Elastic Volume Change Research Articles

M-Voronoi and other random open and closed-cell elasto-plastic cellular materials: Geometry generation and numerical study at small and large strains

The present study deals with a numerical design strategy of a novel class of three-dimensional random Voronoi-type geometries, called M-Voronoi. These materials comprise random, non-quadratic convex void shapes and non-uniform intervoid ligament thicknesses, and can span high-to-low relative densities. The starting point for their generation is a random adsorption algorithm (RSA) construction with spherical voids embedded in an incompressible, nonlinear elastic matrix phase. The initial RSA geometry is subjected to large elastic volume changes by prescribing Dirichlet boundary conditions. Due to the incompressibility of the matrix phase, the externally imposed volume changes lead to significant void growth. The numerical growth process may be stopped at any desired porosity. The proposed M-Voronoi process is general and allows the formation of isotropic (or anisotropic) designs. As a byproduct of the developed approach, we also present a novel remeshing technique allowing to read arbitrary geometries of one or multiple phases. The elasto-plastic properties of the M-Voronoi porous materials are numerically investigated at small strains as well as large compressive and shear loads. Their response is assessed by comparison with other well-known random and periodic porous geometries such as polydisperse porous materials with spherical voids (RSA), classical TPMS Gyroid geometries and random Spinodoid topologies. The results show that M-Voronoi and RSA (with spherical voids) geometries exhibit the stiffest elastic and highest flow stress response compared to the other two geometries. This study shows unambiguously that randomness may or may not lead to enhanced mechanical response such as higher stiffness or flow stress.

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.

Extracting true stresses and strains from nominal stresses and strains in tensile testing

AbstractSeemingly a simple task, the extraction of the flow curve (true stress vs. true plastic strain) from nominal stresses and strains in standard tensile testing still has its unsolved points. This study addresses two of them: (i) in materials without yield point phenomenon (or generally in the region of homogeneous plastic deformation), the true stress is typically calculated assuming constant volume, ignoring the elastic volume changes. Here, we derive a set of exact analytical solutions for true stresses and strains with remarkable simplicity and beauty that fully account for the elastic volume changes. This set of exact solutions is cross‐checked by finite element simulations as well as zeroth‐ and first‐order approximations; perfect agreement has been found. (ii) In materials with a pronounced yield point phenomenon, a complicated three‐dimensional stress state inevitably arises at the edge of the Lüders bands, which masks the real (or inherent) material behaviour. To determine the real material behaviour in the Lüders region, here we use a new macroscopic analytical approach characterised by a high true upper yield point, a typical strain hardening behaviour common for many materials, and the triaxiality of the stress state that inevitably develops at the edges of the Lüders bands and that determines the stress level at the observed lower yield point. This approach is verified by experiments (including video observations as well as digital image correlation (DIC) strain distribution measurements) and finite element simulations with very good agreement.

Plastically-Induced Volume Deformation of Nanocrystalline α-Fe with a <110> Columnar Structure

Volume changes accompanying the plastic deformation at 300 K of nanocrystalline samples of α-Fe with a columnar grain structure possessing a ⟨11¯0⟩ random fiber texture has been obtained from molecular dynamics (MD) simulations. The samples were strained in tension along the common axial direction of the columnar grains. After removal of the elastic volume change, the evolution of plastic volume strain was obtained. Small but non-negligible volume dilations or contractions are observed depending on size (samples of very small grain size show volume contraction). The rate of volume change is high during the first 10% plastic deformation and continues at a low pace thereafter; the first 10% deformation represents a transient in the stress–strain behavior too. The complex behavior observed is reasonably explained by the superposition of contributions from different plastically-induced structural changes to the mass density change: Mainly from changes of grain size, grain boundary structure, dislocation density and density of point-defects. The results are of interest for the development of crystal plasticity theories not restricted by the volume conserving assumption.

