Non-linear Strain Hardening Research Articles

A computational approach to modeling flow-induced large deformation of thin-walled compliant vessels

We present a computational method capable of modeling 3D flow-induced deformation of thin, highly compliant, hyperelastic vessels conveying viscous, inertial fluid. The method can uniformly consider vessel extension and collapse. Very large inflation, transient deformation, complex flow features as well as highly complex buckling shapes are well resolved by this method. The methodology combines finite volume and spectral methods for fluid motion, finite element method for structural mechanics of the vessel wall, and the immersed boundary method for two-way coupling between the wall and fluid. A hybrid of the continuous forcing and the ghost node methodologies capitalizing on the strengths of each is developed. The method avoids the surface instability encountered with the continuous forcing methods, as well as the need for domain remeshing as required in the iterative and partitioned approaches. The vessel wall can follow linear or nonlinear (strain softening and hardening) material models, and the fluid inertia can vary over a wide range. We demonstrate the versatility of the method by considering vessel inflation and collapse with large, complex, and transient deformation. Remarkable differences in vessel inflation at low versus moderate inertia are observed; this includes steady versus oscillatory motion, emergence of flow recirculation and pressure wave reflection which are well resolved. For the collapsing vessels, well-defined shapes with different buckling modes as well as highly complex buckling with fine surface folds are predicted. Additionally, a second-order correction to the well-known law of Laplace is developed and used to validate our computational results for vessel inflation.

Cohesive Model Application in the Assessment of Plastic Zone Magnitude for One Particular Case of Crack Loading

The answer of the thin, infinite, central cracked plate, subjected to in-plane loading, is investigated. The plate is made from a ductile metallic material. The two pairs of the concentrate forces, F, act on the crack surface in the direction perpendicular to it. The other edges of the plate, at infinity, are free of loading. The forces, F, open the crack and they are monotonously increased. The small plastic zones around crack tips will appear. It is assumed an isotropic and non-linear strain hardening of a plate material which can be good described by the Ramberg-Osgood´s equation. The investigations were carried out for the several different values of the strain hardening exponent n which is changed among the discrete values n = 2, 3, 4, 5, 7, 10, 15, 25, 50 and 1000. One well-known cohesive model (Dugdale´s model) was applied in the crack tip plasticity investigating. It was assumed that the cohesive stresses within the plastic zone are changed according to non-linear law. Also, a new algorithm was established which enables direct calculation of plastic zone magnitude depending on the magnitude of external loads. The contemporary mathematical tools, like the software package Wolfram Mathematica, were used. The solutions are presented through the special, Gamma and the Hypergeometric functions.

Mechanical Properties of Graphene Composite Materials and Mesonumerical Experiments on the Mechanical Properties of Unsaturated Soil‐Rock Mixtures

Graphene, as an emerging two‐dimensional carbon nanomaterial, has attracted widespread attention and in‐depth research by domestic and foreign researchers. With its excellent mechanical properties, graphene is used as a reinforcing material in polymers, ceramics and rubber, and other matrices, which can significantly improve the toughness of the matrix. However, under the action of natural factors such as continuous rainfall or heavy rain, the accumulation layer landslide is often in an unsaturated state, which is very easy to induce disasters. Based on this background, we use micronumerical simulation methods and graphene composite materials to study the mechanical properties of unsaturated soil‐rock mixtures to understand the mechanical properties of unsaturated soil‐rock mixtures and evaluate and predict its stability. This paper takes the soil of a landslide zone in a certain city as the numerical test object. Through the automatic generation technology of the mesostructure model of the soil‐rock mixture, a series of numerical experiments were carried out on the random mesostructure model of the soil‐rock mixture, and the gravel content was analyzed in depth. Experiments show that the model can reasonably describe the volume expansion of the soil‐rock mixture under low confining pressure, the volume compression under high confining pressure, and the phenomenon that the peak strength of the soil‐rock mixture increases with the increase of confining pressure, which verifies that the model is simulating soil and rock. This shows that the stress‐strain relationship curves of different soil‐rock interface parameters, rock content, saturation, and the number of wet and dry cycles all show obvious nonlinear characteristics and strain hardening. This shows that graphene composites can be used in the study of the mechanics of unsaturated soil‐rock mixtures, which is of great significance for improving the landslide environment and enhancing its mechanical properties.

