Elastoplastic Relations Research Articles

A state-dependent bimodal soil water retention model considering evolutions of pore-scale soil–water interaction

Existing soil water retention models can capture the effects of void ratio and/or net mean stress on the changes in soil water retention curve (SWRC). However, most of them, especially those for bimodal soil that is composed of macro- and micro-pore systems, do not consider the simultaneous evolutions of pore structure and particle contacts, and neglected the drainage processes of bulk water and meniscus water when subjected to any external hydro-mechanical loading condition. This paper proposes a state-dependent bimodal SWRC model considering pore structure evolution and pore-scale water drainage. In this model, an elastoplastic relationship is introduced to describe the variations of void ratio with net mean stress and suction, whilst the corresponding changes in the pore structure are modelled by the shift and scaling of the pore-size distribution and the volumetric proportion between the macro- and micro-pore systems. By relating stress-induced changes in void ratio and coordination number to the mean pore radius and total meniscus water volume, respectively, the soil water content at different stages of water drainage can be determined. The model is validated against existing and new data, and can capture the effects of void ratio, isotropic stress, and K0 stress for unimodal and bimodal soils.

An enhanced stress resultant plasticity model for shell structures with application in sheet metal roll forming

AbstractThe proposed Kirchhoff-Love shell stress resultant plasticity model extends a previously reported model for plates by complementing the constitutive law of elastoplasticity with membrane effects. This enhanced model is designed for bending dominant settings with small to moderate membrane forces. It is thus implemented in a purpose-built nonlinear mixed Eulerian–Lagrangian finite element scheme for the simulation of sheet metal roll forming. Numerical experiments by imposing artificial strain histories on a through-the-thickness element are conducted to test the model against previously reported stress resultant plasticity models and to validate it against the traditional continuum plasticity approach that features an integration of relations of elastoplasticity in a set of grid points distributed over the thickness. Results of actual roll forming simulations demonstrate the practicality in comparison to the computationally more expensive continuum plasticity approach.

Determination of fault damage zones in sandstone rocks using numerical models and statistical analyses

The width of fault damage zones is usually assessed through scaling relationships using fault displacements measured from outcrops. However, field data show a large dispersion, indicating that other variables, such as rock properties, can affect the development of damage zones. This article proposes a novel, practical and efficient methodology to predict the width of fault damage zones in sandstone reservoirs, including geomechanical properties’ impact. Firstly, a deterministic model based on elastoplastic relationships and the Finite Element Method (FEM) is defined to assess the damage zone width. Next, empirical correlations between the porosity and the geomechanical parameters are established. Then, planned numerical experiments considering specific domains for each input parameter are generated using the Design of Experiments (DOE) technique. The corresponding results are used to build response surfaces. Finally, a statistical analysis is carried out to define a regression model to express the relationship between the damage zone width, the rock porosity, and the fault displacement. The fit quality is adjusted considering the ANOVA table, Pareto charts, and regression analysis. The results from the regression models indicate a perfect fit with the information predicted by the deterministic model and field data.

Investigating the micro and nanomechanical properties of CoCrFeNi-Cx high-entropy alloys containing eutectic carbides

In this study, we systematically investigated the effect of the carbon content on the phase structure evolution and macro and nanomechanical properties of the equiatomic CoCrFeNi alloy. A series of CoCrFeNi-based high-entropy alloys with 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.7, and 0.9 wt% carbon were fabricated by vacuum arc melting. The results showed that the alloys retained their single face-center-cubic (FCC) structure with large grains at the carbon contents up to 0.2 wt%. However, in the case of the alloys with carbon contents higher than 0.3 wt%, the single phase structure transformed into the dendrite structure. The inter-dendrite regions of these alloys were eutectic carbides containing lath M7C3 carbides and the FCC phase. The tensile yield strength of the CoCrFeNi alloy increased from 295 to 512 MPa with the addition of 0.9 wt% carbon. The strengthening mechanisms of the alloys were investigated, including the solid solution strengthening due to the interstitial carbon atoms and the precipitation strengthening due to the M7C3 carbides. In addition, the nanoindentation results revealed that the M7C3 carbides showed a high nanohardness of ~17.7 GPa, which is almost four times of that of the FCC phase. We also investigated the elasto-plastic relationships, plastic properties and wear resistance of the FCC phase, while elucidating the eutectic carbide regions and M7C3 carbides. The eutectic carbide regions exhibited brittle fracture, whereas the FCC phase showed plastic fracture.

