Elastic-perfectly Plastic Material Model Research Articles

On elastoplastic behavior of porous enamel–An indentation and numerical study

The micro/nano pores in natural mineralized tissues can, to a certain extent, affect their responses to mechanical loading but are generally ignored in existing indentation analysis. In this study, we first examined the void volume fraction of sound and caries lesion enamels through micro-computed tomography (micro-CT). A Berkovich indentation study was then carried out to characterize the effect of porous microstructure on the mechanical behavior of the human enamels. The indentation tests were also modeled using the nonlinear finite element analysis technique to simulate indentation load-displacement curves, which showed reasonable agreement with the experimental measurements. From the simulation results, the extent of densification in the plastic zone was identified and the corresponding stress and contact pressure evolutions were quantified. Further, a conventional elastic-perfectly plastic material model without considering micropores was also developed to investigate the compaction effect of the porous structure. The simulation results reveal that conventional elastic perfect-plastic constitutive models become less reliable to model the mechanical behavior of carious lesion enamel with increasing loss of mineral content as it underestimates the yield stress and plastic energy dissipation. This study divulges the importance of compaction of porous enamel structure beneath the indented area. Note that understanding the effect of porous microstructures on plastic behavior is vital as the involved inelastic deformation mechanism associated with irreversible processes, such as wear and localized microcracking, has a significant bearing on wear and fatigue behavior of enamel. Statement of significanceBased on micro-CT and nano-indentation characterization, a numerical model was developed aiming to precisely describe the deformation behavior of naturally porous enamel. Inelastic properties and energy dissipation characteristics of porous enamel were investigated in detail. This work demonstrated that the existence of micro-pores in White Spot Lesions (WSLs) contributes to mechanical stability, which can mitigate the reduction in Young's modulus and fracture toughness resulting from loss of mineral components. The knowledge gained from this study can be used to explain the mechanisms related to irreversible processes, such as contact induced cracking and wear, and strengthen understanding of the mechanical behavior of porous mineralized tissues.

System Reliability of a Semi-Submersible Drilling Rig Considering the Effects of the Main Nodes

In this paper, structural systems reliability analysis was used to estimate the system reliability of a typical semi-submersible based on the characteristic structure failure mechanisms under extreme wave loads. First, a three-dimensional simulation model was created for the chosen semi-submersible platform using an elastic-perfectly plastic material model, neglecting the effect of the strain hardening assumption. Then, under design wave conditions, and characteristic structural failure mechanisms of a semi-submersible platform were examined, and a system reliability model was developed based on the failure mechanism of the chosen platform. Finally, system reliability methods were used to determine the platform’s system reliability. It was discovered that the main node’s system reliability makes a significant contribution to the overall structure reliability, so it is strongly advised that the reliability of the main nodes be taken into account when determining the overall structure’s reliability. This research aims to apply reliability theory in offshore engineering and, ideally, to encourage the reliability-based design of semi-submersible platforms and other similar structures.

A Practical Analysis Framework for Assessment of Printed Circuit Heat Exchangers in High-Temperature Nuclear Service

Abstract Printed circuit heat exchangers (PCHEs) have high thermal efficiency because of the numerous minuscule channels. These minuscule channels result in a high thermal exchange area per unit volume, making PCHE a top contender for an intermediate heat exchanger (IHX) in high-temperature reactors. Thousands of minuscule channels make finite element analysis of the PCHE computationally infeasible. A two-dimensional analysis is usually performed for the PCHE core, which cannot simulate the local channel level responses reasonably because of the absence of global constraint influence. At present, there is no analysis technique available in the ASME Code or literature that is computationally efficient and suitable for engineers to estimate PCHE local responses. A novel but practical two-step analysis framework is proposed for performing PCHE analysis. In the first step, the channeled core is replaced by orthotropic solids with similar stiffness to simulate the global thermomechanical elastic responses of the PCHE. In the second step, local submodel analysis with detailed channel geometry and loading is performed using the elastic-perfectly plastic (EPP) material model. The proposed two-step analysis technique provides a unique capability to estimate the channel corner responses to be used for PCHE performance assessment. This study first developed a methodology for calculating the elastic orthotropic properties of the PCHE core. Next, the two-step analysis is performed for a realistic size PCHE core, and different issues observed in the results are scrutinized and resolved. Finally, a practical finite element analysis framework for PCHEs in high-temperature nuclear service is recommended.

