Inelastic Components Research Articles

Intergranular Clay Films Control Inelastic Deformation in the Groningen Gas Reservoir: Evidence From Split‐Cylinder Deformation Tests

AbstractProduction of oil and gas from sandstone reservoirs leads to small elastic and inelastic strains in the reservoir, which may induce surface subsidence and seismicity. While the elastic component is easily described, the inelastic component, and any rate‐sensitivity thereof remain poorly understood in the relevant small strain range (≤1.0%). To address this, we performed a sequence of five stress/strain‐cycling plus strain‐marker‐imaging experiments on a single split‐cylinder sample (porosity 20.4%) of Slochteren sandstone from the seismogenic Groningen gas field. The tests were performed under in situ conditions of effective confining pressure (40 MPa) and temperature (100 °C), exploring increasingly large differential stresses (up to 75 MPa) and/or axial strains (up to 4.8%) in consecutive runs. At the small strains relevant to producing reservoirs (≤1.0%), inelastic deformation was largely accommodated by deformation of clay‐filled grain contacts. High axial strains (>1.4%) led to pervasive intragranular cracking plus intergranular slip within localized, conjugate bands. Using a simplified sandstone model, we show that the magnitude of inelastic deformation produced in our experiments at small strains (≤1.0%) and stresses relevant to the Groningen reservoir can indeed be roughly accounted for by clay film deformation. Thus, inelastic compaction of the Groningen reservoir is expected to be largely governed by clay film deformation. Compaction by this mechanism is shown to be rate insensitive on production timescales and is anticipated to halt when gas production stops. However, creep by other processes cannot be eliminated. Similar, clay‐bearing sandstone reservoirs occur widespread globally, implying a wide relevance of our results.

Theory of ultrafast x-ray scattering by molecules in the gas phase.

We recast existing theory of ultrafast time-resolved x-ray scattering by molecules in the gas phase into a unified and coherent framework based on first-order time-dependent perturbation theory and quantum electrodynamics. The effect of the detection window is analyzed in detail and the contributions to the total scattering signal are discussed. This includes the coherent mixed component caused by interference between scattering amplitudes from different electronic states. A new, detailed, and fully converged simulation of ultrafast total x-ray scattering by excited H2 molecules illustrates the theory and demonstrates that the inelastic component can contribute strongly to the total difference scattering signal, i.e., on the same order of magnitude as the elastic component.

An efficient method for optimizing the seismic resistance of reinforced concrete frame structures

A practical and efficient optimization procedure for designing reinforced concrete frame structures with improved resistance to seismic loading was developed. The design methodology used the optimality criteria method in an iterative analysis-and-redesign scheme. A damage ratio–based procedure was proposed by employing the inelastic component rotations from nonlinear dynamic analysis to strengthen the severely damaged components in each iteration. The optimization approach is intuitive, simple, and easy to apply, since only analysis tools are required. The approach was applied to optimize the seismic response of two prototype frames, and sensitivity analysis established the relationship between seismic performance and the additional material cost of strengthening. The proposed method can substantially reduce the maximum interstory drift for a slight increase of material cost, indicating that the proposed method is a feasible design procedure for improving the earthquake resistance of reinforced concrete frame structures. Also, the procedure can deal with the cases of single and multiple ground motions. The effectiveness of the proposed method was also verified through extensive time-history analyses.

Subsurface Imaging of Cell Organelles by Force Microscopy.

The development of high-resolution, label-free, noninvasive, and subsurface microscopy methods of living cells remains a formidable problem. Force-microscopy-based stiffness measurements contribute to our understanding of single-cell nanomechanics. The elastic properties of the cell’s outer structures, such as the plasma membrane and actin cytoskeleton, dominate stiffness measurements, which in turns prevents the imaging of intracellular structures. We propose that the above limitation could be overcome by combining 2D sections of the cell’s viscoelastic properties. We show the simultaneous imaging of the outer cell’s cytoskeleton and the organelles inside the nucleus. The elastic component of interaction force carries information on the cell’s outer elements as the cortex and the actin cytoskeleton. The inelastic component is sensitive to the hydrodynamic drag of the inner structures such the nucleoli.

