Elastoplastic Constitutive Equations Research Articles

Elastoplastic finite element simulation of domino fault formation associated with tilting of highly structured ground

Ground deformation on the Earth’s surface layer is strongly affected by the nonlinearity of geomaterials. However, the formation process of such deformation has yet to be described in a unified manner based on mechanics. The present study focuses on the normal faults in a submarine ground with highly developed soil skeleton structures and attempts to reproduce the process of normal fault formation associated with the tilting of a horizontally deposited submarine ground using an elastoplastic finite element simulation. The simulation was conducted using the soil–water coupled finite deformation analysis code GEOASIA, which incorporates an elastoplastic constitutive equation of the soil skeleton based on the modified Cam-clay model and the soil skeleton structure concept. The key findings are as follows:1) Normal faults are formed from the ground surface to depth as shear bands, where shear strain is localized while exhibiting softening behavior with plastic volume compression.2) Multiple normal faults are almost equally spaced and parallel to each other, with the inter-fault blocks rotating backward. The morphology of normal faults formed by the tilting of the ground shows domino-style characteristics.3) The degree of the soil skeleton structure influences the formation of normal faults.This study demonstrates that elastoplastic geomechanics can explain the formation process of ground deformation, which has usually been interpreted from the perspectives of geomorphology and geology.

A convex cone programming based implicit material point method

For conventional Material Point Method (MPM), both explicit-based and implicit-based MPM have shortcomings: explicit MPM has high requirements on time steps, and implicit MPM has high requirements on convergence. To circumvent these limitations, this paper innovatively proposes a convex cone programming-based implicit MPM (CP-MPM) algorithm, which ensures excellent convergence of solving complex problems involving large deformation, regardless of the chosen time step. In the proposed CP-MPM, the governing equations are initially transformed into a stationary point of a multivariable functional, leveraging the generalized Hellinger-Reissner (HR) variational principle. This stationary point problem is subsequently reformulated as a min-max convex cone optimization problem, with constraints originating from elastoplastic constitutive equations. In addition, a novel particle-based adhesive-frictional contact algorithm is proposed to effectively tackle the interaction between MPM domain and rigid bodies. The contact inequality between material points and rigid bodies is transformed into convex cone constraints, which rigorously prevent material point penetration and facilitate the imposition of irregular boundary conditions. Both elastic and elastoplastic problems involving contact under static or dynamic loading are ultimately represented as standard second-order cone programming (SOCP) problems, which is effectively solved by employing the Primal-Dual Interior Point (PDIP) method. The robustness, accuracy and convergence of the proposed method are validated through a series of elastic and elastoplastic benchmark problems. All results demonstrate the CP-MPM is a very promising method for implicitly solving complex practices.

Study on predicting rolling contact fatigue of pitch bearing raceway in offshore wind turbine

Pitch bearing is the critical component that are widely used to ensure the operation of offshore wind turbine blades and enable efficient capture of wind energy. Uncertain environmental factors and extreme load conditions can induce early fatigue failure in pitch bearings, and lead to major accidents such as blade detachment. In this study, a damage coupling fatigue simulation model, considering residual stress (RS) and surface hardness effect, was constructed following the continuum damage mechanics (CDM) to investigate the rolling contact fatigue (RCF) of pitch bearing under ultimate loading conditions. Different ultimate loading conditions were calculated on an integrated load simulation platform established using Python script. The damage-coupled elastoplastic constitutive equation and damage-controlling equations considering RS and surface hardness were derived and programmed in the material user subroutine UMAT. The effects of ultimate loading conditions, RS, and surface hardness on RCF were studied. Results show that increasing the surface hardness or increasing the compressive RS enhances the anti-fatigue performance of pitch bearing.

In situ experimental characterization and numerical investigation of Fe-TiB2 Steel Matrix Composite behavior considering fully coupled damage model: Simulation during incremental forming process

The recent and increasing use of Steel Matrix Composites (SMCs) reinforced with titanium particles (TiB2) in engineering applications highlights the need for a deeper understanding of their behavior under various complex loading and forming processes. This paper aims to predict the mechanical behavior related to damage of SMC of reinforced with TiB2 via both experimental techniques and numerical investigations. In situ four-point bending test conducted on Fe-TiB2 SMC highlights a rather heterogeneous plastic deformation accompanied by TiB2 mono and polycrystalline transgranular rupture under bend loading. A fully coupled damage model is considered to simulate the progressive failure and deformation behavior of Fe-TiB2 SMC undergoing plastic deformation and applies it to an incremental forming process. The proposed elastoplastic constitutive equations incorporate a non-linear mixed (isotropic and kinematic) hardening with isotropic damage model. The identified damage parameters obtained provide a satisfactory prediction of composite incremental forming capability and illustrates valuable guide to predict Fe-TiB2 composite sheet's behavior deformation via an SPIF (Single-Point Incremental Forming) process.

