Arbitrary Loading Histories Research Articles

Elastic-viscoplastic behaviors of polymer-blend geocell sheets: Numerical and experimental investigations

Polymer-blend geocell sheets (PBGS) have been developed as substitute materials for manufacturing geocells. Various attempts have been made to test and predict the behaviors of commonly used geogrids, geotextiles, geomembranes, and geocells. However, the elastic-viscoplastic behaviors of novel-developed geocell sheets are still poorly understood. Therefore, this paper investigates the elastic-viscoplastic behaviors of PBGS to gain a comprehensive understanding of their mechanical properties. Furthermore, the tensile load-strain history under various loading conditions is simulated by numerical calculation for widespread utilization. To achieve this goal, monotonic loading tests, short-term creep and stress relaxation tests, and multi-load-path tests (also known as arbitrary loading history tests) are performed using a universal testing machine. The results are simulated using the nonlinear three-component (NLTC) model, which consists of three nonlinear components, i.e. a hypo-elastic component, a nonlinear inviscid component, and a nonlinear viscid component. The experimental and numerical results demonstrate that PBGS exhibit significant elastic-viscoplastic behavior that can be accurately predicted by the NLTC model. Moreover, the tensile strain rates significantly influence the tensile load, with higher strain rates resulting in increased tensile loads and more linear load-strain curves. Also, parametric analysis of the rheological characteristics reveals that the initial tensile strain rates have negligible impact on the results. The rate-sensitivity coefficient of PBGS is approximately 0.163, which falls within the typical range observed in most geosynthetics.

Stress tensor in the linear viscoelatsic incompressible half-space beneath axisymmetric bodies in normal contact

We present a simple method to determine the stress state in a linear viscoelastic half-space in frictionless unilateral normal contact with an axisymmetric rigid indenter for arbitrary loading histories. The procedure consists in the superposition of elastic solutions for flat punch or parabolic contact along the line load within the framework of the method of dimensionality reduction. We provide simple expressions for all stress components and the hydrostatic pressure gradient, which is of particular interest in the biomechanical field. The method brings advantages especially in its numerical application, since no convolution in time over the entire contact history is necessary.

Machine learning enabled identification of sheet metal localization

The Forming Limit Curve (FLC), which describes the maximum applicable strain before localization, depends on the particular material, but also on the applied load and history of the load. Recent investigations have shown that the non-proportional loading effect on the FLC can be predicted with data-driven or machine-learning-based methods. Here we compare different ML methods to their applicability in predicting localization points under multi-segmented non-proportional loading. Therefore, an FE-based metamodel is developed that allows imposing an arbitrary loading history on sheet metal to predict the point of localization. A series of virtual experiments are conducted with this metamodel to generate a database of bi-linear loading paths that are used for training. Different ML-based methods were used to predict the localization point based on the strain history data. The 1D-Convolutional Neural Network (1D-CNN), with the ability to learn dependency between input features, has the best accuracy in predicting the localization point.

Formulation and implementation of a hypoplastic constitutive model for interface behavior of mechanical joints

The effects of the contact interface must be considered during the design process of the assembly structures connected by mechanical joints. An advanced three-dimensional (3D) constitutive model is needed to describe the complex behavior of the contact interface in a detailed finite element (FE) model. However, the simplified Coulomb friction law, which is a bilinear model without considering the microslip behavior and stiffness degradation, is often applied to the surface-surface contact element for modeling the interface in commercial FE programs. In this paper, a new 3D hypoplastic constitutive model for the nonlinear interface behavior is presented. This model is built on the framework of hypoplasticity developed by Kolymbas and the hypothesis of continuous media. First, the general hypoplastic model is derived based on the kernel formula and several restrictions and simplified according to the characteristics of the contact interface. Then, the coefficients of the model are associated with the widely used physical parameters by combining the model with the initial stiffness ratio, normal contact law and Coulomb law. Benefiting from the hypoplastic theorem, the deduced constitutive model has a simple mathematical formulation in which only five parameters are contained. Simulations of several monotonic and cyclic shear tests show that the model can represent the salient characteristics of the joint interface (e.g. stick/microslip/macroslip behaviors, motion coupling and pressure-dependency). Thus, it can be used to predict the response of the joint interface from arbitrary multi-axial load histories more precisely. The constitutive model is then implemented in a commercial FE program via analysis of a double-beam structure subjected to harmonic excitation. And vibration experiments on several preload levels are performed to validate the effectiveness and the applicability of the proposed model to the real joints. The results calculated from the FE model with the improved reduction techniques are in good agreement with the experimental data.