On process-step parallel computability and linear superposition of mechanical responses in additive manufacturing process simulation

We study linearity assumptions in the transient macroscale mechanical aspect of additive manufacturing (AM) process simulation. Linearity assumptions are often resorted to in combination with calibrated inelastic deformation components to arrive at computationally tractable yet reasonably accurate AM process models. We point out that linearity assumptions permit the independent computation of the response increment in each step of the AM process, and the total mechanical response is the superposition of all the process-step increments. In effect, process-step increments are computed with respect to the stress-free reference configuration in each step. The implication is that the mechanical response increment in each linearised AM process step may be computed in parallel. Trivial process-step-wise parallel computability breaks down, however, if nonlinearity (i.e. geometric or material) is modelled. In our investigation the influence of geometric nonlinearity on part distortion is small (but this is of course part-geometry specific), and more realistic stresses are obtained by imposing a nonlinear elastoplastic material law after the parallel computation and superposition of the linear AM response increments. It is demonstrated that simulation wall-clock time is reduced by exploiting process-step parallel computability in the linear regime. Moreover, numerical experiments suggest that process-step parallelization scales better (in wall-clock time) than conventional parallelization in the sequential computation of each response increment.

Inelastic Deformation of the Slochteren Sandstone: Stress‐Strain Relations and Implications for Induced Seismicity in the Groningen Gas Field

AbstractPore pressure reduction in sandstone reservoirs generally leads to small elastic plus inelastic strains. These small strains (0.1%–1.0% in total) may lead to surface subsidence and induced seismicity. In current geomechanical models, the inelastic component is usually neglected, though its contribution to stress‐strain behavior is poorly constrained. To help bridge this gap, we performed deviatoric and hydrostatic stress cycling experiments on Slochteren sandstone samples from the seismogenic Groningen gas field in the Netherlands. We explored in situ conditions of temperature (T = 100 °C) and pore fluid chemistry, porosities of 13% to 26% and effective confining pressures (≤320 MPa) and differential stresses (≤135 MPa) covering and exceeding those relevant to producing fields. We show that at all stages of deformation, including those relevant to producing reservoirs, 30%–50% of the total strain measured is inelastic. Microstructural observations suggest that inelastic deformation is largely accommodated by intergranular displacements at small strains of 0.5%–1.0%, with intragranular cracking becoming increasingly important toward higher strains. The small inelastic strains relevant for reservoir compaction can be described by an isotropic, Cam‐clay plasticity model. Applying this model to the depleting Groningen gas field, we show that the in situ horizontal stress evolution is better represented by taking into account combined elastic and inelastic deformation than it is by representing the total deformation behavior using poroelasticity (up to 40% difference). Therefore, inclusion of the inelastic contribution to reservoir compaction has a key role to play in future geomechanical modelling of induced subsidence and seismicity.

Ab Initio Calculation of Total X-ray Scattering from Molecules.

We present a method to calculate total X-ray scattering cross sections directly from ab initio electronic wave functions in atoms and molecules. The approach can be used in conjunction with multiconfigurational wave functions and exploits analytical integrals of Gaussian-type functions over the scattering operator, which leads to accurate and efficient calculations. The results are validated by comparison to experimental results and previous theory for the molecules H2 and CO2. Importantly, we find that the inelastic component of the total scattering varies strongly with molecular geometry. The method is appropriate for use in conjunction with quantum molecular dynamics simulations for the analysis of new ultrafast X-ray scattering experiments and to interpret accurate gas-phase scattering experiments.

Electronic Coherence in Ultrafast X-Ray Scattering from Molecular Wave Packets.

Simulations of nonresonant ultrafast x-ray scattering from a molecular wave packet in H_{2} are used to examine and classify the components that contribute to the total scattering signal. The elastic component, which can be used to determine the structural dynamics of the molecule, is also found to carry a strong signature of an adiabatic electron transfer that occurs in the simulated molecule. The inelastic component, frequently assumed to be constant, is found to change with the geometry of the molecule. Finally, a coherent mixed component due to interferences between different inelastic transitions is identified and shown to provide a direct probe of transient electronic coherences.

