Stress Formulation Research Articles

Numerical experiment based on non-linear micropolar finite element to study micro-rotations generated by the non-symmetric Maxwell stress tensor

The main aim of the present work is to investigate the role of the Maxwell stress tensor in the study of active materials. Despite the importance of this tensor in modeling mechatronic devices used in sophisticated applications, its non–symmetry still generates controversies in the literature, probably because classical continuum mechanics assumes a symmetric Cauchy stress, although the sum of Cauchy and Maxwell stresses is non–symmetric. In the framework of generalised continuum mechanics–a more advanced formalism than the classical one–, each material point has an associated microstructure so that the micro–rotations of the electric/magnetic dipoles present in real active materials may be simulated. To this end, a modified total stress formulation, including an angular momentum balance, is developed and implemented into a finite element research code using a complex–step formulation. It is concluded that generalised mechanics allows for incorporating both symmetric and non–symmetric contributions of the Maxwell tensor. Consequently, the rotations generated by the electromagnetic field may be analysed. The influence of the complete Maxwell tensor in a magnetostrictive actuator is studied by several magneto–mechanical numerical experiments of a Terfenol–D rod encircled by air, and several conclusions are highlighted.

Planar turbulent wakes under pressure gradient: Integral and self-similarity analyses

By using a combination of integral and self-similarity analyses, the generalized analytical solutions for the mean transverse velocity and Reynolds shear stress are rigorously derived for the first time for the far field of planar turbulent wakes under arbitrary pressure gradients. Specifically, by assuming self-similarity for the mean axial velocity, the analytical formulation for the mean transverse velocity is obtained from the integral of the mean continuity equation, and the analytical formulation for the Reynolds shear stress is obtained from the integral of the momentum equation. The generalized analytical formulations for the mean transverse velocity and Reynolds shear stress consist of multiple components, each with its unique scale and physical mechanism. In the zero pressure gradient limit, the generalized formulations recover the single-scale equations reported by Wei, Liu, and Livescu. Furthermore, simpler approximate formulations for the mean transverse velocity and Reynolds shear stress are also obtained, and show excellent agreement with the experimental measurements. The findings provide new insights into the properties of planar turbulent wakes under pressure gradients, filling some long-standing gaps in the existing literature.

Elastic and anelastic adjoint tomography with and full Hessian kernels

SUMMARYThe elastic and anelastic structures of the Earth offer fundamental constraints for understanding its physical and chemical properties. Deciphering small variations in the velocity and amplitude of seismic waves can be challenging. Advanced approaches such as full-waveform inversion (FWI) can be useful. We rewrite the anelastic Fréchet kernel expression of Fichtner & van Driel using the displacement–stress formulation. We then derive the full Hessian kernel expression for viscoelastic properties. In these formulations, the anelastic Fréchet kernels are computed by the forward strain and a shift of the adjoint strain. This is complementary to the quality factor Q (i.e., inverse attenuation) Fréchet kernel expressions of Fichtner & van Driel that are explicit for the velocity–stress formulation. To reduce disk space and I/O requirements for computing the full Hessian kernels, the elastic full Hessian kernels are computed on the fly, while the full Hessian kernels for Q are computed by a combination of the on-the-fly approach with the parsimonious storage method. Applications of the Fréchet and full Hessian kernels for adjoint tomography are presented for two synthetic 2-D models, including an idealized model with rectangular anomalies and a model that approximates a subduction zone, and one synthetic 3-D model with an idealized geometry. The calculation of the full Hessian kernel approximately doubles the computationally cost per iteration of the inversion; however, the reduced number of iterations and fewer frequency stages required to achieve the same level of convergence make it overall computationally less expensive than the classical Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) FWI for the 2-D elastic tested models. We find that the use of full Hessian kernels provides comparable results to the L-BFGS inversion using the improved anelastic Fréchet kernels for the 2-D anelastic models tested for the frequency stage up to 0.5 Hz. Given the computational expense of the Q full Hessian kernel calculation, it is not advantageous to use it in Q inversions at this time until further improvements are made. For the 3-D elastic inversion of the tested model, the full Hessian kernel provides similar image quality to the L-BFGS inversion for the frequency stage up to 0.1 Hz. We observe an improved convergence rate for the full Hessian kernel inversion in comparison to L-BFGS at a higher frequency stage, 0.1–0.2 Hz, and we speculate that at higher frequency stages the use of full Hessian kernels may be more computationally advantageous than the classical L-BFGS for the tested models. Finally, we perform 3-D elastic and Q L-BFGS inversions simultaneously using the rederived Q kernels, which can reduce the computational cost of the inversion by about 1/3 when compared to the classical anelastic adjoint tomography using the additionally defined adjoint source. The recovered Q model is smeared when compared to the recovered elastic model at the investigation frequencies up to 0.5 Hz. Q inversion remains challenging and requires further work. The 2-D and 3-D full Hessian kernels may be used for other purposes for instance resolution analysis in addition to the inversions.