Accelerated high-cycle phase field fatigue predictions

Phase field fracture models have seen widespread application in the last decade. Among these applications, its use to model the evolution of fatigue cracks has attracted particular interest, as fatigue damage behaviour can be predicted for arbitrary loading histories, dimensions and complexity of the cracking phenomena at play. However, while cycle-by-cycle calculations are remarkably flexible, they are also computationally expensive, hindering the applicability of phase field fatigue models for technologically-relevant problems. In this work, a computational framework for accelerating phase field fatigue calculations is presented. Two novel acceleration strategies are proposed, which can be used in tandem and together with other existing acceleration schemes from the literature. The computational performance of the proposed methods is documented through a series of 2D and 3D boundary value problems, highlighting the robustness and efficiency of the framework even in complex fatigue problems. The observed reduction in computation time using both of the proposed methods in tandem is shown to reach a speed-up factor of 32, with a scaling trend enabling even greater reductions in problems with more load cycles.

Generalized cyclic bond-slip model of rebar embedded in concrete under lateral pressure: Parameter calibration and numerical implementation

For some reinforced concrete members, the bond-slip between rebar and concrete is sometimes affected by the lateral pressure, e.g., the beam-column joint with the axial load induced by the column. For such cases, a cyclic bond-slip behavior taking into account the effect of lateral pressure is of great significance for seismic numerical analysis of these members/structures. So far, however, there is no available numerical approaches which can consider the cyclic bond-slip behavior of RC member under lateral pressure. Therefore, this study presents a generalized bond-slip model, which can consider the effect of cyclic loads and lateral pressure simultaneously. Based on the existing test data, the key parameters of the model are calibrated, so that the model can be used for arbitrary cyclic loading history and is easy to be implemented into existing displacement-based numerical code. Furthermore, a four-node zero-thickness bond element is developed in commercial software ABAQUS. The proposed model is implemented into the bond element and verified by the experimental results. The bond element is preliminarily applied to the force–displacement analysis of reinforcing bars in the beam-column joint, and the feasibility of the model in member-level analysis is discussed based on the numerical results.

Energy Response Characteristics of Laterally Loaded Piles

A bounding surface plasticity p − y model is used to examine the internal energy responses of a laterally loaded pile in static and dynamic simulations. The model response is first compared with those observed in physical centrifuge tests, including monotonic and cyclic loading, in a normally consolidated fine-grained soil. Then, the model is used to examine hypothetical static and dynamic situations. The monotonic load capacities determined by the model and an upper-bound limit analysis method are in agreement with that inferred from the physical test. The work done by external loads in static conditions is principally balanced by the plastic work in the p − y springs and the elastic strain energy in the structural pile elements, which are comparable in the cases examined. The numerical model is capable of reproducing accurately the observed test structural responses as well as the characteristics of plastic energy dissipation. In a dynamic free-vibration simulation, the pile is highly damped as a result of the significant plastic energy dissipation. The simple work-hardening elastic–plastic p − y model is theoretically sound, applicable to arbitrary loading histories, and requires the same level of effort to use as traditional p − y methods.

The Finite Segment Method—A Numerical Rolling Contact Fatigue Life Model for Bearings Subjected to Stochastic Operating Conditions

Abstract Fatigue life calculation in bearings is an issue that has been the focus of decades of research culminating in national and international standards that are easily applicable to a wide variety of applications. However, almost all research has focused on simple, repetitive operating conditions. This paper explains why these approaches are not completely applicable to bearings under certain conditions, particularly not to those with a change in the load position over time undergoing inconstant movement. Based on existing standards, namely ISO 281, the paper then proposes a numerical approach to calculate the life of a bearing under stochastic operating conditions. The bearing life for any arbitrary load history and movement patterns can be calculated using the presented approach. The approach is presented and some example applications are given, notably including the life calculation of a rotor blade bearing in a wind turbine.