Mechanical and osmotic consolidation of geosynthetic clay liners: a laboratory study

This study aims to assess the effect of pore water salinity (sodium chloride (NaCL) solution) on the consolidation behaviour of GCLs (geosynthetic clay liners) using one-dimensional oedometer test apparatus. The experiments include two testing conditions: (1) an investigation of mechanical consolidation of GCL specimens saturated with water having different salinity levels, and (2) an investigation of the effect of pore water salinity on the volume change of GCL specimens under different constant vertical stress levels (i.e. osmotic consolidation). The mechanical consolidation test results indicated that the compression and swelling indices decrease as the liquid salinity increases, whereas an elastic hysteresis volume change behaviour was observed in the osmotic consolidation test results. The results of this study also show that the compression and swelling indices, and the hydraulic conductivity of a GCL specimen are almost reversible when it is subjected to an osmotic cycle.

DETERMINATION OF STRESS-STRAIN STATE OF THE BODY SURFACE OR ITS AREA IN CASE OF PERFECT PLASTICITY AT GIVEN STRESS AND DISPLACEMENT VECTORS

Ideally plastic state of material under conditions of Mises plasticity, proportionality of stress and strain deviators (deformation theory of plasticity) and elastic volume change is considered. Given the Cauchy stress and displacement vectors specified on the body surface (with indicated state) or its area, all six components of the stress tensor, all six components of the strain tensor, and also three components of the rotation vector are restored on this surface. This method for determining the stress-strain state can be related to the methods of rapid assessment of the structure state (body surface), since differential equations inside the body are not involved.

Novel hyperelastic models for large volumetric deformations

Materials such as elastomeric foams, lattices, and cellular solids are capable of undergoing large elastic volume changes. Although many hyperelastic constitutive formulations have been proposed for deviatoric (shape changing) behaviour, few variations exist for large deformation volumetric behaviour. The first section of this paper presents a critical analysis of current volumetric hyperelastic models and highlights their limitations for large volumetric strains. In the second section of the paper we propose three novel volumetric strain energy density functions, which: (1) are valid for large volumetric deformations, (2) offer separate control of the volumetric strain stiffening behaviour during shrinkage (volume reduction) and expansion (volume increase), and (3) provide precise control of non-monotonic volumetric strain stiffening. To illustrate the ability of the novel formulations to capture complex volumetric material behaviour they are fitted and compared to a range of published experimental data.

In-Situ Nanoindentation Measurement of Local Mechanical Behavior of a Li-Ion Battery Cathode in Liquid Electrolyte

The state-of-the-art cathode materials experience severe structural and mechanical degradation over lithiation cycles albeit their small deformation. It has been a great challenge to characterize the mechanical behavior of composite electrodes in-situ and in real-time because of their environmental sensitivity and intricate microscopic heterogeneity. We use nanoindentation to measure the in-situ mechanical behavior of individual phases in a cathode composite electrode LiNixMnyCozO2. We focus on the understanding of the mechanical properties of the constituents in dry and wet conditions. We evaluate the influence of electrolyte soaking on the elastic modulus, hardness, and volume change of the conductive matrix with different degrees of porosity. More interestingly, we measure the modulus, hardness, and fracture strength of agglomerated active particles and sintered pellets, and compare their mechanical properties in the dry and liquid environment. We show that the electrolyte enhances the fracture strength of NMC agglomerated particles. The increase in interfacial strength may be a result of the additional capillary force between primary particles. Results offer mechanistic understanding of the complex behavior of composite electrodes and will feed chemomechanical models on Li-ion batteries.

Elastic modulus deterioration index to identify the loosened zone around underground openings

In order to effectively identify the loosened zone around underground openings by using continuum modeling, this paper proposes an index called elastic modulus deterioration index based on the following two steps. First, the response of surrounding rock mass in underground openings as obtained from ultrasonic tests before and after excavation is investigated. Based on the attenuation of the P-wave velocities of the rock mass after excavation compared to the P-wave velocities before excavation obtained from ultrasonic tests, an index (χ) is defined to assess the excavation-induced rock mass damage. Second, by introducing an empirical relationship between the static and dynamic elastic moduli, the index χ is modified to represent the static elastic modulus evolution, volume change, and stress redistribution of the rock mass based on an elasto-plastic numerical model. Furthermore, this study verifies the performance of the elastic modulus deterioration index to identify the loosened zone around underground openings by comparing its predictions with the results from ultrasonic testing of the loosened zones around two tunnels in the Jinping II hydropower station. The comparisons show that the loosened zones as identified by the elastic modulus deterioration index agree well to those from ultrasonic testing. Analysis of the effects of key input parameters and initial shear strength parameters on the elastic modulus deterioration index in identifying the loosened zone demonstrate that: (1) the sensitivity of the index to the key input parameters except the residual static elastic modulus is not significant; and (2) the index has better fault tolerance performance compared to the indices based on plastic zone in terms of the selection of initial shear strength parameters.