Micromechanical modeling of the effects of adiabatic heating on the high strain rate deformation of polymer matrix composites

Fiber reinforced polymer matrix composites are increasingly being used to fabricate energy-absorbing aerospace structural components susceptible to impact loading, such as jet engine containment structures subjected to blade-out events. The development and certification of such structures necessitates a detailed understanding of the dynamic behavior of the constituent materials, particularly the strain rate, temperature, and pressure dependent polymer matrix, and their complex interaction. As the rate of deformation increases, the thermodynamic condition transitions from isothermal to adiabatic. The conversion of plastic work to heat causes local adiabatic heating in the polymer matrix, but the rapid nature of impact events does not allow sufficient time for heat to dissipate; ballistic impact events can therefore be regarded as fully adiabatic. Local adiabatic heating can significantly affect the high rate deformation response if thermal softening effects outweigh strain and strain rate hardening effects and therefore, must be explicitly modeled at the appropriate length scale. In this paper, an existing isothermal viscoplastic strain rate and pressure-dependent polymer constitutive formulation is extended to nonisothermal conditions by modifying the inelastic strain rate tensor components to explicitly depend on temperature based on the Arrhenius equation for nonisothermal processes. A methodology based on shifting neat resin dynamic mechanical analysis data is utilized to determine the polymer elastic properties over a range of strain rates and temperatures. Temperature rises due to the conversion of plastic work to heat are computed, assuming adiabatic conditions. It is demonstrated that the modified polymer constitutive model is capable of capturing strain rate and temperature dependent yield as well as thermal softening associated with the conversion of plastic work to heat at high rates of strain. The nonisothermal polymer constitutive model is then embedded within the Generalized Method of Cells micromechanics framework to investigate the manifestation of matrix thermal softening, due to the conversion of plastic work to heat, on the high strain rate response of a T700/Epon 862 unidirectional composite. Adiabatic model predictions for high strain rate composite longitudinal tensile, transverse tensile, and in-plane shear loading are presented. Results show a substantial deviation from isothermal conditions; significant thermal softening is observed for matrix dominated deformation modes (transverse tension and in-plane shear), highlighting the importance of accounting for local adiabatic heating in the polymer matrix in the high strain rate analysis of polymer matrix composite structures.

Improved fatigue life of the newly developed Fe-15Mn-10Cr-8Ni-4Si seismic damping alloy

Fe-15Mn-10Cr-8Ni-4Si is a newly developed alloy for seismic damper applications. The low- and high-cycle fatigue (LCF and HCF) properties of this alloy was investigated in this study. The LCF resistance of this alloy was found to be superior to that of other materials. The inelastic component was established to be the main contributor to the superior fatigue life of Fe-15Mn-10Cr-8Ni-4Si, including at relatively low strain levels. This alloy demonstrated a gradual and mild cyclic hardening behavior at a wide range of strains. In terms of the HCF property, the fatigue limit was 262.5 MPa, which is 96% of 0.2% proof stress of 274 MPa. A surface observation of the post-fatigued specimen tested at a stress amplitude of 250 MPa for 107 cycles without failure showed that while surface relief developed, no cracks with a size of at least several grains were detected. Since Fe-high Mn alloys generally exhibit several unique deformation modes involving the deformation-induced phase transformation, the microstructure of Fe-15Mn-10Cr-8Ni-4Si after fatigue was investigated using electron-backscatter diffraction (EBSD) microscopy. As a result, ε-martensite formed via the deformation-induced γ→ε martensitic transformation was detected in all specimens tested under different conditions. Even at a stress level lower than the fatigue limit, ε-martensite formed while the amount of it was very limited. Except for the specimen tested at a low stress level of 275 MPa, a well-developed deformation-induced microstructure was found near the crack; α′-martensite formed by the two-stage phase transformation γ→ε→α′ was detected only in the region near the crack in a specimen tested at a total strain range of 2%.