Anti-oxidative properties of nanocrocin in Zearalenone induced toxicity on Hek293 cell; The novel formulation and cellular assessment.

Zearalenone (ZEA) is a mycotoxin produced by fungi and induces cytotoxicity by the generation of reactive oxygen species. The aim of this study was to evaluate and compare the nephroprotective effects of crocin and nano-crocin against ZEA-induced toxicity in HEK293 cell line via modulation of oxidative stress and special formulation to make nano-crocin. Nano-crocin physicochemical properties, such as size, load, appearance, and drug release profile were determined. Also, the viability of intoxicated HEK293 cells was evaluated by MTT assay. Furthermore, lactate dehydrogenase lipid Peroxidation (LPO), and oxidative stress biomarkers were measured. The best nano-crocin formulation with superior entrapment effectiveness (54.66 ± 6.02), more significant drug loading (1.89 ± 0.01), better zeta potential (-23.4 ± 2.844), and smaller particle size (140.3 ± 18.0nm) was chosen. This study showed that treatment with crocin and nano-crocin in ZEA-induced cells, significantly decreased LDH and LPO levels and increased superoxide dismutase (SOD), catalase (CAT) activities, and total antioxidant capacity (TAC) levels compared to the control group. Moreover, nano-crocin had a more curative effect against oxidative stress than crocin. Niosomal structure of crocin, when administered with the special formulation, may be more beneficial in reducing ZEA-induced in vitro toxicity than conventional crocin.

An isogeometric boundary element formulation for stress concentration problems in couple stress elasticity

An isogeometric boundary element method (IGABEM) is developed for the analysis of two-dimensional linear and isotropic elastic bodies governed by the couple stress theory. This theory is the simplest generalized continuum theory that can effectively model size effects in solids. The couple stress fundamental solutions are explicitly derived and used to construct the boundary integral equations. A new boundary integral equation arises to obtain the moments and rotations introduced by the couple stress formulation. A new analytical solution is also derived in the present work for an elliptical opening in an infinite sheet under uniaxial far-field stress. Several stress concentration problems are examined to illustrate and validate the application of the IGABEM in couple stress elasticity. It is shown that the IGABEM scheme exhibits advantageous convergence properties in comparison with the conventional BEM for boundary value problems within the framework of couple stress elasticity.

A DG method for a stress formulation of the elasticity eigenproblem with strongly imposed symmetry

We introduce a pure–stress formulation of the elasticity eigenvalue problem with mixed boundary conditions. We propose an H(div)-based discontinuous Galerkin method that imposes strongly the symmetry of the stress for the discretization of the eigenproblem. Under appropriate assumptions on the mesh and the degree of polynomial approximation, we prove the spectral correctness of the discrete scheme and derive optimal rates of convergence for eigenvalues and eigenfunctions. Finally, we provide numerical examples in two and three dimensions.

Computational analysis of ventricular mechanics in hypertrophic cardiomyopathy patients

Hypertrophic cardiomyopathy (HCM) is a genetic heart disease that is associated with many pathological features, such as a reduction in global longitudinal strain (GLS), myofiber disarray and hypertrophy. The effects of these features on left ventricle (LV) function are, however, not clear in two phenotypes of HCM, namely, obstructive and non-obstructive. To address this issue, we developed patient-specific computational models of the LV using clinical measurements from 2 female HCM patients and a control subject. Left ventricular mechanics was described using an active stress formulation and myofiber disarray was described using a structural tensor in the constitutive models. Unloaded LV configuration for each subject was first determined from their respective end-diastole LV geometries segmented from the cardiac magnetic resonance images, and an empirical single-beat estimation of the end-diastolic pressure volume relationship. The LV was then connected to a closed-loop circulatory model and calibrated using the clinically measured LV pressure and volume waveforms, peak GLS and blood pressure. Without consideration of myofiber disarray, peak myofiber tension was found to be lowest in the obstructive HCM subject (60 kPa), followed by the non-obstructive subject (242 kPa) and the control subject (375 kPa). With increasing myofiber disarray, we found that peak tension has to increase in the HCM models to match the clinical measurements. In the obstructive HCM patient, however, peak tension was still depressed (cf. normal subject) at the largest degree of myofiber disarray found in the clinic. The computational modeling workflow proposed here can be used in future studies with more HCM patient data.