МОДЕЛИРОВАНИЕ УСТАЛОСТНОЙ ДОЛГОВЕЧНОСТИ ПОЛИКРИСТАЛЛИЧЕСКИХ КОНСТРУКЦИОННЫХ СПЛАВОВ ПРИ СОВМЕСТНОМ ДЕЙСТВИИ МЕХАНИЗМОВ МАЛО- И МНОГОЦИКЛОВОЙ УСТАЛОСТИ

Processes of fatigue life of polycrystalline structural alloys under a combined effect of low- and high-cycle fatigue are considered. In the framework of mechanics of damaged media (MDM), a mathematical model is developed, which describes processes of plastic deformation and fatigue damage accumulation. The MDM model consists of three interrelated parts: relations defining cyclic elastoplastic behavior of the material, accounting for its dependence on the failure process; equations describing fatigue damage accumulation kinetics; a strength criterion of the damaged material. The version of defining relations of elastoplasticity is based on the notion of yield surface and the principle of orthogonality of the plastic strain rate vector to the yield surface at the loading point. This version of equations of state reflects the main effects of the cyclic plastic deformation process of the material for arbitrarily complex loading trajectories. The version of kinetic equations of damage accumulation is based on introducing a scalar parameter of damage degree. The construction uses energy-based principles and accounts for the main effects of the process of nucleation, growth and merging of microdefects under arbitrarily complex multiaxial loading regimes. A combined form of the evolutionary equation of fatigue damage accumulation in the regions of low-cycle (LCF) and high-cycle (HCF) fatigue is proposed. It is shown that, under regular cyclic loading of the material, the stress amplitude of the cycle decreases by degrees during the transition from LCF to HCF and depends on the physical interaction of these mechanisms in the transition zone. The condition when the damage degree attains its critical value is taken as the strength criterion of the damaged material. A methodology of numerically determining parameters of the evolutionary equation of fatigue damage accumulation in the conditions of HCF is presented. To assess the reliability and the limits of applicability of the defining relations of MDM, processes of plastic deformation and fatigue damage accumulation in a number of structural alloys in cyclic tests have been numerically studied, and the obtained numerical results have been compared with the data of full-scale experiments. The results of comparison of the numerical and experimental data reveal that the developed model of mechanics of damaged media adequately describes durability of structures subjected to a combined effect of low- and high-cycle fatigue mechanisms. It is shown that the introduced MDM model qualitatively and, accurately enough for practical engineering purposes, quantitatively describes the main effects of the processes of plastic deformation and fatigue damage accumulation in structural alloys under cyclic loading.

The Benefits of Using a Consistent Tangent Operator for Viscoelastoplastic Computations in Geodynamics

AbstractStrain localization is ubiquitous in geodynamics and occurs at all scales within the lithosphere. How the lithosphere accommodates deformation controls, for example, the structure of orogenic belts and the architecture of rifted margins. Understanding and predicting strain localization is therefore of major importance in geodynamics. While the deeper parts of the lithosphere effectively deform in a viscous manner, shallower levels are characterized by an elastoplastic rheological behavior. Herein we propose a fast and accurate way of solving problems that involve elastoplastic deformations based on the consistent linearization of the time‐discretized elastoplastic relation and the finite difference method. The models currently account for the pressure‐insensitive Von Mises and the pressure‐dependent Drucker‐Prager yield criteria. Consistent linearization allows for resolving strain localization at kilometer scale while providing optimal, that is, quadratic convergence of the force residual. We have validated our approach by a qualitative and quantitative comparison with results obtained using an independent code based on the finite element method. We also provide a consistent linearization for a viscoelastoplastic framework, and we demonstrate its ability to deliver exact partitioning between the viscous, the elastic, and the plastic strain components. The results of the study are fully reproducible, and the codes are available as a subset of M2Di MATLAB routines.