Study on mechanical properties of high strength sorbite stainless steel S600E under monotonic and cyclic loadings

A new kind of high strength sorbite stainless steel named S600E was developed recently, which has the 65% corrosion resistance, but three times higher yield strength than commonly used austenitic stainless steel S30408. In addition, the price of S600E is only 70% of S30408 owning to the low nickel content of 1.5–2.5%. Fundamental investigations on the mechanical behaviours of S600E were presented in this study. Two monotonic and seventeen cyclic material tests were conducted subjected to different strain-controlled loading protocols including the constant strain amplitude ranging from 0.25% to 2.5%, as well as the varied strain amplitudes. Monotonic test results show that S600E presents the typical feature of rounded nonlinear strain hardening, but the 0.2% proof stress is extremely high, up to 750 MPa, and the elongation after fracture is over 20%. In the cyclic tests, little cyclic hardening was occurred in the initial few cycles, while cyclic softening tended to appear at the remaining cycles. Based on the test results, the isotropic component in the constitute model was neglected, key material parameters for the nonlinear kinematic hardening model with two pairs of backstresses were obtained and validated using the numerical analysis in ABAQUS. At last, the cyclic material properties were compared with commonly used stainless steel to reveal the advantages of S600E. The results of this study could be used in finite element modeling of members, joints and structures of S600E.

Investigation of the thermoelastoplastic behaviors of multilayer FGM cylinders

A finite difference numerical solution for the thermoelastoplastic performance of rotating multilayer (sandwich) cylinders is presented while considering the materials' properties temperature dependency. Each layer is treated as a composite with volume fractions being constant, independent on the position, and unique. The cylinder is rotating with a variable (exponential) angular speed leading to the presence of shear stress. Regarding plasticity analysis, von Mises failure criterion is considered while the constituent materials have a nonlinear strain hardening. Different case studies are examined and discussed. Results revealed that the layers' arrangement and the maximum temperature position substantially influence the cylinder's performance. Additionally, cylinders with smaller size are able to sustain the prescribed loads compared to larger ones.

Implementation and validation of true material constitutive model for accurate modeling of thick-walled cylinder swage autofrettage

The fatigue life prediction and associated fail-safe design of autofrettaged tubes require accurate stress modeling of each specific high-strength thick-walled cylinder during and after the autofrettage process, which depends largely on the elastoplastic behavior of the original steel tubes. However, the complex material behavior is dominated by the Bauschinger effect. Modeling swage autofrettage of such steel tubes remains problematic. This is a crucial issue that has not been resolved by any available modeling software. Therefore, the modeling and design of the autofrettage process for current and future materials depends upon extending the capability of current software.This research aims to develop a user-programmable function (UPF), USERMAT, to realize a user-defined material model that features true material constitutive behavior with the corresponding algorithms for accurate stress analysis of high strength thick-walled cylinders during the autofrettage process. The material constitutive model to be implemented can be formulated with high accuracy via an available material characterization, which can adapt to both nonlinear and linear strain hardening during the initial tensile loading, while the elastic modulus can be reduced during reversed-loading. It also incorporates the Bauschinger effect as a function of the prior tensile plastic strain during the nonlinear compressive reversed-loading phase and fits the experimental data of the true material model. Swage autofrettaged thick-walled cylinder case studies were reported. The results for residual radial and hoop stress and for elastic strain components were compared with independent, available neutron diffraction measurements, and they are in good agreement. Developing and integrating such a UPF into a standard finite element analysis software package is potentially the most significant unsolved fundamental modeling issue relating to re-yielding, fracture and fatigue of modern autofrettaged cylinders and pressure vessels. It can not only provide a fundamental understanding of the deformation mechanism and stress development within the high strength steel tubes during the autofrettage process, but also provide guidance for the design and optimization of the autofrettage manufacturing processes and of material selection for high intensity pressure vessels, a potential market of billions of dollars.