Subloading-elastoplastic constitutive equation of glass

Elastoplastic constitutive equation of glass is proposed in this article, which is formulated based on the subloading surface model which possesses the various distinguished advantages for the description of the plastic deformation, i.e., the smooth elastic-plastic transition, the continuous variation of the tangent stiffness modulus tensor, the automatic controlling function to attract the stress to the yield surface during the plastic deformation process, etc. It would be the firstly proposed three-dimensional elastoplastic constitutive equation of glass, which is furnished with the basic properties, e.g. the ellipsoidal yield surface with the dependence of the third deviatoric stress invariant, undergoing the flattering to the deviatoric direction with the plastic compression and the plastic volumetric hardening with the associated flow rule. The validity of the description of the deformation behavior of glass will be verified by comparisons with some test data for silica glass specimens.

Novel procedure to determine the stress-strain relation of Lithium-ion Batteries through indentation test

This study proposes a novel approach to convert the load–depth curve measured in the experimental indentation test into stress–strain curves. Due to the lack of the tensile test results for the cylindrical lithium-ion battery (LIB) cell, a combination of the analytical analysis and the inverse optimization approach is first conducted as a reference point to determine the elastoplastic constitutive equation, which can predict the response of cylindrical LIB cell cells under the cylindrical indenter. The obtained load-depth curves from the robust optimization algorithm are in good agreement with the experimental loading–unloading curves. This novel approach includes a new definition of the contact area between the cylindrical indenter and the cylindrical LIB cell. Finite element models validate the measured contact area values from the analytical approach. The analytical approach in this study can accurately capture the stress–strain curve validated with optimization results. Afterward, different single indentation tests are conducted to estimate the reduction of Young’s modulus through the increasing indentation depth. Noteworthy, a definition of the indentation strain can physically interpret the indentation strain in the case of two crossed cylinders. The cell voltage is measured during the indentation test to detect the internal short circuit in the LIB cell. In homogenized modeling, the damage of the LIB cell is considered, which is an essential indicator of the internal short circuit of a LIB cell and possible thermal runaway.

A computational framework based on 3D microstructure modelling to predict the mechanical behaviour of polycrystalline materials

In this work, a computational framework is proposed to predict the microstructure sensitive mechanical behaviour of polycrystalline materials i.e., fatigue crack initiation life and anisotropic deformation behaviour. A methodology is developed to generate 3D microstructural RVEs using Laguerre tessellation technique in Abaqus software at a particular location of the component. In any commercial software (Abaqus), the modelling of morphology of 3D polycrystalline microstructures is quite challenging due to the complex geometries of grains, and large number of interfaces or grain boundaries, however it can be achieved efficiently and automatically with the developed methodology. The continuum damage mechanics based elasto-plastic constitutive model is used to predict the microstructure sensitive fatigue crack initiation life of titanium alloy notched specimens. To capture an accurate fatigue response, damage coupled elasto-plastic constitutive equations are implemented via user defined material subroutine UMAT. The predicted fatigue crack initiation lives show good agreement with the experimental data. To further showcase the application of the developed framework, an anisotropic analysis is performed by generating 3D polycrystalline microstructure of β-titanium alloy. The developed methodology enhances the capabilities of commercial software in the field of microstructure modelling of complex problems.