An Analytical Solution of Pressure and Displacement Induced by Recovery of Poroelastic Reservoirs and Its Applications

Summary An analytical solution of induced pressure and displacement fields during reservoir production enables rapid yet accurate prediction, as well as optimization of reservoir performance. Traditionally, such solutions are primarily obtained for infinite or semi-infinite domains using Green’s function method, which requires time-consuming numerical integral operations. In this work, we have developed a series solution of transient pressure and displacement fields of a finite-size reservoir using the eigenfunction expansion method. The solution is derived based on the stress formulation of geomechanical governing equations. We have validated the developed solution and applied it to a series of case studies, including the stress concentration effect induced by neighboring horizontal wells and subsidence induced by production. The results demonstrate that, compared to Green’s function method, the series solution is more convenient in implementation and more flexible in handling boundary effects.

Proposed method of combining continuum mechanics with Einstein Field Equations

The paper proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress–energy tensor for a system with an electromagnetic field leads to the solution of Einstein Field Equations indicating a relationship between the electromagnetic field tensor and the metric tensor. In this EFE solution, the cosmological constant is related to the invariant of the electromagnetic field tensor, and additional pulls appear, dependent on the vacuum energy contained in the system. In flat Minkowski spacetime, the vanishing four-divergence of the proposed stress–energy tensor expresses relativistic Cauchy’s momentum equation, leading to the emergence of force densities which can be developed and parameterized to obtain known interactions. Transformation equations were also obtained between spacetime with fields and forces, and a curved spacetime reproducing the motion resulting from the fields under consideration, which allows for the extension of the solution with new fields.

EXPERIMENTAL REPORT ON GLASS PANELS AGAINST STATIC AND REPEATED IN-PLANE COMPRESSION LOADING

Primary load-bearing members used in glass structures, such as columns consisting of glass panels, are frequently subjected to in-plane loading. Its allowable stress for safety design appears to be a significant subject. By analyzing the results of static (without repeated loading) and cycling compression loading tests, the authors explore the mechanical features and failure mechanism of the tempered glass panels subjective to in-plane compression loading, including its ultimate stress and buckling load. In addition, a statistical method based on the experimental results is adopted to evaluate the allowable compressive stress. The experimental results show that the ultimate loads of specimens with high slenderness ratios satisfy Euler's critical load formula. In contrast, the ultimate loads of specimens with low thickness ratios distribute in a certain variance range. For the cycling loading test, after 30 times of repeated loading with maximum stress equivalent to 2/3 of the ultimate static stress, the average strength is almost the same or bigger than that of static loading tests. No fatigue fracture due to repeated loading was found for the tempered glass panels. Consequently, the allowable stress for in-plane compressive loading can be formulated based on Euler's critical load formula for a glass panel with a bigger slenderness ratio. The formulation for the allowable compressive stress of a glass panel with a smaller slenderness ratio is promoted using statistical analysis with a 95 percent confidence level for the safety design.

Peridynamic formulation of the mean stress and incubation time fracture criteria and its correspondence to the classical Griffith’s approach

Peridynamic formulation of the mean stress and incubation time fracture criteria and its correspondence to the classical Griffith’s approach

A new equivalent stress approach based on complex invariants: The COIN LiWI method

In this paper, a new equivalent stress approach is presented, which builds on the basic ideas of linear wave interference (LiWI) and thus leads to physically valid signals. Complex invariants (COIN) were introduced for the derivation, whereby a generalized calculation method with consideration of the tension shear strength ratio could be derived following the formulation of Mertens (1988). The LiWI approach was also applied to an equivalent stress formulation from the German FKM guideline (Rennert et al., 2021). Both approaches were tested and compared with signed von-Mises using existing experiments with a wide range of different loads, e.g. nonproportional, variable, frequency superimposed.