Prediction of slamming pressure considering fluid-structure interaction. Part I: numerical simulations

ABSTRACT Marine structures are subjected to slamming loads characterised by high hydrodynamic pressure within short time durations. Such loads can cause local and global damages to structures. This paper, which is Part I in a series, reports a numerical investigation of slamming loads acting on flat stiffened plates and their dynamic response. The nonlinear explicit finite element code LS-Dyna with the Multi-Material Arbitrary Lagrangian-Eulerian (MMALE) solver was adopted to simulate the slamming impact on marine structures. The numerical method was validated by the relevant experimental data from the open literature in a comparison of slamming pressure and deflection data, as well as existing formulations. The Eulerian formulation was applied to describe the fluid flow, and a Lagrange formulation was employed to model flat stiffened plates. A penalty coupling algorithm was utilised to realise the fluid-structure interaction (FSI) between the plate and the fluid. Bilinear strain hardening with no strain-rate hardening and effect of the heat-affected zone (HAZ) were considered for the numerical simulation of the aluminum model, while nonlinear strain hardening and strain-rate hardening were adopted to verify the steel models. Effects of key influenced parameters such as water impact velocity, material behaviour, and air cushion on the slamming response were addressed accordingly. Additionally, a simulation of water hitting structure was proposed to investigate the slamming load characteristics acting on the bottom decks of offshore structures. As the next paper in this continuing series, Part II will present empirically derived formulations for prediction of slamming loads based on extensive parametric studies of actual scantlings of offshore structures, using the simulation methodology of water hitting proposed herein in Part I.

Strain Rate Dependence of Hardness for PE and SME TiNi Alloys

In this paper, the strain rate dependence of hardening behavior of polycrystalline pseudoelastic (PE) and shape memory effect (SME) TiNi alloy under impact loading was investigated by experiments. Measurements of stress–strain curves, hardening modulus, hysteresis loop area, and temperature variation are synchronized using in situ infrared detector system at the strain rate range from 300/s to 2000/s. It is shown that with the strain rate increasing, for PE specimens, strain rate hardening is observed, while SME specimens perform a strong nonlinear strain hardening. The results of synchronous temperature measurement show that in stress-temperature space, for PE samples, the dynamic transformation path is strain rate independent, but for the SME samples, the opposite is true. Thermal-mechanical coupling does not seem to explain this difference, and hardening from microstructure variation should be considered for such difference.

Bridging chains mediate nonlinear mechanics of polymer nanocomposites under cyclic deformation

Elastomer-based nanocomposites, mixtures of elastomeric rubber with hard nanoparticles, generally exhibit strain stiffening under large strains while also showing strain softening at low strain during large cyclic deformations due to the Mullins Effect. Numerous studies have documented the Mullins effect over the last 50 years, and many models have been developed to explain (and predict) the Mullins effect as it is closely related to material failure. Even with this rich history, relatively few studies have connected experimentally measured changes in nanocomposite chain structure with nonlinear strain hardening and nanofiller dispersion. In this work, we quantify the strain hardening mechanics, and chain anisotropy in situ in silica-filled acrylonitrile butadiene rubber (NBR) nanocomposites under cyclic tensile loading. Macroscopic strain hardening and molecular chain anisotropy increased after the first loading cycle, as a strong Mullins effect appeared, for nanocomposites with sufficient filler volume fraction. In composites with low filler content, we observed little increase in strain hardening or chain anisotropy and a barely-visible Mullins effect. Our results provide strong experimental support that chain delamination from the filler surface is related to the Mullins effect in nanocomposite materials.

A new nonlinear viscoelastic model and mathematical solution of solids for improving prediction accuracy

We developed an innovative material nonlinear viscoelastic model with physical mechanism and mathematical solution to improve existing ones. The relaxation modulus transits from the glassy stage to the rubbery stage through a time-dependent viscosity in a continuous spectrum considering the nonlinear strain hardening. Experimental results of differential solid materials including asphalt concrete, agarose gel, vaginal tissue, polymer, agar, bone, spider silk, and hydrogel demonstrate that the developed model is superior to generalized Maxwell model or Prony series for more accurate prediction outside of the range for data fitting while using much less model parameters. Numerical simulation results indicate that the new model has improved accuracy. It is stable numerically, and does not reduce computation speed. Therefore, the model may be used to simulate a broad range of viscoelastic solids for predicting experimental data and responses with improved accuracy.