Behaviour and design of welded stainless steel beams with compact sections under flexure and shear

The present study explores the flexural and shear behaviour of welded stainless steel beams with compact sections. A total of eleven specimens fabricated with austenitic, duplex and lean duplex stainless steel were tested under four-point and three-point loading strategies to obtain their failure modes, bearing capacities and ductility performance. Three-dimensional finite element models were then developed and validated with experimental results to numerically investigate the flexural and shear performance of the compact stainless steel beams. The obtained results from tests and numerical simulations were synthesised to comprehensively assess the applicability of existing codes of practice in terms of the bending, shear and moment-shear interaction design. It is found that the current design guidance for stainless steel beams adopts the elastic-perfectly plastic material model and conservatively predicted the bending, shear, as well as combined moment-shear strength. Accordingly, revised design methods considering the strain hardening effect of stainless steel beams were proposed.

The elastic modulus reduction method for upper bound limit analysis of pressure vessels incorporating material strain hardening effect

Pressure vessel is a kind of special equipment which is involved in various industries. Once it is damaged, it will cause great loss to people’s life and property. The traditional elastic modulus reduction method for upper bound limit analysis of pressure vessels adopts the elastic-perfectly plastic material model. This method will result in waste of materials without considering the material strain hardening effect. So the material strain hardening effect is introduced into upper bound limit analysis. Firstly, the equivalent yield strength considering material strain hardening effect is established. Then, the formula of limit load multiplier which is expressed by the equivalent yield strength is derived based on the upper bound theorem. Combined with the strategy for elastic modulus adjustment, the elastic modulus reduction method for upper bound limit analysis of pressure vessels incorporating material strain hardening effect is constructed. The limitation of the elastic-perfectly plastic model for the upper bound analysis method is eliminated by the method proposed in this paper. The result calculated by this method is closer to the true limit load of pressure vessels.

Theoretical Local Buckling Behavior of Thin-Walled UHPC Flanges Subjected to Pure Compressions.

To enhance structural performance of concrete and reduce its self-weight, ultra-high-performance concrete (UHPC) with superior structural performance has been developed. As UHPC members with 180 MPa or above of the compressive strength can be designed, a rational assessment of thin-walled UHPC structural member may be required to prevent unexpected buckling failure that has not been considered while designing conventional concrete members. In this study, theoretical local buckling behavior of the thin-walled UHPC flanges was investigated using geometrical and material nonlinear analysis with imperfections (GMNIA). For the failure criteria of UHPC, a concrete damaged plasticity (CDP) model was applied to the analysis. Additionally, an elastic-perfectly plastic material model for steel materials was considered as a reference to establish differences in local buckling behavior between the UHPC and steel flanges. Finite element approaches were compared and verified based on test data in the literature. Finally, this study offers several important findings on theoretical local buckling and local bending behavior of UHPC flanges. The inelastic local buckling behavior of UHPC flanges was mainly affected by crack propagation due to its low tensile strength. Based on this study, possibility of the local buckling of UHPC flanges was discussed.

Determination of Collapse Load of Engineering Structures using Iterative Node-based Smoothed Finite Element Analysis Method

This paper presents an iterative limit analysis scheme modeled within a three-node node-based smoothed finite element framework incorporating a so-called modified elastic compensation method to determine the ultimate bearing capacity of ductile structures. More explicitly, the approach iteratively reduces those elemental Young’s modulus associated with a high-stress intensity such that the inelastic behavior of the elastic-perfectly plastic material model is taken into account. The approach provides good accuracy and convergence of solution through a series of standard linear elastic analyses that make possible the application in large-scale engineering structures, even the one with complex geometric configurations, and hence eminently accessible to structural engineers. As a result, complex inelastic analyses are eliminated and computational cost is significantly reduced. Several benchmark examples, one of which reported, illustrates the efficiency and robustness of the iterative limit analysis approach in tracing the load multipliers of in-plane ductile structures from the beginning until convergence of collapse load solution or failure state occurs. The yield areas at the ultimate state gradually appear in the graph of elastic modulus distribution.