Fatigue Life and Crack Initiation in Monopile Foundation by Fatigue FE Analysis

The construction of new renewable energy infrastructures and the development of new ocean resources continues to proceed apace. In this regard, the increasing size and capacity of offshore wind turbines demands that the size of their accompanying supporting marine structures likewise increase. The types of marine structures utilized for these offshore applications include gravity base, monopile, jacket, and tripod structures. Of these four types, monopile structures are widely used, given that they are comparatively easy to construct and more economical than other structures. However, constant exposure to harsh cyclic environmental loads can cause material deterioration or the initiation of fatigue cracks, which can then lead to catastrophic failures. In this paper, a 3D fatigue finite element analysis was performed to predict both the fatigue life and the crack initiation of a welded monopile substructure. The whole analysis was undertaken in three steps. First, a 3D non-steady heat conduction analysis was used to calculate the thermal history. Second, a thermal load was induced, as an input in 3D elastoplastic analysis, in order to determine welding residual stresses and welding deformation. Finally, the plastic strain and residual stress were used as inputs in a 3D fatigue FE analysis in order to calculate fatigue crack initiation and fatigue life. The 3D fatigue finite element analysis was based on continuum damage mechanics (CDM) and elastoplastic constitutive equations. The results obtained from the 3D fatigue finite element analysis were compared with hot spot stresses and Det Norske Veritas (DNV-GL) standards.

A layer-wise plasticity-based approach for the analysis of reinforced concrete shell structures using a mixed finite element

The analysis of reinforced concrete shell structures accounting for material nonlinearity is addressed. The structural response is numerically evaluated using a mixed shell finite element and a plasticity-based material behaviour. The finite element is a quadrilateral with four nodes and is based on self-equilibrated assumed stresses. The kinematic fields are interpolated only along the element boundary by polynomials up to the third order. The generalised shell stresses are evaluated through layer-wise integration of the Cauchy pointwise stresses. This allows appropriated three-dimensional elastoplastic constitutive equation to be employed and to include multiple reinforcing layers. The integration of the constitutive laws is performed using a dual decomposition method which preserves the assumed stress interpolation. Results, including civil engineering applications, show that the proposed approach is reliable and accurate in evaluating the static nonlinear equilibrium path. Additionally, the mixed finite element shows a quadratic rate of convergence in the collapse load and low error even for coarse meshes.

Subloading-Overstress Model: Unified Constitutive Equation for Elasto-Plastic and Elasto-Viscoplastic Deformations Under Monotonic and Cyclic Loadings

Various elasto-plastic models for the rate-independent deformation, various elasto-viscoplastic models for the rate-dependent deformation and their combinations have been proposed during a long time more than one or more centuries. Firstly, the history of the development of the elastoplasticiy and the elasto-viscoplasticity is reviewed comprehensively. Unfortunately, each of these models possesses their own drawbacks and limitations. The unified constitutive equation of the elasto-plastic and the elasto-viscoplastic deformations is provided by incorporating the subloading surface model into the overstress model in this article, which is capable of describing the monotonic and the cyclic loadings at the general rate ranging from the quasi-static to the impact loading. The validity of the unified model is verified by the comparison with various test data of metals under various loading conditions. Consequently, the elastoplastic constitutive equation can be disused hereinafter, while it is expressed by the cumbersome formulation including the complicated plastic modulus but limited to the description of the purely static deformation which is not induced actually.

Finite-Deformation Cam-Clay Model Considering Elastic Dilatancy and Soil Skeleton Structure

Elastoplastic constitutive equations for soils often employ the nonlinear rate-type isotropic Hooke’s law, which is based on the additive decomposition of strain rate and considers the pressure dependency in the elastic part. Hooke’s law has independent isotropic and deviatoric components, and therefore, it cannot express elastic dilatancy as confirmed in experiments. In this model, although the elastic volume change is path-independent, the shear strain exhibits a significant residual when subjected to an effective stress cycle. This study proposes a rate-type elastic constitutive equation for soil applicable to elastoplastic constitutive equations based on finite deformation theory using an objective stress rate and additive decomposition of stretching; these equations cover these shortcomings of the rate-type Hooke’s law. The proposed rate-type elasticity constitutive equation is based on the hyperelastic body in the infinitesimal deformation theory proposed by Einav and Puzrin or Houlsby et al. and has confining pressure dependence, path independence of elastic volume change, and elastic dilatancy. Further, the residual strain is considerably smaller than that of the rate-type Hooke’s law. Moreover, this study improves the elasto-plastic constitutive equation, SYS Cam-Clay model, based on the skeleton structure concept by introducing the proposed elastic constitutive equation. The basic behavior of the elastoplastic constitutive equation for clay and sand is demonstrated to show that the newly acquired elastic dilatancy improves the mean effective stress reduction behavior during shear stress unloading under undrained conditions and the stiffness recovery behavior during liquefaction, which is essential for describing cyclic mobility.