Coupling of fluid flow to permeability development in mid- to upper crustal environments: a tale of three pressures

Abstract Orogenic gold systems are open, flow-controlled thermodynamic systems and generally occur in mid- to upper crustal environments where there is strong coupling between fluid flow and dilatant plastic deformation. This paper considers the principles involved in such coupling, with an emphasis on the elastic and plastic volume changes and their influence on the fluid, mechanical and thermodynamic pressures. Some misconceptions regarding the magnitudes of these three distinctly different pressures and their influences on fluid flow and chemical equilibrium are addressed, with examples at both the tens of metres scale and the crustal scale. We show that the mean stress is less than twice the lithostatic stress for Mohr–Coulomb materials with cohesion and the thermodynamic pressure only has meaning under isentropic conditions and hence is less than many previously published estimates based on high mean stresses. At the crustal scale, we also include the role of critical behaviour in influencing the geometry and magnitudes of fluid pressure gradients and fluid flow velocities in open, flow-controlled systems.

Co3O4 Nanosheets with In-Plane Pores and Highly Active {112} Exposed Facets for High Performance Lithium Storage

Recently, two-dimensional transition metal oxide nanomaterials have been extensively investigated as promising candidates for the lithium-ion battery anode materials due to their elastic volume change, efficient ion/electrical pathways, and additional interfacial lithium storage sites. Herein, we report a simple wet-chemical method followed by thermal treatment to synthesize Co3O4 nanosheets with the in-plane pores. The as-prepared nanosheets are found to selectively expose the highly active {112} facets as the dominant surfaces. When fabricated into the anode configuration, a specific capacity of 1717 mA h g–1 can be reliably retained after 100 cycles at a current density of 200 mA g–1. While increasing the current density to 1 A g–1 and prolonging the cycle life to 400 cycles, the nanosheets can still deliver a capacity of 1090 mA h g–1 with a Coulombic efficiency of 99.5%. This excellent electrochemical performance can be attributed to the unique morphological structures of our porous nanosheets for th...

Deformation and stability of compressible rubber O-rings

BackgroundIn rubber elastic models it is generally assumed that the bulk modulus is infinite, resulting in a material that does not change its volume and a pressure that cannot be evaluated from the material model.MethodsWe have developed a general procedure that incorporates a finite bulk modulus. Using the developed framework accurate results can be obtained without the need for special finite elements. It gives the correct results even in the limit of infinite bulk modulus.ResultsIt was shown that material compressibility causes additional stresses mostly associated with an additional hydrostatic pressure. It was also demonstrated that once a bulk modulus is included in the constitutive model, stability analyses of rubber-like materials subject to large deformation become numerically stable and accurate. Hence, it is essential to use compressibility with neo-Hookean solids for accurate stress and lifing predictions. The role of twist in the formation of stress-strain states in rubber O-rings has been evaluated. Such a twist causes elastic instabilities resulting in highly deformed O-ring shapes. Numerical analysis using compressible material models predicted the stable deformed states that O-ring do not remain circular. The ring is buckled and reaches a “chair” –type non-planar shape just beyond inside-out twist.ConclusionsThe results indicate that elastic material volume change causes additional stresses mostly associated with an additional hydrostatic pressure. Simulations using various rubber elastic models showed that allowing volume changes allows accurate stress state prediction, reduces numerical difficulties and improves the numerical stability.