Numerical evaluation of buckling in steel pipe piles during vibratory installation

The buckling of steel pipe piles during installation is numerically studied. Generally, numerical simulation of installation processes is challenging due to large soil deformations. However, by using advanced numerical approaches like Multi-Material Arbitrary Lagrangian-Eulerian (MMALE), such difficulties are mitigated. The Mohr-Coulomb and an elastic-perfectly plastic material model is used for the soil and pile respectively. The pile buckling behavior is verified using analytical solutions. Furthermore, the model is validated by an experiment where a pipe pile is driven into sand using vibratory loading. Several case scenarios, including the effects of heterogeneity in the soil and three imperfection modes (ovality, out-of-straightness, flatness) on the pile buckling are investigated. The numerical model agrees well with the experimental measurements. As a conclusion, when buckling starts, the penetration rate of the pile decreases compared to the non-buckled pile since less energy is dedicated to pile penetration given that it is spent mainly on buckling.

Spring back of infinite honeycomb sheets beyond plastic deformation

Cellular structures are promising for applications where high stiffness and strength are required with the minimal use of material. They are often used in applications where the plastic deformation plays an important role, such as those involving crashworthiness, energy absorption, and stents. The elastic analysis of a honeycomb sheet has been carried out in the past [1]. The present analysis extends this classical work in the elasto-plastic regime. Recoil analysis due to elastic recovery is absent from the published literature. This work aims to develop an analytical model to calculate the spring back for a simplified case, that of an infinite honeycomb sheet. An elastic-perfectly plastic material model is assumed. The recoil for a clamped beam with a load and moment applied at the free edge is analytically calculated first. This is carried out by relating the stress distribution of the cross section to the final deformed shape. The part corresponding to the elastic contribution is subsequently subtracted in order to obtain the final configuration after the external load is removed. This simple elasto-plastic analysis is then incorporated into the analysis of an infinite sheet made of uniform hexagonal cells. The translational symmetry of the lattice is exploited along with the analysis of a beam under tip loading through to plastic stage and recoil. The final shape of the struts upon the removal of the remote stress is completely determined by the plastic deformation which cannot be recovered. The expression for the beam thus obtained is then used to build an analytical model for an infinite honeycomb sheet loaded in both directions.

Nonlinear inelastic response history analysis of steel frame structures using plastic-zone method

A beam–column element formulation and solution procedure for nonlinear inelastic analysis of planar steel frame structures under dynamic loadings is presented. The spread of plasticity is considered by tracing the uniaxial stress–strain relationship of each fiber on the cross section of sub-elements. An elastic perfectly-plastic material model with linear strain hardening is employed for deriving a nonlinear elemental stiffness matrix, which directly takes into account geometric nonlinearity and gradual yielding. A solution procedure based on the combination of the Hilber–Hughes–Taylor method and the Newton–Raphson method is proposed for solving nonlinear equations of motion. The nonlinear inelastic time-history responses predicted by the proposed program compare well with those given by the commercial finite element package known as ABAQUS. Shaking table tests of a two-story steel frame were carried out with an aim to clarify the inelastic behavior of the frame subjected to earthquakes generated by the proposed program. A more practical analysis method for seismic design can be developed by comparing it with the presented frames for verification.

Evaluation of Cutting Forces During Single Pass Microtrenching of Poly (Methyl Methacrylate)

Research was conducted to evaluate a microtrenching process to create microchannels on the surface of poly (methyl methacrylate) (PMMA) for applications in tissue engineering. Experiments with a trenching tool included an exaggerated cutting edge radius (48 μm) to study the impact of a highly negative effective rake angle on forces during single pass microtrenching at subradius cutting conditions. During microtrenching, forces were measured by dynamometer and compared to a finite element (FE) model using an elastic-perfectly plastic material model for an undeformed chip thickness from 9 to 64 μm. During experiments, cutting was first observed when the ratio of undeformed chip thickness to cutting edge radius was 0.33. Measured and predicted values of thrust force exceeded cutting force up to an undeformed chip thickness equivalent to the cutting edge radius. The FE model predicted a linear trend in cutting force with feed (r = 0.99) and was substantiated by linear regression of experimental data (r = 0.99). However, at lower values of feed the model overestimated force, with a maximum difference of 42% at a feed of 22 μm. Thrust force was also predicted to be linear (r = 0.99), but at greater feed the experiments indicated a nonlinear decline in thrust force, resulting in a maximum difference of 27% at 64 μm. Finally, an analysis of nodal velocity plots from the FE model revealed a material stagnation zone developed along the cutting edge, rising from the workpiece surface in proportion to feed and then remaining fixed at 63 deg (stagnation angle) for all feeds greater than 35 μm. While the application of an elastic-perfectly plastic material model for PMMA was sufficient to predict microtrenching forces by the FE method, differences between predicted and measured thrust forces at greater undeformed chip thickness implies a more complex rheological model may add value.