Probe damage evaluation in frequency-modulation shear-force acoustic near-field microscopy

Shear-force acoustic near-field microscopy (SANM) and Whispering Gallery Acoustic Sensing have recently been introduced as a tandem system to characterize the viscoelastic response of fluids confined between two solid-boundaries in relative oscillatory lateral motion. SANM uses a) a laterally oscillating tapered probe (attached to a quartz tuning fork QTF) as one of the trapping boundaries, and b) an acoustic sensor (attached to the other flat-substrate boundary) that independently monitors the fluid’s acoustic emission. On the other and, WGAS is another technique that uses an acoustic transducer (attached to the frame holding the probe) to monitor the probe’s lateral motion amplitude. Steps towards improving the standing of the SANM/WGAS system as a nanometrology tool include i) to integrate frequency modulation methods, to thus be able to discriminate the elastic from the inelastic component of the probe-fluid interactions, and ii) evaluate the integrity and robustness of the probe to endure such surface interactions, since eventual deformation of the probe affect the reproducibility of the measurements. Here we report using the WGAS signal (or alternatively the QTF electrical response) to control the probe’s motion in frequency modulation modality. In addition, systematic evaluation of eventual probe damage (acquiring scanning electron micrograph before and after the probe exerts one approach/retraction trip to/from the substrate) are also presented. The non-monotonic behavior of the fluid’s acoustic emission (first increasing and then decreasing) as the probe approaches the sample—which occurs before the probe touches the surface, as revealed by the lack of damaged observed on the probe—constitutes one of the main findings reported here. The acoustic signal provides clues on the fluid’s dynamic response when subjected to nanoscale confinement.

Analysis of Finite Elasto-Plastic Strains: Integration Algorithm and Numerical Examples

The paper is devoted to the development of a calculation technique for elasto-plastic solids with regard to finite strains. The kinematics of elasto-plastic strains is based on the multiplicative decomposition of the total deformation gradient into elastic and inelastic (plastic) components. The stress state is described by the Cauchy stress tensor. Physical relations are obtained from the equation of the second law of thermodynamics supplemented with a free energy function. The free energy function is written in an invariant form of the left Cauchy–Green elastic strain tensor. An elasto-plasticity model with isotropic strain hardening is considered. Based on an analog of the associated rule of plastic flows and the von Mises yield criterion, we develop the method of stress projection onto the yield surface (known as the radial return method) with an iterative refinement of the current stress-strain state. The iterative procedure is based on the introduction of additional virtual stresses to the resolving power equation. The constitutive relations for the rates and increments of the true Cauchy stresses are constructed. In terms of the incremental loading method, the variational equation is obtained on the basis of the principle of possible virtual powers. Spatial discretization is based on the finite element method; an octanodal finite element is used.We present the solution to the problem of tension of a circular bar and give a comparison with results of other authors.

Peculiar atomic dynamics in liquid GeTe with asymmetrical bonding: Observation by inelastic x-ray scattering

Collective dynamics in liquid GeTe was investigated by inelastic x-ray scattering at $2\ensuremath{\le}Q\ensuremath{\le}31\phantom{\rule{4pt}{0ex}}{\mathrm{nm}}^{\ensuremath{-}1}$. The dynamic structure factor shows clear inelastic excitations. The excitation energies at low $Q$ disperse with increasing $Q$, consistent with the behavior of a longitudinal-acoustic excitation. The dispersion curve has a flat-topped region around the pseudo-Brillouin-zone boundary, similar to what is observed in liquid Bi [Inui et al., Phys. Rev. B 92, 054206 (2015)]. The dynamic structure factor shows a low-frequency excitation, and its coupling with the longitudinal-acoustic mode plays an important role for a flat-topped dispersion. From these results, it is inferred that atomic dynamics in liquid GeTe is strongly affected by a Peierls distortion similar to liquid Bi. By comparing the momentum transfer dependence of the excitation energy and quasielastic linewidth to partial structure factors obtained by our own ab initio molecular dynamics simulation for liquid GeTe, the quasielastic and inelastic components were found to be correlated with Te-Te and Ge-(Ge,Te) partial structure factors, respectively.