A data-driven harmonic approach to constructing anisotropic damage models with a minimum number of internal variables

A data-driven approach is proposed to construct anisotropic damage models with a minimal number of internal variables from numerical simulations on Representative Volume Elements (RVEs) of quasi-brittle materials. The approach resorts in particular to a harmonic analysis of damage. The orientation distribution functions of two elastic moduli are numerically determined while accounting for the effects of the nucleation and propagation of microcracks by the phase-field method. Given these two functions, the effective elastic tensor of a material without or with microcracks is uniquely determined. The expansions into two Fourier series of the relative variations of these two functions related to an undamaged reference state and to a damage state make appear damage internal variables naturally. The number and natures of these variables can be optimized by truncating the Fourier series according to the degree of approximation desired. Thus, 2D and 3D anisotropic damage models can be constructed without resorting to usual assumptions made in damage mechanics. This construction holds for complex microstructures including image-based ones and for arbitrary loading history. Two- and three-dimensional applications are provided to evaluate the accuracy of the damage models constructed and to show the potential of the approach proposed.

A framework for the analysis of fully coupled normal and tangential contact problems with complex interfaces

An extension to the interface finite element with eMbedded Profile for Joint Roughness (MPJR interface finite element) is herein proposed for solving the frictional contact problem between a rigid indenter of any complex shape and an elastic body under generic oblique load histories. The actual shape of the indenter is accounted for as a correction of the gap function. A regularised version of the Coulomb friction law is employed for modeling the tangential contact response, while a penalty approach is introduced in the normal contact direction. The development of the finite element (FE) formulation stemming from its variational formalism is thoroughly derived and the model is validated in relation to challenging scenarios for standard (alternative) finite element procedures and analytical methods, such as the contact with multi-scale rough profiles. The present framework enables the comprehensive investigation of the system response due to the occurrence of tangential tractions, which are at the origin of important phenomena such as wear and fretting fatigue, together with the analysis of the effects of coupling between normal and tangential contact tractions. This scenario is herein investigated in relation to challenging physical problems involving arbitrary loading histories.

A stress-weighted ductile fracture model for steel subjected to Ultra Low Cycle Fatigue

A new criterion is proposed to simulate the initiation of ductile fracture due to Ultra-Low Cycle Fatigue (ULCF). Building on previous research, the new fracture criterion broadens the scope of ULCF models to account for a broader range of multi-axial stress and strain states that may be encountered in steel structures. The model formulation, supported by observations from finite element plasticity simulations of void growth and fractographic analyses of fracture surfaces, describes damage accumulation as a function of plastic strain, stress triaxiality, and the Lode stress parameter. The damage rate model is integrated over arbitrary cyclic loading histories of local strains and stresses to predict ULCF fracture. The proposed criterion (termed the Stress Weighted Ductile Fracture Model – SWDFM) is supported by a series of 66 coupon scale experiments on two grades of low-carbon structural steel (A572 and A36). These tests interrogate a range of positive and negative stress triaxiality with absolute values between 0.1 and 1.6, Lode stress parameters between 0 and 1, and monotonic and cyclic loading histories. The SWDFM criterion, which requires the calibration of only two material parameters for the materials investigated in this study, is evaluated against the experimental test data using an average-error assessment as well as a cross-validation analysis. Three other ULCF rupture criteria are similarly assessed and compared. The SWDFM is shown to accurately predict ULCF initiation over a wide range of stress states and loading histories, suggesting that the model represents well the micro-mechanical mechanisms of ULCF.

A complete analytical solution for axial pipeline walking considering seabed resistance as rigid plastic behaviour

Offshore pipelines are important infrastructure for transporting oil and gas. They are subjected to cycles of high temperature and pressure variation during operation and shutdown periods, and are therefore susceptible to the stability problem of axial walking due to the asymmetry between the expansion and contraction. Axial walking can cause damage to subsea pipeline systems, for instance to the connected manifolds and steel catenary risers. This paper provides a complete analytical solution to examine the process of pipeline walking based on underlying principles of mechanics, considering the pipeline–seabed sliding response as rigid plastic. The analytical solution allows calculation of the cumulative displacement, strain, axial force and soil resistance along the pipeline under arbitrary temperature or internal pressure change histories, accounting for the coupled contributions from seabed slopes and end tension forces. A dimensionless parameter η is proposed to explain the triggering mechanism for walking by comparing the activating force to the soil resistance. New criteria are established to judge whether pipeline axial walking is possible. Calculation examples are presented in the final part of this paper to demonstrate the analytical solution. This study can be used as a rigorous benchmark and a simple practical tool to evaluate pipeline walking under arbitrary loading histories of temperature and internal pressure variations.