A nominally second-order cell-centered Lagrangian scheme for simulating elastic–plastic flows on two-dimensional unstructured grids

In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic–plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs the von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.

Progressive failure analysis of composite pi joint with 3D FE modeling

Aimed at the complex failure modes of composite pi joint, the material elastic modulus degradation method was applied to simulate the progressive failure procedure. A three-dimensional finite element model of one type composite pi joint was established based on the commercial finite element software Abaqus. Two progressive failure analysis subroutines considering both the composite laminates and adhesive failures were developed within Abaqus/Standard. One of them is based on Hashin three-dimensional failure criteria and Ye-delamination criterion to distinguish five failure modes of composite laminates: fiber breakage, fiber buckling, matrix tensile cracking, matrix compression, and delamination failure. The other is based on Tsai-Wu criterion to discriminate the composite failure. Additionally, an elastic-perfectly plastic material model was applied in the subroutines to simulate the adhesive failure. The established pi joint model was analyzed under given increasing tensile loads. The numerical results s...

Eigenstrain modelling of residual stresses generated by laser shock peening

This paper presents an eigenstrain (misfit strain) model of the residual stresses generated by laser shock peening (LSP). The shock wave is first modelled as a dynamic pressure load in an explicit finite element (FE) model and the stabilised plastic strain distribution is extracted. This strain distribution is then incorporated as an eigenstrain distribution in a static FE model and the residual stresses generated by the original shock wave are obtained as the elastic response to the eigenstrain. In order to focus on the basic mechanics, an elastic-perfectly plastic material model is assumed. Similarly, a simplified pressure/time variation (a triangular ramp with the peak pressure occurring at the half the total pulse duration) is assumed in order to characterise the pressure pulse. The peak pressure and the duration of the pressure pulse are determined in a way that they are consistent with experimental results. The analysis is extended to study the case of multiple pulses and the results show that the process generates compression in a surface layer of about 1.5–2mm deep. Furthermore, the results demonstrate that the magnitudes of subsurface tensile stresses are of the order of one fifth of the material's yield strength for typical peening conditions.

A comparison of plastic collapse and limit loads for single mitred pipe bends under in-plane bending

This paper presents a comparison of the plastic collapse loads from experimental in-plane bending tests on three 90° single un-reinforced mitred pipe bends, with the results from various 3D solid finite element models. The bending load applied reduced the bend angle and in turn, the resulting cross-sectional ovalisation led to a recognised weakening mechanism. In addition, at maximum load there was a reversal in stiffness, characteristic of buckling. This reversal in stiffness was accompanied by significant ovalisation and plasticity at the mitre intersection. Both the weakening mechanism and the post-buckling behaviour are only observable by testing or by including large displacement effects in the plastic finite element solution. A small displacement limit solution with an elastic-perfectly plastic material model overestimated the collapse load by more than 40% and could not reproduce the buckling behaviour. The plastic collapse finite element solution, with large displacements, produced excellent agreement with the experiment. Sufficient experimental detail is presented for these results to be used as a benchmark for analysts in this area. Given the robustness of non-linear solutions in commercial finite element codes and the ready availability of computing resources, it is argued that pressure vessel code developers should now be recommending large displacement analysis as the default position for limit and plastic collapse analyses, rather than expecting engineers to anticipate weakening mechanisms and related non-linear phenomena.