Unified modeling of soil behaviors before/after flow liquefaction

Flow liquefaction of soil involves a phase transition process from solid to fluid. A constitutive model that can describe the soil behaviors of both the solid and fluid phases in a unified way was proposed. The constitutive model adopts a phase transition criterion to detect the onset of flow liquefaction and associates an elastoplastic relation and a fluid relation in a single framework. The simulated results demonstrated that the proposed model can describe the fundamental behaviors of soil in both the solid and fluid phases with a smooth transition from soil-like behavior to fluid-like behavior during the phase transition process.

Logarithmic rate implementation in constitutive relations of finite elastoplasticity with kinematic hardening

AbstractThe objective of this article is the evaluation of the validity range of two objective rates, the nowadays most frequently used Jaumann rate and the recently introduced logarithmic rate, in material behaviour prediction due to large deformations. For that purpose the model subjected to large monotonic uniaxial elastoplastic deformation has been examined as well as the initially prestressed models which are afterwards exposed to the cyclic process of combined elastic lengthening and shearing. It is shown that whenever the participation of shear deformation to the total deformation stays in the small deformation range both rates are almost equal in constitutive relations implementation since the outputs for both rates are nearly congruent. Otherwise, if the influence of rotations is significant the Jaumann rate gives theoretically and experimentally unexpected results whereas the logarithmic rate results are stable and consistent with the notion of elasticity, i.e. without any residual stresses at the end of the elastic deformation cycles.

Analysis of some basic approaches to finite strain elasto-plasticity in view of reference change

There is a large variety of concepts used to generalize the classical Prandtl–Reuss relations of infinitesimal elasto-plasticity to finite strains. In this work, some basic approaches are compared in a qualitative way with respect to a certain invariance property. These basic approaches include the additive hypoelasto-plasticity with corotational stress rates, additive plasticity in the logarithmic strain space, and multiplicative hyperelasto-plasticity.The notion of weak invariance is introduced in this study. Roughly speaking, a material model is weakly invariant under a certain transformation of the local reference configuration if this reference change can be neutralized by a suitable transformation of initial conditions, leaving the remaining constitutive relations intact. We analyse the basic models in order to find out if they are weakly invariant under arbitrary volume-preserving transformations of the reference configuration.It is shown that the weak invariance property corresponds to a generalized symmetry which provides insights into underlying constitutive assumptions. This property can be used for a systematic study of different frameworks of finite strain elasto-plasticity. In particular, it can be used as a classification criterion.

Elastoplastic invariant relation for deformation of solids

This paper considers the basic laws of localized plastic flow in solids obtained from an experimentally established relation invariant for plastic and elastic deformation that determine the propagation velocities of localized plasticity autowaves, the dispersion of these waves, and the dependence of the autowave length on the grain size. The relationship of the equations of localized plasticity and the equations of dislocation dynamics is established.

A General Form of Constitutive Relations in Non-Smooth Elastoplasticity

A general formulation of constitutive relations in non-smooth elastoplasticity is presented. The treatment applies to general non-smooth plasticity problems and to problems characterized by non-smooth yield criteria or dealing with non-differentiable functions. The mathematical tools and instruments of convex analysis and subdifferential calculus are suitably applied since they provide the proper mathematical instruments for dealing with non-smooth problems and non-differentiable functions. General formulations of constitutive relations and evolutive laws in non-smooth elastoplasticity are illustrated within the presented theoretical framework. Connections between the proposed mathematical treatment and the classical relations in elastoplasticity are illustrated and discussed in detail. The presented generalized treatment is equipped with considerable advantages since it shows to be ideally suited for the development of variational formulations of structural problems in non-smooth elastoplasticity.

On Constitutive Relations in Non-Smooth Elasto/Viscoplasticity

A general treatment of constitutive relations in elastoplasticity and elasto/viscoplasticity is presented. The treatment holds for general non-smooth problems and it applies to non-smooth yield criteria and to functions characterized by non-differentiability. The formulation is developed by resorting to the tools provided by convex analysis and subdifferential calculus which are the appropriate instruments for dealing with convex criteria and non-smooth functions. General formulations of constitutive relations and evolutive laws are presented for elastoplasticity and elasto/viscoplasticity and connections are illustrated between the general elastoplastic model problem and the general elasto/viscoplastic model problem. The presented generalized treatment proves to be well-suited for the development of variational formulations for structural problems in elastoplasticity and elasto/viscoplasticity.