A unified direct method for ratchet and fatigue analysis of structures subjected to arbitrary cyclic thermal-mechanical load histories

In this paper, the distinction between material ratchetting and structural ratchetting is clarified, and the concept of constant life diagram is extended to depict low cycle fatigue life boundary in structural design. To provide a novel one-stop solution for structural fatigue and ratchetting problems, a Unified Procedure for Fatigue and Ratchet Analysis (UPFRA) has been proposed. The UPFRA has been successfully applied to two different engineering structures considering complex geometry and temperature-dependent material properties. By comparing the results with ABAQUS step-by-step inelastic analysis, the UPFRA has been verified to be a robust engineering tool with great accuracy, usability, and efficiency.

Smart constitutive laws: Inelastic homogenization through machine learning

Homogenizing the constitutive response of materials with nonlinear and history-dependent behavior at the microscale is particularly challenging. In this case, the only option is generally to homogenize numerically via concurrent multiscale models (CMMs). Unfortunately, these methods are not practical as their computational cost becomes prohibitive for engineering-scale applications. In this work, we develop an alternative formulation to CMMs that leverage state-of-the-art micromechanical modeling and advanced machine learning techniques to develop what we call smart constitutive laws (SCLs). We propose a training scheme for our SCLs that makes them suitable for arbitrary loading histories, making them equivalent to traditional constitutive models. We also show how to implement a SCL into a traditional finite element solver and investigate the response of an engineering-scale component. We compare our results to those obtained via a high fidelity simulation. Our findings indicate that SCLs can dramatically boost the computational efficiency and scalability of computational homogenization for nonlinear and history-dependent materials with arbitrary microstructures, enabling in this way the automatic and systematic generation of microstructurally-informed constitutive laws that can be adopted for the solution of macro-scale complex structures.

On Applications of Semi-Analytical Methods of Contact Mechanics

This paper is concerned with possible applications of semi-analytical methods of frictional contact mechanics. The semi-analytical solutions, such as the Method of Memory Diagrams, enables to write the load-displacement relationship for contact of two axisymmetric bodies with friction as an analytical expression with parameters calculated via a numerical procedure. As a result, a complex history-dependent solution is obtained for an arbitrary loading history in a computationally efficient way. This fact allows one to calculate hysteretic responses to extremely complex loading histories such as random vibrations. Another case when complex loading histories appear is a harmonic excitation of a dynamic contact system in which inertia is taken into account. The both examples are considered here. The random excitation case can be used as a basis for modeling for wear in frictional contacts while the second one may be extended to describe coupled dynamic contact systems, stick-slip phenomena, or friction-induced instabilities.

On relevance of time-dependent Poisson\u2019s ratio for determination of relaxation function parameters

The current study concerns the determination of materialconstants of a three-dimensional linear viscoelastic model. It is assumed that the constitutive equation utilizes a Prony series as a memory function. A method for the evaluation of relaxation function parameters is presented which can be used for arbitrary loading histories. The proposed methodology is applied to the identification of the viscoelastic constants of acrylonitrile butadiene styrene (ABS). For that purpose, a number of rheological tests in tension have been performed on ABS standard dogbone specimens. The significance of the time-dependent Poisson’s ratio for the determination of material parameters is investigated. It is found that taking into account the measurements of specimen’s lateral contraction over time has a particularly strong influence on the identified values of parameters responsible for the bulk behavior. Several boundary value problems have been analyzed in order to assess the influence of the material parameter values on the obtained solutions. It is demonstrated that some oversimplifications assumed during the determination of viscoelastic constants can lead to a loss of precision or even wrong results.