Design by analysis of ductile failure and buckling in torispherical pressure vessel heads

Thin shell torispherical pressure vessel heads are known to exhibit complex elastic–plastic deformation and buckling behaviour under static pressure. In pressure vessel Design by Analysis, the designer is required to assess both of these behaviour modes when specifying the allowable static load. The EN and ASME boiler and pressure vessel codes permit the use of inelastic analysis in design by analysis, known as the direct route in the EN Code. In this paper, plastic collapse or gross plastic deformation loads are evaluated for two sample torispherical heads by 2D and 3D FEA based on an elastic-perfectly plastic material model. Small and large deformation effects are considered in the 2D analyses and the effect of geometry and load perturbation are considered in the 3D analysis. The plastic load is determined by applying the ASME twice elastic slope criterion of plastic collapse and an alternative plastic criterion, the Plastic Work Curvature criterion. The formation of the gross plastic deformation mechanism in the models is considered in relation to the elastic–plastic buckling response of the vessels. It is concluded that in both cases, design is limited by formation of an axisymmetric gross plastic deformation in the knuckle of the vessels prior to formation of non-axisymmetric buckling modes.

Resistance of stainless steel CHS columns based on cross-section deformation capacity

A conceptually new structural design approach has recently been proposed by the authors to predict the resistance of stainless steel members subjected to various types of loading with cross-sections formed from thin flat plates including angles, channels, lipped channels, I-sections and rectangular hollow sections (RHS). The proposed method does not follow the traditional cross-section classification approach, which primarily relies on the assumption of a bilinear, elastic–perfectly-plastic material model. Instead, deformation capacity of a cross-section is determined directly from the local buckling characteristics of the constituent plate elements. This is then used to obtain the corresponding local buckling stress utilising an appropriate material model. This basic concept is extended herein to predict compression resistance of stainless steel columns with circular hollow sections (CHS). Available test and finite element (FE) results have been used to develop the basic design equation to predict the compression resistance of cross-sections and to propose column curves to determine flexural buckling resistances. The predicted resistances have been compared to those obtained using the current Eurocode; the predictions are significantly more accurate and more consistent than those given by the existing Eurocode.

Effect of underloads or overloads in fatigue crack growth by crack-tip blunting

Crack-tip blunting under tensile loads and re-sharpening of the crack-tip during unloading is one of the basic mechanisms for fatigue crack growth in ductile metals. Here, based on an elastic-perfectly plastic material model, crack growth computations are continued up to 700 full cycles by using re-meshing at several stages of the plastic deformation. A compressive underload in one of the cycles tends to increase the rate of cyclic crack growth, and this effect is studied in detail for a single underload, based on the blunting re-sharpening mechanism. Subsequently, the increased rate of crack growth due to periodically occurring underloads is analysed. A single overload has the opposite effect of giving a significant delay in the subsequent fatigue crack growth. An analysis is carried out to compare the effect of a small overload to that of a larger overload.

Overload effects in fatigue crack growth by crack-tip blunting

A basic mechanisms for fatigue crack growth in ductile metals is that depending on crack-tip blunting under tensile loads and re-sharpening of the crack-tip during unloading. In the present paper, the effect of an overload in one of the cycles is studied based on this mechanism. In a standard numerical analysis accounting for finite strain, it is not possible to follow the blunting/re-sharpening process during many cycles, as severe mesh distortion at the crack-tip results from the huge geometry changes developing during the cyclic plastic straining. Here, based on an elastic-perfectly plastic material model, crack growth computations are continued up to 700 full cycles by using remeshing at several stages of the plastic deformation. Crack growth results for purely cyclic loading are compared with predictions for cases where an overload is applied, and it is shown how crack growth slows down after the overload. Different load amplitudes, and an overload at different cycle numbers are considered.

Elastic and elastic-plastic finite element analysis of hollow tubes with axisymmetric internal projections under combined axial and pressure loading

This paper discusses the behaviour of hollow tubes with axisymmetric internal projections subjected to combined axial and internal pressure loading. Predictions from an extensive elastic and elastic-plastic finite element analysis are presented for a typical geometry and a range of loading combinations, using a simplified bilinear elastic-perfectly plastic material model. The axial loading case, previously analysed, is extended to cover the additional effect of internal pressure. All the predicted stress and strain data are found to depend on the applied loading conditions. The results are normalized with respect to material properties and can therefore be applied to geometrically similar components made from other materials, which can be represented by the same material models.