Indentation Tests for Sintered Silver in Die-Attach Interconnection After Thermal Cycling

Abstract Thermomechanical reliability assessment for sintered silver is a crucial issue as sintered silver is a promising candidate of die-attachment materials adopted for power devices. In this paper, the nano-indentation tests are performed for sintered silver in typical die-attach interconnection under different thermal cycles. Based on thermal cycling test, the Young's modulus and hardness of sintered silver layer have been presented. It is found that the Young's modulus and hardness of sintered silver layer changes slightly although the microstructure of sintered silver also presents some variations. The stress and strain curves for different thermal cycling tests of sintered silver are also given based on reverse analysis of nano-indentation. The results show that the elastoplastic constitutive equations change significantly after thermal cycling tests, and the yielding stress decreases remarkably after 70 thermal cycles. The experimental investigation also shows that the cracking behaviors of sintered silver depend on its geometry characteristics, which implies that the possible optimization of sintered silver layer could enhance its thermomechanical performance.

Modeling and simulation of ductile damage in forged steel used to encapsulate high-level radioactive waste

Andra, the French national radioactive waste management agency, is in charge of studying the disposal of high-level and long-lived intermediate-level waste (HLW and ILW-LL) in a deep geological repository. According to the reference concept, it is planned to encapsulate high-level waste in non-alloy P285NH steel overpacks before inserting them into horizontal steel cased micro-tunnels. This work is a part of the study about the long-term behavior of a welded steel overpack subjected to external hydrostatic pressure and several localized loading paths. Indeed, the main objective of this work is to develop the most suitable model for non-alloy steel P285NH to be used in the prediction of the long-term overpack behavior. Dealing with a ductile steel, elastoplastic constitutive equations accounting for mixed nonlinear isotropic and kinematic hardening strongly coupled with ductile isotropic damage are adopted. They are formulated based on the classical thermodynamics of irreversible processes framework with state variables at the macroscopic scale, (Germain, 1973) (Lemaitre 1985, Saanouni 2012). In this paper, a new coupling formulation between the scalar isotropic ductile damage and the deviatoric and spherical part of the Cauchy stress and elastic strain tensors is proposed. In order to calibrate the developed model on P285NH steel, multiple tensile tests are performed using classical cylindrical specimens, notched specimens and double notched specimens. In the last part, some experimental fields are measured using digital image correlation. Application is made to a simplified overpack represented by thick walled cylinder subject to compressive loading path. A FEM (Finite Element method) crushing operation of an overpack’s cylindrical part has simulated and analysed.

A low cycle fatigue cracking simulation method of non-ordinary state-based peridynamics

We established a simulation method for low cycle fatigue elastoplastic fracture under the framework of the Non-ordinary State-based peridynamics. It used mixed hardening models and failure criteria based on accumulated plastic strain. Furthermore, the numerical solution method of the elastoplastic constitutive equation was given. In order to verify the simulation method, the simulations of 316L steel strain control symmetric cyclic test and Q235 low cycle fatigue failure test were conducted, which showed good agreement with the experimental results. Our findings demonstrated the suitability of the proposed simulation method for damage fracture analysis with elastoplastic low cycle fatigue.

Structural mechanics model for anisotropic damage and fatigue life prediction method of face-centered cubic metal materials

Based on the characteristics of the sliding surface, sliding direction, and fatigue damage mechanism of metal materials, the mechanical model of a body-bar-plate structure is proposed with consideration to the plastic damage mechanism. The damage evolution law of the body-bar-plate mechanical model was investigated, and the elastoplastic constitutive equations and damage constitutive equations of the face-centered cubic (FCC) structure subjected to multi-axial cyclic loading were derived. Then, the meso-damage evolution equation and failure criterion were established. Subsequently, the relationship between the fatigue performance and microstructure under multi-axial proportional loading was investigated, and a damage mechanics-finite element method (FEM) method with consideration to the damage evolution is proposed. The simulation results are consistent with the experimental data. Therefore, the proposed model and method can accurately predict the fatigue life of FCC metal material under proportional loading and lay the foundation for the further analysis of non-proportional loading fatigue damage.