Geometry and Self-stress of Single-Wall Carbon Nanotubes and Graphene via a Discrete Model Based on a 2nd-Generation REBO Potential

The main purpose of this paper is to evaluate the self-stress state of single-walled Carbon NanoTubes (CNTs) and Flat Graphene Strips (FGSs) in their natural equilibrium state, that is, the state prior to the application of external loads. We model CNTs as discrete elastic structures, whose shape and volume changes are governed by a Reactive Empirical Bond-Order (REBO) interatomic potential of second generation. The kinematical variables we consider are bond lengths, bond angles, and dihedral angles; to changes of each of these variables we associate a work-conjugate nanostress. To determine the self-stress state in a given CNT, we formulate the load-free equilibrium problem as a minimum problem for the interatomic potential, whose solution yields the equilibrium nanostresses; next, by exploiting the nonlinear constitutive dependence we derive for nanostresses in terms of a list of kinematical variables, we determine the equilibrium values of the latter; finally, from the equilibrium values of the kinematical variables we deduce the natural geometry and, in particular, the natural radius. Our theoretical framework accommodates CNTs of whatever chirality. In the achiral case, the stationarity conditions implied by energy minimization are relatively easy to derive and solve numerically, because we can count on maximal intrinsic symmetries and hence the number of independent unknowns is reduced to a minimum; for chiral CNTs, we prefer to solve the minimum problem directly. The natural-radius predictions we achieve within our discrete-mechanics framework are in good agreement with the results of calculations based on Density Functional Theory (DFT) and Tight Binding (TB) theory; the same is true for our predictions of the self-energy, that is, the energy associated with self-stress (called cohesive energy in the literature); we surmise that our discrete mechanical model may serve as a source of benchmarks for Molecular-Dynamics (MD) simulation algorithms. We find that self-stress depends on changes in both bond and dihedral angles in achiral CNTs and, in addition, on changes in bond length in chiral CNTs. Our analysis applies also to FGSs, whose self-stress and self-energy we evaluate; we find that in FGSs self-stress is associated exclusively with changes in bond angle.

Reversible polyamorphic transitions in Ce65.5Al10Cu22.5Co2 metallic glass

We report here on a reversible polyamorphic transition in Ce65.5Al10Cu22.5Co2 metallic glasses under high pressure investigated by in situ angle-dispersive x-ray diffraction. The alloy is found to display a strong hysteresis in polyamorphic-phase transition upon application and subsequent release of pressure. We demonstrate that, the hysteresis behavior was caused by the densification of Ce-based metallic glasses under high pressure, which was resulted by the irreversible annihilation of free volume and elastic volume change. The transition is strongly correlated 4f-electron delocalization of Ce metal. These results provide a guidance for understanding mechanism of polyamorphic-phase transition in metallic glasses.

Cyclic heating effects on thermal volume change of silt

This study focuses on the thermal volume change of compacted, saturated silt during temperature cycles. A temperature-regulated oedometer with backpressure control was used to measure the thermal consolidation of silt specimens under normally consolidated to heavily overconsolidated initial stress states. During initial heating, the silt specimens displayed thermal volume changes similar to those reported in the technical literature, with the normally consolidated specimen showing contraction and the heavily overconsolidated specimens showing expansion. The specimens all showed elastic contraction during cooling, as expected. However, subsequent heating and cooling cycles led to additional permanent volume change. This observation contradicts thermo-elasto-plastic theories, which predict plastic contraction only during initial heating of soils with low overconsolidation ratios and elastic volume changes during subsequent heating and cooling cycles. A source of error in the experiments was a softer response during heating due to differential radial expansion of the oedometer ring, followed by exaggerated axial expansion of the soil during cooling when the ring contracted. Nonetheless, the accumulation of permanent strain during cyclic heating and cooling indicates that the thermal yield surface history may not be locked in during the cooling process, implying that kinematic thermal hardening or thermal creep mechanisms should be explored.