Thermo-mechanical fatigue behavior of nickel-based 23Cr-45Ni-7W alloy for boiler pipes and tubes

This study focuses on thermo-mechanical fatigue (TMF) behaviors of nickel-based 23Cr-45Ni-7W alloy for pipes and tubes in high-efficiency power boilers. TMF tests (maximum temperature = 700 °C; minimum temperature = 100 °C) were conducted under in-phase (IP) and out-of-phase (OP) conditions. The lives under the IP condition is 0.30–0.44 times of that under the OP condition when same total strain range, Δεt, is applied. The TMF properties obtained via the tests are compared with the results of isothermal fatigue (ITF) tests conducted at 700 °C and bithermal fatigue (BTF) tests with maximum and minimum temperatures of 700 °C and 100 °C, respectively. The fracture morphology for each type of TMF, ITF, and BTF is similar under the test conditions of this study. Intergranular cracking is predominant under application of cyclic tensile creep strain during the fatigue tests, and transgranular cracking is predominant under application of cyclic compressive creep strain during the fatigue tests. The inelastic strain range–fatigue life (Δεin–Nf) relation in the TMF test and the inelastic strain range components–life (Δεij–Nij) relation determined using the strain range partitioning method show a good agreement within a factor of 1.5 scatter band. These results indicate the possibility of predicting the TMF life of the 23Cr-45Ni-7W alloy using the results of the ITF test by considering the amount and direction (tension or compression) of creep strain applied to the alloy.

Printing of hybrid magneto active polymers with 6 degrees of freedom

3D printing techniques offer a versatile method for the fabrication and structuring of magnetoactive polymer (MAP) components and devices for research prototype development. MAP materials enjoy an advantage in that the particulate content may be manipulated by external magnetic fields during the forming and curing processes. Controlled particle diffusion within the polymer matrix, by means of external fields applied during the printing process, influences a further three spatial dimensions. This permits control of the spatial particle concentration and makes free displacement of particle accumulations possible during the crosslinking phase. Particles which are susceptible to electric or magnetic fields can thereby be shifted into regions previously free of particles. The additional 3 graded dispersion axes effectively results in what can be described as 6 degrees of freedom (6DOF) printing.Electrically conductive polymers combined with non-conductive areas, provide an additional benefit for the production of complex hybrid structures. This may be augmented by the combination of magnetically active thermoplastics as inelastic structural components together with mechanically deformable elastomers.The combination of all fabrication methods in one hybrid printing process makes the production of complex sensor and actuator systems in one manufacturing sequence possible. This far exceeds the capabilities of conventional casting and machining operations and opens new possibilities for the fabrication of soft material elements.

Efficient Inelasticity-Separated Finite-Element Method for Material Nonlinearity Analysis

Material nonlinearity analyses are widely used to determine the safety of structural components or engineering structures. Although advanced computer hardware technology has considerably improved the computational performance of such analyses, large and complex emerging structures and expensive computational process still attract the attention of researchers toward finding more efficient and accurate numerical solution methods. This paper combines an inelasticity-separated (IS) concept with the finite-element method (FEM) to establish a novel and efficient framework (IS-FEM) for structures with material nonlinear behavior that only occurs within certain small local domains. The IS concept presented in this paper begins by decomposing the strain on a nonlinear material into its linear-elastic and inelastic components and runs through the whole framework. Based on the principle of virtual work, a novel governing equation for structures with an IS form is derived by treating the decomposed inelastic strain as additional degrees of freedom. Moreover, the changing stiffness matrix in the classical FEM is expressed as the sum of the invariant global linear elastic stiffness matrix and another changing inelastic stiffness matrix with a small rank, and it represents the material nonlinearity of local domains so that the efficient solution method can be applied to perform nonlinear analyses via the mathematical Sherman–-Morrison–Woodbury (SMW) formula. Because the unchanging global stiffness matrix is used throughout the whole nonlinear analysis and the computational effort only focuses on a small dimension matrix that represents the local inelastic behavior, the efficiency of the proposed IS-FEM is improved greatly. The proposed method is validated against the results of classical FEM via three separate numerical examples and its value and potential for use in any material nonlinearity analyses are also demonstrated.

