their viability and benefits for practical applications, especially for fill and transition regions of low interest.