Pore-Scale Flow Simulations: Model Predictions Compared with Experiments on Bi-Dispersed Granular Assemblies

A method is presented for the simulation of pore flow in granular materials. The numerical model uses a combination of the discrete element method for the solid phase and a novel finite volume formulation for the fluid phase. The solid is modeled as an assembly of spherical particles, where contact interactions are governed by elasto-plastic relations. Incompressible Stokes flow is considered, assuming that inertial forces are small in comparison with viscous forces. Pore geometry and pore connections are defined locally through regular triangulation of spheres, from which a tetrahedral mesh arises. The definition of pore-scale hydraulic conductivities is a key aspect of this model. In this sense, the model is similar to a pore-network model. Permeability measurements on bi-dispersed glass beads are reported and compared with model predictions, validating the definition of local conductivities.

Divergence Instability and Diffuse Failure in Granular Media

The question of divergence instability and diffuse failure, which is a common failure mode for granular materials like soils, is tackled here from an experimental, theoretical and numerical perspective. The necessary condition of instability as given by the loss of definite-positiveness of the elasto-plastic matrix (the so-called “second order work criterion”) is considered to analyze some experimental tests leading to diffuse failure, the link between kinetic energy and second order work is established, a discrete element method is used to simulate these failure conditions and eventually a 3D bifurcation analysis is performed with incrementally piecewise and non-linear elasto-plastic relationships. Essentially in relation with the non-associate character of the plastic strains of granular materials, a whole bifurcation domain in the stress space emerges from these analyses, leading to novel views of failure for non-associative materials.

Geomechanical issues of anthropogenic CO 2 sequestration in exploited gas fields

Anthropogenic CO 2 sequestration in deep geological formations may represent a viable option to fulfil the requirements of the 1997 Kyoto protocol on the reduction of greenhouse gas emissions. Scenarios of CO 2 sequestration through three injection wells in an exploited gas field located in the Po sedimentary basin (Italy) are simulated with the final target to understand the geomechanical consequences of the injection of carbon dioxide. Investigated scenarios include, as a hypothetical case, the long-term injection of CO 2 until the initial reservoir pressure is exceeded by as much as 40% over a period of about 100 years. The process is analyzed from the geomechanical point of view using a finite element–interface element (FE–IE) model with the following main issues addressed: (1) prediction of the possible land vertical uplift and corresponding impact on the ground infrastructures; (2) evaluation of the stress state induced in the reservoir formation with the possible generation of fractures and (3) a risk analysis for the activation of existing faults. The geomechanical constitutive law of the Northern Adriatic basin relying on the radioactive marker interpretation is implemented into the FE model, while an elasto-plastic relationship based on the Mohr–Coulomb criterion is used for the IE reproducing the fault behaviour. The in situ stress prior to the gas field exploitation is compressive with the principal horizontal stress in the direction perpendicular to the major faults equal to the vertical stress. The results show that the ground surface rebound due to the overpressure generated by the CO 2 sequestration partially mitigates the land subsidence experienced by the area because of the previous gas field depletion with differential displacements that are confined within the safety bounds suggested in the literature for the surface infrastructures. Activation of a few faults lying close to the northern reservoir boundary points to a slip of a couple of centimetres only and occurs before the CO 2 plume reaches the activated faults, so there is little chance for a CO 2 escape. The caprock is also proven to maintain its full integrity during the injection process. Finally the shear stress appears to approach the limiting state prone to the rock shear failure exclusively within the reservoir on a quite local scale and can hardly jeopardize the overall effectiveness of the CO 2 sequestration.