Design and simulation studies on the development of a high pressure cell upto 1.0 GPa for industrial and scientific metrological application

Abstract The accurate, precise and traceable measurements are always considered the prime issues in any metrological and scientific applications. Another important issue is the safety and handling of the parts, components, equipments and devices, especially in high pressure metrology. If design parameters of the high pressure instruments are not optimized, tested and maintained properly, sometimes it can be very dangerous and lead to fatal accidents. Therefore, a thorough design analysis is essentially required to avoid such accidents. In the present paper, authors describe the results obtained on the design and simulation studies carried out on a pressure cell under high pressure conditions upto 1.0 GPa. A mathematical model based on elasto-plastic material behavior with nonlinear strain-hardening was adopted and used for determining the maximum bearing pressure. The optimization of the design parameter such as thickness of pressure cell is performed and validated using finite element analysis (FEA). The thickness of pressure cell is considered 5.5 mm and the stress values have been compared with and without autofrettage process. A significant improvement in the stresses due to the autofrettage in the cylinder is observed. The findings revealed that with the applied load of 1 GPa, maximum stress generated is 1908.2 MPa, 1045.5 MPa for without consideration of autofrettage and with consideration of autofrettage respectively. The strain distribution is evaluated to know the behavior of the strain pattern over the periphery of the pressure cell. The pressure cell thus designed and optimized is very useful and would find applications in pressure measurements by measuring the strain across the periphery as a function of applied pressure. Further work on the experimental testing and development as a pressure sensor is undergoing and would be reported in due course.

Nonlinear material and geometric analysis of thick functionally graded plates with nonlinear strain hardening using nonlinear finite element method

The present paper deals with three dimensional nonlinear geometrically and elastoplastic analyses of thick functionally graded plates with nonlinear strain hardening. The boundary conditions are assumed to be general. The plate consists of ceramic (SiC) and metal (Al) phases varying smoothly through the thickness. The effective elastic material properties are obtained by Mori-Tanaka scheme where the plastic behavior of the FG plate is described by the von-Mises yield criterion, nonlinear isotropic strain hardening and the Prandtl-Reuss constitutive equations in combination with the TTO model. The governing equations are obtained from the incremental theory of plasticity in conjunction with the Green-Lagrange nonlinear kinematics. In order to investigate the nonlinear elastoplastic response of the FGM, the nonlinear graded finite element method is developed from three-dimensional continuum concepts that admit arbitrarily large displacements and rotations. This formulation has been implemented and the effect of material gradient index, boundary conditions and thickness-to-length ratio on the nonlinear elastoplastic analysis of the FG plate as well as the development of plastic zone are presented and discussed.

Is pallial mucus involved in oyster defense against the parasite Bonamia ostreae?

The present paper deals with three dimensional nonlinear geometrically and elastoplastic analyses of thick functionally graded plates with nonlinear strain hardening. The boundary conditions are assumed to be general. The plate consists of ceramic (SiC) and metal (Al) phases varying smoothly through the thickness. The effective elastic material properties are obtained by Mori-Tanaka scheme where the plastic behavior of the FG plate is described by the von-Mises yield criterion, nonlinear isotropic strain hardening and the Prandtl-Reuss constitutive equations in combination with the TTO model. The governing equations are obtained from the incremental theory of plasticity in conjunction with the Green-Lagrange nonlinear kinematics. In order to investigate the nonlinear elastoplastic response of the FGM, the nonlinear graded finite element method is developed from three-dimensional continuum concepts that admit arbitrarily large displacements and rotations. This formulation has been implemented and the effect of material gradient index, boundary conditions and thickness-to-length ratio on the nonlinear elastoplastic analysis of the FG plate as well as the development of plastic zone are presented and discussed.

More accurate mathematical description in the assessment of plastic zone magnitude around the crack tip

The thin infinite central cracked plate, made of ductile metallic material, is observed. The plate is loaded with uniformly distributed continuous loading, according to the Fig. 1a. The small plastic zones around crack tips will appear. It is assumed anisotropic and non-linear strain hardening of a plate material which can be good described by the Ramberg-Osgood equation. The investigations were carried out for the several discrete values of the strain hardening exponent n, i.e. for n = 3, 5, 7, 10, 25, 50 and 1000. The magnitude of plastic zone is investigated on the basis of the premises of the Dugdale´s cohesive model. In the frame of applied cohesive model, the problem is formulated fully exact. The analytical methods were applied. Our intention is to contribute in a more accurate mathematical description of the phenomena occurring within the cohesive zones and to solve the problems, in so called closed-form, without any additional assumptions, as for example, about small plastic zones (SSY), elastic-perfectly plastic material and so on. The commercial software Wolfram Mathematica 7.0 is used and the solutions are presented through the special, the Gamma and the Hypergeometric functions.