Seismic Damage Detection of Moment Resisting Frame Structures Using Time‐Frequency Features

To detect seismic damage of moment resisting frame (MRF) structures, a data‐driven method using the fractal dimension (FD) of time‐frequency feature (TFF) of structural seismic dynamic responses at measured stories is extended and refined. The TFF is defined as the real part of Gabor wavelet transform of translational interstory displacement, and FD is used to give a quantitative value to describe the calculated TFF. Static condensation method is first used to reduce the degrees‐of‐freedom (DOFs) of MRF and to express the rotational displacements using translational displacements. For linear MRF, the FDs of TFFs at all stories are the same using the definition of TFF and modal superposition principle. For damaged MRF with plastic hinges at the ends of beams and columns, the force analogy method is implemented to establish transformation matrix from plastic hinge rotations to translational interstory inelastic displacements. Due to the sparseness of the transformation matrix, plastic hinges only generate interstory inelastic displacements, which are low‐frequency contents, in the vicinity of plastic hinges. Correspondingly, the FDs of TFFs of interstory displacements with inelastic component are different from the FDs of TFFs of the interstory displacements that do not contain inelastic component. A numerical simulation on a 16‐story MRF was conducted. The simulation included 10 cases such as no damage or linear structure, plastic hinges in single‐story beams, plastic hinges in single‐story columns, plastic hinges in single‐story beams and columns, and plastic hinges in multiple story beams and columns. The robustness to measurement noise was also investigated. The seismic damage detection results demonstrated that the proposed method was capable of locating the stories where the plastic hinges occurred.

Real-Time Procurement Strategies of a Proactive Distribution Company With Aggregator-Based Demand Response

In this paper, we present a real-time trading framework for distribution networks where a rational aggregator is identified as a broker by contracting with individual demands and dealing with the distribution company. Demand response capability is characterized by the coexistence of elastic and inelastic demand components. A one-leader multi-follower bi-level model is proposed to derive the procurement strategies, i.e., the upper-level problem intends to maximize the profit of the proactive distribution company, while the lower-level expresses the profit maximization per rational aggregator. The proposed model is then transformed into a solvable mathematical program with equilibrium constraints through a primal-dual approach. A modified 33-bus distribution network is utilized to demonstrate the effectiveness of the proposed model.

07.01: New developments in the Direct Strength Method (DSM) for design of cold‐formed steel sections under localised loading

ABSTRACTA consistent and simplified Direct Strength Method (DSM) for design of cold‐formed (or thin‐walled) sections under localised loading, which is called web crippling, is proposed. The development of this method proposes generalised equations for design of thin‐walled sections under the four different localised load cases which are the interior one‐flange (IOF), the end one‐flange (EOF), the interior two‐flange (ITF) and the end two‐flange (ETF). The same parameters are used in the DSM equations for both the IOF and EOF load cases. However, the ITF and ETF load cases require different parameters in the DSM equations to predict the capacities of structural members. The equations contain both an inelastic reserve component and a yield load component which are different from those proposed previously in this regard.This paper briefly introduces the calculation of the buckling load and the yield load. From these two main input variables, DSM equations are used to determine the capacities of structural members under localised loading. Calibration is performed against all available experimental data to validate the accuracy of the DSM predictions.

Incompressible inelasticity as an essential ingredient for the validity of the kinematic decomposition [formula omitted

The multiplicative decomposition of the total deformation F=FeFi between an elastic (Fe) and an inelastic component (Fi) is standard in the modeling of many irreversible processes such as plasticity, growth, thermoelasticity, viscoelasticty or phase transformations. The heuristic argument for such kinematic assumption is based on the chain rule for the compatible scenario (CurlFi=0) where the individual deformation tensors are gradients of deformation mappings, i.e. F=Dφ=D(φe∘φi)=(Dφe)∘φi(Dφi)=FeFi. Yet, the conditions for its validity in the general incompatible case (CurlFi≠0) has so far remained uncertain. We show in this paper that detFi=1 and CurlFi bounded are necessary and sufficient conditions for the validity of F=FeFi for a wide range of inelastic processes. In particular, in the context of crystal plasticity, we demonstrate via rigorous homogenization from discrete dislocations to the continuum level in two dimensions, that the volume preserving property of the mechanistics of dislocation glide, combined with a finite dislocation density, is sufficient to deliver F=FeFp at the continuum scale. We then generalize this result to general two-dimensional inelastic processes that may be described at a lower dimensional scale via a multiplicative decomposition while exhibiting a finite density of incompatibilities. The necessity of the conditions detFi=1 and CurlFi bounded for such systems is demonstrated via suitable counterexamples.