Numerical verification of sharp corner behavior for Giesekus and Phan-Thien–Tanner fluids

We verify numerically the theoretical stress singularities for two viscoelastic models that occur at sharp corners. The models considered are the Giesekus and Phan-Thien–Tanner (PTT), both of which are shear thinning and are able to capture realistic polymer behaviors. The theoretical asymptotic behavior of these two models at sharp corners has previously been found to involve an integrable solvent and polymer elastic stress singularity, along with narrow elastic stress boundary layers at the walls of the corner. We demonstrate here the validity of these theoretical results through numerical simulation of the classical contraction flow and analyzing the 270° corner. Numerical results are presented, verifying both the solvent and polymer stress singularities, as well as the dominant terms in the constitutive equations supporting the elastic boundary layer structures. For comparison at Weissenberg order one, we consider both the Cartesian stress formulation and the alternative natural stress formulation of the viscoelastic constitutive equations. Numerically, it is shown that the natural stress formulation gives increased accuracy and convergence behavior at the stress singularity and, moreover, encounters no upper Weissenberg number limitation in the global flow simulation for sufficiently large solvent viscosity fraction. The numerical simulations with the Cartesian stress formulation cannot reach such high Weissenberg numbers and run into convergence failure associated with the so-called high Weissenberg number problem.

Temperature-dependent lateral earth pressures in partially saturated backfills

Stability analysis of retaining structures supporting variably saturated backfills is a topic of great significance in civil engineering. However, the backfill soil may be exposed to elevated temperature; this may result in changes of the saturation state, thus posing temperature-dependent effective stress, variable suction stress and different hydro-mechanical characteristics to partially saturated soils. In the present work, the significant impact of elevated temperature is incorporated into the soil-water retention curve and suction stress-based effective stress formulations. Accordingly, the lower bound theorems of limit analysis in conjunction with finite element and second-order cone programming are adopted so as to thoroughly examine the impact of elevated temperature on the coefficients of lateral earth pressure acting on a model retaining wall backfilled by two hypothetical partially saturated soils; a granular material (sand) and a cohesive material (clay). The effective stress-based formula for the strength of variably saturated soils is implemented to modify the conventional Mohr–Coulomb yield criterion. In general, it was shown that for unsaturated clay backfills, the active lateral earth pressure decreases while the passive lateral earth pressure increases with increasing the induced temperature; however these influences were observed to be small for the sand backfill.

A Continuum-mechanics solution of laminate free edges based on asymmetric stress and strain tensors

A meaningful attempt is made to investigate the impact of using asymmetric stress and strain formulations in the prediction of free-edge response of laminated orthotropic materials. The paper contributes to the process of making the singular free-edge stresses and strains in the literature more proximate to the bounded (realistic) solutions. Related to the singularity issue, it was previously identified that the symmetry assumption for stress and strain tensors could lead to a contradiction with the predicted free-edge stress functions. It is, therefore, reasonable to assert that the classical continuum mechanics based on tensor symmetries is unfaithful for the modelling of free edges. The present study demonstrates that for the free-edge region, stress and strain tensors naturally become asymmetric when they are enabled to be, to reach the minimum strain energy. By comparing with strain predictions generated by Digital Image Correlation technique, the new framework is shown to be able to address the notable discrepancy between the classical theoretical result and experimental result, which suggested the higher fidelity of the new framework. Moreover, by resolving the contradiction, the model is also made less sensitive to mesh refinement which sets an important basis for reaching a bounded solution in the future.

Systematic Methods to Increase the Lifetime of Mechanical Products Such as Refrigerators by Employing Parametric Accelerated Life Testing