Fatigue life prediction method of face‐centered cubic single‐crystal metals under multiaxial nonproportional loading based on structural mechanical model

AbstractBased on the characteristics of the sliding surface, sliding direction, and fatigue damage mechanism of metal materials, the mechanical model of a body–bar–plate structure is proposed with consideration to the plastic damage mechanism. The elastoplastic constitutive equations and damage constitutive equations of the face‐centered cubic (FCC) structure subjected to multiaxial cyclic loading were derived, and the damage evolution law of the body–bar–plate mechanical model was investigated. Then, the meso‐damage evolution equation was established under multiaxial nonproportional loading. Subsequently, the relationship between the fatigue performance and microstructure under multiaxial nonproportional loading was investigated, and a damage mechanics–finite element method (FEM) with consideration to the damage evolution is proposed. The proposed model and method provide a new approach for predicting the fatigue life of metal materials.

A Cyclic Elasto-Plastic Constitutive Equation and Its Application

A Cyclic Elasto-Plastic Constitutive Equation and Its Application

Elastoplastic solution of drained expansion of a cylindrical cavity in structured soils considering structure degradation

An elastoplastic solution of drained cylindrical cavity expansion is presented based on a well-known critical state model for soils exhibiting a natural structure. The model referred to as the structured Cam-clay (SCC) model is capable of describing the properties of the soil structure and its subsequent stress-induced degradation. The asymmetric stiffness matrix of the elastoplastic constitutive equation for structured soils is derived due to the assumption of the non-associated plastic flow rule. The solution procedure is formulated by transforming the boundary value problem of cylindrical cavity expansion into the problem of solving four ordinary differential equations with three stress components and the specific volume as the basic unknown variables. The theoretical solution is numerically calculated and validated against the existing solution and finite element simulation results. Furthermore, the significance of the soil structure and its stress-induced degradation in the expansion response, and the interaction between the soil structure and overconsolidation are emphasized by extensive parametric analyses. The results demonstrate that the soil structure has a substantial influence on the cavity expansion response, and its degradation is closely related to overconsolidation. Particularly, among the solutions considered, the solution considering the soil structure provides higher effective stress values near the cavity surface due to the additional strength conveyed by the natural structure.

The impact of drilling and slitting construction on damage field: evolution characteristics in low-permeability coal seam

ABSTRACT The fracture field of coal and rock mass is the main channel for gas migration and accumulation. Exploring the evolution law of fracture field of coal and rock mass under the condition of drilling and slitting construction has important theoretical significance for guiding efficient gas drainage. The generation and evolution process of coal and rock fissures is also the development and accumulation process of its damage. Therefore, based on damage mechanics and finite element theory, the mathematical model is established. The damage variable of coal mass is defined by effective strain, the elastoplastic damage constitutive equation is established and the secondary development of finite element program is completed by FORTRAN language. Using this program, the numerical simulation of drilling and slitting construction of the 15-14120 mining face of Pingdingshan No. 8 Mine is carried out, and the effects of different single borehole diameters, different kerf widths and different kerf heights on the distribution area of surrounding coal fracture field and the degree of damage are studied quantitatively. These provide a theoretical basis for the reasonable determination of the slitting and drilling arrangement parameters at the engineering site.

Dynamic plastic impact behavior of CNTs/fiber/polymer multiscale laminated composite doubly curved shells

In the present paper, the dynamic elastoplastic response of carbon nanotube (CNT) fiber/polymer multiscale laminated composite (CNTFPC) doubly curved shell subjected to low-velocity impact of the projectile is investigated. For this purpose, the effective material properties of the multiphase composite are calculated by combining the Halpin-Tsai model and a micromechanical approach that strengths are estimated by an empirical equation and modified through a mixture rule. The elastoplastic constitutive equations are obtained incrementally using Hoffman’s criterion and isotropic hardening model. Also, the Green-Lagrange type of nonlinear kinematics is extracted in terms of displacement terms based on Reddy’s higher-order shear deformation theory for the CNTFPC shell. All incremental relations are regulated in the framework of the updated Lagrangian formulations to solve by an iterative finite element procedure through conforming isoparametric quadrilateral elements. Moreover, an elastoplastic Brake’s contact model is developed to determine truly the contact force between the CNTFPC plate and impactor. Temporal discretization is done by the Newmark’s average acceleration scheme. The results are validated with the data available in the literature to demonstrate the accuracy of the model. A parametric study was carried out to analysis stress and investigate the yield conditions and the effects of plastic deformation, weight percentage of CNTs, fiber volume fraction and curvature radius on the contact force history, indentation, permanent indentation depth, central deflection. Numerical results show that in the low velocity impact analysis, the stresses occurring in the shell for the areas further away from the contact area are also yielded.