The Influence of the Initial Concrete Strength on its Deformation Under Triaxial Compression

The results of the experimental research of the influence of the initial strength of С20/25, С30/40, С40/50, С70/85 concrete classes on the principles of linear, volumetric and shear strains development in the conditions of triaxial compression are introduced in this article. Experimental research techniques and realized loading programs are described. The program of the triaxial uniform hydrostatic compression in the conditions of σ1 = σ2 = σ3 < 0 has been realized during the first stage of the experiment. The testing has resulted in defining the relation “mean stress σ0 –relative volumetric strain change Θ” for relatively high levels of loading. The values of additional plastic strains of the relative volume change Θpl characterizing deviations of experimental strain values Θ from their design values according to the law of the elastic volume change Θel have been defined. However, higher values of Θpl correspond to lower strength concretes. The programs of non-uniform loading of the stress deviator at a mean stress invariable value (σ0 = const) have been realized during the second stage of the test. Experimental concrete specimens stress-strain curves in the directions of coordinate axes, diagrams of deviatoric stress and strain tensor components connection “τi – γi” as well as quantitative characteristics of the orthotropic concrete deformation process have been obtained. The determining influence of shear strains on dilatation effects in the concrete structure has been confirmed.

Metric theory of nematoelastic shells.

We consider three-dimensional reshaping of a thin nematoelastic film upon nematic-isotropic transition in the field of a charge one topological defect, leading to either cone or anticone (d-cone) shells. The analysis is based on the relation between the shell metric and the tensor order parameter under the assumption of no elastic deformation and volume change. The shape of the shell can be modified by doping, creating cones with curved generatrices. Anticones necessarily have an even number of radial creases. The curvature singularity at the apex is resolved due to decay of the nematic order parameter at the defect core.

Effect of hydrostatic pressure on reinforcing bulk metallic glasses investigated by synchrotron radiation and molecular dynamics simulations

Volume change of bulk metallic glasses (BMGs) during the repeated loading and unloading was investigated using in situ high-pressure synchrotron diffraction. Molecular dynamics simulations, which were used for further research of the microstructure change, were presented on an approximately 5.0×105 atom sample of an amorphous Fe80P20 model. The results show that the first compression process includes irreversible annihilation of free volume and elastic volume change. The main form of annihilation of free volume is that smaller atoms are extruded into the larger atomic clearance. Hydrostatic pressure can make the microstructure of BMGs more stable and dense. As a result of the decrease in free volume, hardness and bulk modulus of BMGs treated with hydrostatic pressure are obviously improved.

The influence of elastic compressibility of the mantle on thermal-gravitational convection: The convective instability of the gravitational stress pattern

The set of equations for the problem of thermal-gravitational convection accounts for compressibility of solid bodies, which changes for elementary volumes moving during convection process in fields of the initial temperature and the initial gravitational stress pattern for rheology of an elastic-viscous Maxwell body. It was shown that equations of momentum conservation in the vertical direction and heat transfer for steady convection differ from the equation for incompressible liquid by terms containing the rate of elastic volume change and the connected rate of heat change. It was established that an additional term in the momentum conservation equation defines a new class of the instable state of a solid body, which is able to form huge deformations at the expense of plasticity and creep at large segments of time—flow in the field of gravity force—instability of the gravitational stress pattern of elastic-plastic body. Analysis of different boundary conditions for which this instability can be realized in the form of convective cells showed that the convection rate is totally defined by reconstruction processes of vertical stresses on horizontal boundaries close to the initial gravitation pattern. Alignment process of these stresses can be provided not only by erosion and denudation processes occurring on the Earth’s surface, but also by processes on the inner boundaries of the tectonosphere which provide isostasy in the mantle.

Finite Deformations and Internal Forces in Elastic-Plastic Crystals: Interpretations From Nonlinear Elasticity and Anharmonic Lattice Statics

Large deformation kinematics and internal forces arising from defects in crystalline solids are addressed by a nonlinear kinematic description and multiscale averaging concepts. An element of crystalline material with spatially uniform properties and containing defects such as dislocation lines and loops is considered. The average deformation gradient for this element is decomposed multiplicatively into terms accounting for effects of dislocation flux, recoverable elastic stretch and rotation, and residual elastic deformation associated with self-equilibrating internal forces induced by defects. Two methods are considered for quantifying average residual elastic deformation: continuum elasticity and discrete lattice statics. Average residual elastic strains and corresponding average residual elastic volume changes are negligible in the context of linear elasticity or harmonic force potentials but are not necessarily inconsequential in the more general case of nonlinear elasticity or anharmonic interactions.