Numerical modeling of complex plastic deformation of metals along plane and spatial trajectories of arbitrary curvature and torsion

The mathematical model of thermoplasticity describing the processes of complex plastic deformation of structural materials (metals and their alloys) along plane and spatial trajectories of arbitrary curvature and torsion is developed. For evaluating the adequacy degree of constitutive relations of elastoplasticity and the range of their applicability, numerical investigations of complex plastic deformation (by the example of steel 45) along the trajectories having the form of a circle and the screw trajectories of constant curvature and torsion are carried out. The obtained numerical results are compared with the data of full-scale experiments. It is shown that the developed model of thermoplaciticity describes qualitatively and quantitatively the main effects of complex plastic deformation of metals under arbitrary non-proportional combined (P-q-M) force loading.

ENHANCEMENT IN FATIGUE CHARACTERISTICS BY ELASTO-PLASTIC ANALYSIS OF PRE-STRESSED HOLES

The holes made to accommodate the fasteners in many of the engineering applications as in aircraft structures are subjected to cyclic loads. The improvement in fatigue characteristics by the cold expansion process is the established practice. It has been the ongoing research trend to quantify the enhancement in the fatigue strength due to the induction of residual stresses by prestressing the drilled hole. The optimization of the fatigue strength and to establish corresponding percentage of expansion of the fastener hole is the focus of this paper. Expanding into Taylor series, the functional relation between cyclic stress and mean stress given by Soderberg and subsequent application of interface theory lead to the formulation of the objective function. The expansion is linear in the elastic zone governed by Hooke's law and non-linear in plastic zone obeying the Holloman's law. The elasto-plastic relation between stress and strain provides the constraint condition. The non-linear relation of optimization is solved by a novel method to get the optimum enhancement fatigue strength due to cold expansion of the hole. The analytical results are compared with the experimental analysis for justification as reported in previous literature.

トランスバースクラックを有するＣＦＲＰ直交積層板の引張強度

The effect of the transverse crack on the ultimate tensile strength (UTS) for carbon fiber reinforced plastic (CFRP) cross-ply laminates was studied experimentally and analytically. For various stacking sequences of CFRP composites, quasi-static tensile tests were carried out. And the fiber bundle strength of 0-degree ply was almost constant. Therefore, it was concluded that there was little notch sensibility in spite of the existence of transverse cracks. A new numerical model based on the finite element method was proposed to investigate the inner micro damage process. In the model the elastoplastic relation of epoxy matrix was considered effectively and the progress of the inner fiber breakage was obtained. Then, using this model, we conducted the simulation based on the Monte-Carlo method. Based on the analysis results of the proposed model, it was shown that the plastic regions at the tip of transverse crack reduce the concentration of stress, and the bundle strength was not affected by the existence of transverse cracks.

Non-linear boundary element analysis of plates applied to concrete slabs

In this work the BEM non-linear formulation for Kirchhoff's plates in bending applied to model reinforced concrete slabs is discussed. The integral equations of displacements, bending and twisting moments and shear forces are derived and modified properly to model non-linear behaviours. Two models were implemented to analyse reinforced concrete slabs: a simple elastoplastic criterion defined by adopting the Von Mises surface to govern the concrete behaviour in compression complemented by assuming tension cut off; and the Mazars' continuum damage model. For both cases, the reinforcement is governed by the uniaxial stress x strain elastoplastic relationship with constant hardening. Internal forces are approximated by numerical integrals along the plate thickness using a Gauss' scheme, after verifying the non-linear criterion at each point.

Inclusion of expansive clay behaviour in coupled thermo hydraulic mechanical models

This paper discusses the development of a model for the coupled flow of heat, moisture and air in expansive clays. In particular, the results of recent research work on the inclusion of expansive behaviour exhibited by some clays are presented. Initially, a fully coupled thermal/hydro/mechanical (THM) simulation of a heating experiment is presented. The observed THM behaviour in unsaturated soil was predicted by the model, with the best correlation found in the thermal field. The influence of the osmotic potential on the soil via the effect of chemical solute concentration is explored in a non-linear elastic constitutive relationship. The ability of such a model to represent the large strains that can occur during free swelling of expansive soils has been demonstrated. Finally, the representation of the development of irreversible strains within an expansive soil has been investigated via a double structure elasto-plastic relationship. The ability of such an approach to simulate the accumulation of plastic strains during wetting–drying cycles has been shown.