ОСОБЛИВОСТІ ВИКОРИСТАННЯ ІНТЕГРАЛІВ, НЕЗАЛЕЖНИХ ВІД КОНТУРУ ІНТЕГРУВАННЯ, В ЗАДАЧАХ МЕХАНІКИ РУЙНУВАННЯ

In recent decades, the Cherepanov-Rice J-integral has been considered to be the main energy criterion for fracture toughness in solving the problems of fracture mechanics. This parameter is successfully used in the consideration of elastic problems and within the framework of deformation theory of plasticity for stationary cracks. Unfortunately, the theoretical basis on which the J-integral is based does not allow it to be extended to solve problems requiring material inhomogeneity, the presence of temperature influences, an arbitrary load history, mass forces, crack development, and the like. The purpose of the paper is to review other integrals independent of the contour of integration, from the point of view of their theoretical justification, the possibility of experimentally determined and the ease of calculation. The article considers the J-integral, integrals of Wilson-Yu, Gurtins, Blackburn, Kishimoto, Ainsworth, Atluri.

Mechanistic modelling of cyclic voltage-capacity response for lithium-ion batteries

One of the challenging tasks related to lithium-ion batteries (LIBs) remains a comprehensive approach for battery behaviour modelling. An approach is presented that enables modelling the voltage-capacity response of LIBs that are subjected to variable temperature and current load histories. A detailed presentation of the developed macro-scale phenomenological model embedding the mechanistic properties of the Prandtl type hysteresis operator and the concept of the force-voltage analogy is made. The necessary input data preparation for the model calibration is also presented. Accuracy of the model is confirmed with experimental observations for both nested current load history at two different temperatures and for arbitrary current load history. The same measured data is used to calibrate and to simulate response of the first order Thevenin equivalent circuit topology in order to amply compare the obtained results.

Modelling the cyclic elasto-viscoplastic behaviour of polymers

The mechanical behaviour of polymeric materials presents some peculiarities, especially regarding the evolution of their hardening under stresses above the proportional limit. For many types of polymers (Epoxy, Polyamides, Polyvinylidene, etc.) the elastic properties are not rate-dependent, and the behaviour is elasto-viscoplastic. Also, in the case of load-unload tensile tests, preliminary studies show that the kinematic hardening of this kind of material can be much more significant than the isotropic hardening, and a negative plastic strain rate may occur even with a positive stress. Thereby, nonlinear phenomena may occur during tractive load-unload cyclic tests executed above the proportionality limit, leading to dissipation of mechanical energy. The present paper aims at the development of a general elasto-viscoplastic model for polymers, able to describe the progressive accumulation of plastic deformation for an arbitrary loading history. This model considers dissipative phenomena by the coupled effect of the internal variables with nonlinear hardening equations. Since a volume variation can be observed during plastic deformation, a modified von Mises yield criterion that accounts for the influence of the hydrostatic pressure is proposed. All parameters arisen from theory can be identified experimentally from tensile tests with different strain rates and load-unload tensile tests. The model adequacy was tested for particular types of Polyvinylidene fluoride (PVDF) and of Polyamide (PA 12), which are materials commonly used as an internal pressure sheath in offshore flexible pipes in the Brazilian pre-salt basin. One-dimensional numerical simulations were performed aiming to compare the numerical results with the experimental ones, showing a very good agreement.

Analysis of the cyclic tensile behaviour of an elasto-viscoplastic polyvinylidene fluoride (PVDF)

The present paper aims to perform an experimental and theoretical study regarding the inelastic deformation progressive accumulation observed in a polyvinylidene fluoride (PVDF) specimen machined from flexible pipe internal pressure sheaths under cyclic load-unload tensile tests and in monotonic tensile tests. Experiments show that the elastic mechanical behaviour is not rate-dependent because the Young's modulus does not suffer a considerable variation with change in the strain rate. However, the strain hardening induced by the plastic deformation is strongly rate-dependent. Hence, the mechanical behaviour of this polymer is not elasto-plastic or viscoelastic, but elasto-viscoplastic. Also, the kinematic hardening strongly increases with growth of accumulated inelastic strain, making it much more significant than the isotropic hardening. This paper proposes an elasto-viscoplastic mechanical model capable of describing the cyclic and monotonic inelastic behaviour for an arbitrary loading history. The kinenatic hardening observed for this PVDF makes it possible to identify experimentally all material parameters that arise in the model by performing load-unload tests using flat specimens, eliminating buckling problems and the need to control eventual misalignment in the universal test machine grips. Good agreement was noted when comparing the theoretical results with experiments.