This investigation practically explains the implementation of parametric accelerated life testing (ALT) as an algorithm to recognize design imperfection and rectify it in creating a reliable quantitative (RQ) statement by sample size equation. It covers: (1) a module BX life that X% of a collection of system items is unsuccessful with an ALT plan, (2) design for fatigue, (3) ALTs with alterations, and (4) discernment as to if the final design(s) obtains the targeted BX lifetime. A (generalized) life–stress formulation by the linear transport process is recommended for the mathematical work of the parametric model. As a case study, an ice-maker including gear system in a refrigerator was utilized. The gear teeth made of cast iron (carbon, 3 wt% and silicon, 2 wt%) was fracturing in a refrigerator ice-maker. To reproduce the field failure and rectify the problematic designs in the marketplace, a parametric ALT was carried out. At the first ALT, the gear teeth made of cast iron partly cracked and fractured under severe cold conditions (below −20 °C) in the freezer. It was modified by changing the material from cast iron to a sinter-hardened powder metallurgy nickel steel because high fatigue strength in the low temperature was required. At the second ALT, we discovered the fractured helix made of polycarbonates (PC). As a modification, strengthened rib on the front and side of the helix the thickness of gear teeth was attached. At the third ALT, there was no concern, and the life of the auger motor including gear system was manifested to have a B1 life 10 years.

Stress formulation of acoustoelasticity

Acoustoelasticity describes the relationship between elastic wave velocities and the initial stress present in a material. Traditional theories consider successive deformations involving small amplitude wave motion superimposed on an initially deformed material. Then, a constitutive relationship must be applied to relate the initial static deformation to the desired relationships involving initial stress, resulting in expressions of wave velocities involving a mix of elastic stiffness and compliance constants. In this article, a pure stress formulation is developed for acoustoelasticity. In this setting, the problem involves the superposition of a dynamic stress wave on an initially stressed material configuration, rather than the superposition of kinematic variables. The phase velocity of the stress wave is naturally related to the initial stress through only the compliance constants. Thus, compliances are the fundamental constants of acoustoelasticity.

Three-Dimensional Boundary Element Strategy for Stress Sensitivity of Fractional-Order Thermo-Elastoplastic Ultrasonic Wave Propagation Problems of Anisotropic Fiber-Reinforced Polymer Composite Material.

A new three-dimensional (3D) boundary element method (BEM) strategy was developed to solve fractional-order thermo-elastoplastic ultrasonic wave propagation problems based on the meshless moving least squares (MLS) method. The temperature problem domain was divided into a number of circular sub-domains. Each node was the center of the circular sub-domain surrounding it. The Laplace transform method was used to solve the temperature problem. A unit test function was used in the local weak-form formulation to generate the local boundary integral equations, and the inverse Laplace transformation method was used to find the transient temperature solutions. Then, the three-dimensional elastoplastic problems could be solved using the boundary element method (BEM). Initial stress and strain formulations are adopted, and their distributions are interpolated using boundary integral equations. The effects of the fractional-order parameter and anisotropy are investigated. The proposed method’s validity and performance are demonstrated for a two-dimensional problem with excellent agreement with other experimental and numerical results.

On the formulations of the electromagnetic stress–energy tensor

In this work, we review the main existing theories for the electromagnetic stress–energy tensor in dielectric media — a problem directly related to the century-long debate regarding the correct momentum of light in dielectric media, known as Abraham–Minkowski controversy. The theoretical validity of the main existing formulations is analyzed in terms of symmetry and invariance requirements for the tensors. We also present position- and time-dependent numerical simulations of the related electromagnetic forces for a lossless nondispersive medium, highlighting the different expected spatial force distributions. The force densities of different formulations drive forward different momentum and atomic number density distributions of the medium contributing to the total momentum and energy densities associated with the coupled field-medium state of light.

On the prediction of the stress field in adhesive joints using a combined analytical-numerical method

In this paper, the stress field in adhesively bonded joints is predicted by employing an analytical approach together with the finite element method (FEM). To accomplish this, the adhesive joint is considered as a bi-material notch. Then, a unified analytical formulation for the in-plane stress and displacement field of bi-material notches is presented in the form of asymptotic series. Subsequently, a numerical procedure based on an over-determined system of equations is used to obtain the coefficients of the series solution for various types of adhesive joints including single lap joint (SLJ), single fillet lap joint (SFLJ), butt joint (BJ), scarf joint (SJ), and single lap joint with an inside taper and adhesive fillet (SLJ-ITAF). By comparing the results obtained from the analytical stress field with the numerical results, the accuracy of the calculated coefficients is evaluated. It is shown that by using the proposed approach one can obtain the stress field within the adhesive layer by using the stress or displacement fields of the adherend. The obtained results also show that neglecting the higher-order terms can result in significant errors while considering the first three non-singular stress terms besides the singular term reveals very good results.