Modified Kocks–Mecking–Estrin Model to Account Nonlinear Strain Hardening

The dislocation density-based model after Kocks–Mecking–Estrin (KME) is widely used to characterize the thermally activated plastic deformation and dislocation kinetics. According to the model, the slope of the stress–strain curve decreases linearly with stress, which contradicts the experimental observation. In the current study, the evolution of dislocation density in the model is generalized to account for the nonlinearity of the slope.

A mathematical model for fitting and predicting relaxation modulus and simulating viscoelastic responses.

We propose a mathematical model for relaxation modulus and its numerical solution. The model formula is extended from sigmoidal function considering nonlinear strain hardening. Its physical meaning can be interpreted by a macroscale elastic network-viscous medium model with only five model parameters in a simpler format than the molecular-chain-based polymer models to represent general solid materials. We also developed a finite-element (FE) framework and robust numerical algorithm to implement this model for simulating responses under both static and dynamic loadings. We validated the model through both experimental data and numerical simulations on a variety of materials including asphalt concrete, polymer, spider silk, hydrogel, agar and bone. By satisfying the second law of thermodynamics in the form of Calusius-Duhem inequality, the model is able to simulate creep and sinusoidal deformation as well as energy dissipation. Compared to the Prony series, the widely used model with a large number of model parameters, the proposed model has improved accuracy in fitting experimental data and prediction stability outside of the experimental range with competitive numerical stability and computation speed. We also present simulation results of nonlinear stress-strain relationships of spider silk and hydrogels, and dynamic responses of a multilayer structure.

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

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

Preparation and rheological characterization of long chain branching polylactide

Long chain branching (LCB) of polylactide (PLA) was successfully prepared by the successive reactions of PLA with pyromellitic dianhydride (PMDA) and 1,4-phenylene-bis-oxazoline (PBOZ) together. The topological structures of the LCB generated from functional group reactions were investigated thoroughly by gel permeation chromatography (GPC) and rheology. Qualitative information about the branching structures could be readily obtained from linear viscoelasticity, nonlinear oscillatory shear experiments and strain hardening in elongational experiments. For quantitative information on chain structure, linear viscoelasticity combined with branch-on-branch (BOB) dynamic model was used to predict probable compositions and chain topologies of the products, which were reasonably explained by the suggested mechanism of functional group reactions. It was found out that the star-like LCB structure generated in these reactions contributed remarkably to the enhancement of strain hardening under elongational flow.

Parallel blast simulation of nonlinear dynamics for concrete retrofitted with steel plate using multi-solver coupling

The blast damage behaviors for concrete panels retrofitted with steel plates exposed to blast loading are investigated. In order to enhance the reliability of the simulation results, the equation of state, strength, and failure model of materials are implemented in an explicit analysis program, AUTODYN. In particular, the implemented formulation includes the rate-dependent plasticity and damage softening; the non-linear strain and strain-rate hardening and non-linear strain softening. Furthermore, simplified and idealized 2D axis-symmetry, 3D, and parallel 3D simulations are compared in order to achieve accurate and efficient computation running times using multi-solver coupling method. Comparing the 2D axis-symmetry and 3D models, 2D model is stiffer and has a smaller deflection than the 3D models by geometries of retrofit material. The result of 3D numerical simulation becomes mesh size dependent, because of the explosive characteristics and mechanical properties of concrete. The parallel 3D simulation shows good scalability up to 15 processors and can be simulated at very high speed-up, while still consuming a reasonable amount of run times. Also, the retrofitted concrete panels are compared to the non-retrofitted concrete panel; maximum deflection and maximum deflection ratio are reduced by 1 mm, 3 mm, and 5 mm thick steel plates, scabbing can be prevented by retrofitted with steel plates. The simulation result shows good agreement with the experimental result. Finally, discussion on the numerical results with respect to code criteria and damage localization in retrofitted concrete panels is presented.

A cell-centered Lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries

A finite volume cell-centered Lagrangian formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor–corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke’s law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative Eulerian and Lagrangian hydrocodes in addition to analytical and experimental results are made to validate the current approach.