THERMAL STRESSES FOR FUNCTIONALLY GRADED MATERIALS (FGMS) SUBJECT TO HEAT FLUX

In this paper, the thermal stress due to heat flux at the far field is derived for an infinitely extended elastic medium which contains a spherical inclusion made of functionally graded materials (FGMs). The 3-D heat conduction equation subject to uniform heat flux at the far field is solved analytically to derive the temperature distribution. Based on the temperature solution, the thermal stress field due to heat flux is obtained by solving a set of two ordinary differential equations using the method of weighted residuals. Unlike the two-phase homogeneous medium, the von Mises stress distribution is continuous at the interface of the FGM-matrix medium.

Modelling of triaxial fracture processes in heterogeneous quasi-brittle materials using the Embedded Finite Element Method (E-FEM)

This paper studies the use of the Embedded Finite Element Method (E-FEM) for the numerical modelling of triaxial fracture processes in non-homogeneous quasi-brittle materials. The E-FEM framework used in this study combines two kinematics enhancements: a weak discontinuity allowing the model to account for material heterogeneities and a strong discontinuity allowing the model to represent local fractures. The strong discontinuity features enriched fracture kinematics that allow the modelling of all typical fracture modes in three dimensions. A brief review is done of past work using similar enriched finite element frameworks to approach this problem. The work continues by establishing the theoretical basis of each kind of discontinuity formulation and their superposition through the Hu-Washizu variational principle. Afterwards, two groups of simulations have been done for discussing the performance of this combined E-FEM model: homogeneous simulations and simple heterogeneous simulations. Simple homogeneous material simulations aim to test the capabilities of the strong discontinuity model featuring full 3-D kinematics. Simple heterogeneous simulations show numerical applications of the model to the problem of a single spherical inclusion embedded into a homogeneous matrix. Comparisons will be made with another E-FEM model considering a single local fracture mode approach to discuss the differences on the representation of fracture physics under all explored conditions. A concluding statement is made on the benefits and complications identified for the E-FEM framework in this kind of applications.

On Eshelby’s inclusion problem in nonlinear anisotropic elasticity

In this paper, the recent literature of finite eignestrains in nonlinear elastic solids is reviewed, and Eshelby’s inclusion problem at finite strains is revisited. The subtleties of the analysis of combinations of finite eigenstrains for the example of combined finite radial, azimuthal, axial and twist eigenstrains in a finite circular cylindrical bar are discussed. The stress field of a spherical inclusion with uniform pure dilatational eigenstrain in a radially-inhomogeneous spherical ball made of arbitrary incompressible isotropic solids is analyzed. The same problem for a finite circular cylindrical bar is revisited. The stress and deformation fields of an orthotropic incompressible solid circular cylinder with distributed eigentwists are analyzed.

Efficient Global Sensitivity Analysis of Model-Based Ultrasonic Nondestructive Testing Systems using Machine Learning and Sobol' Indices (Invited)

The objective of this work is to reduce the cost of performing model-based sensitivity analysis for ultrasonic nondestructive testing systems by replacing the accurate physics-based model with machine learning (ML) algorithms and quickly compute Sobol' indices. The ML algorithms considered in this work are neural networks (NN), convolutional NN (CNN), and deep Gaussian processes (DGP). The performance of these algorithms is measured by the root mean squared error on a fixed number of testing points and by the number of high-fidelity samples required to reach a target accuracy. The algorithms are compared on three ultrasonic testing benchmark cases with three uncertainty parameters, namely, spherically-void defect under a focused and a planar transducer and spherical-inclusion defect under a focused transducer. The results show that NN required 35, 100, and 35 samples for the three cases, respectively. CNN required 35, 100, and 56, respectively, while DGP required 84, 84, and 56, respectively.

Analytical solution for residual stress and strain preserved in anisotropic inclusion entrapped in an isotropic host

Raman elastic thermobarometry has recently been applied in many petrological studies to recover the pressure and temperature (P–T) conditions of mineral inclusion entrapment. Existing modelling methods in petrology either adopt an assumption of a spherical, isotropic inclusion embedded in an isotropic, infinite host or use numerical techniques such as the finite-element method to simulate the residual stress and strain state preserved in the non-spherical anisotropic inclusions. Here, we use the Eshelby solution to develop an analytical framework for calculating the residual stress and strain state of an elastically anisotropic, ellipsoidal inclusion in an infinite, isotropic host. The analytical solution is applicable to any class of inclusion symmetry and an arbitrary inclusion aspect ratio. Explicit expressions are derived for some symmetry classes, including tetragonal, hexagonal, and trigonal. The effect of changing the aspect ratio on residual stress is investigated, including quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Quartz is demonstrated to be the least affected, while rutile is the most affected. For prolate quartz inclusion (c axis longer than a axis), the effect of varying the aspect ratio on Raman shift is demonstrated to be insignificant. When c/a=5, only ca. 0.3 cm−1 wavenumber variation is induced as compared to the spherical inclusion shape. For oblate quartz inclusions, the effect is more significant, when c/a=0.5, ca. 0.8 cm−1 wavenumber variation for the 464 cm−1 band is induced compared to the reference spherical inclusion case. We also show that it is possible to fit an effective ellipsoid to obtain a proxy for the averaged residual stress or strain within a faceted inclusion. The difference between the volumetrically averaged stress of a faceted inclusion and the analytically calculated stress from the best-fitted effective ellipsoid is calculated to obtain the root-mean-square deviation (RMSD) for quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Based on the results of 500 randomly generated (a wide range of aspect ratio and random crystallographic orientation) faceted inclusions, we show that the volumetrically averaged stress serves as an excellent stress measure and the associated RMSD is less than 2 %, except for diamond, which has a systematically higher RMSD (ca. 8 %). This expands the applicability of the analytical solution for any arbitrary inclusion shape in practical Raman measurements.

Adult-onset neuronal intranuclear inclusion disease, with both stroke-like onset and encephalitic attacks: a case report

Background Neuronal intranuclear inclusion disease (NIID) is a neurodegenerative disease, the clinical manifestations of which are complex and easily misdiagnosed. NIID clinical characteristics are varied, affecting the central and peripheral nervous systems and autonomic nerves. In this study, we present an NIID case with both stroke-like onset and encephalitic attacks, which is a rare case report. Case presentation A 68-year-old Chinese female presented with sudden aphasia and limb hemiplegia as the first symptoms, as well as fever, cognitive impairment and mental irritability from encephalitic attacks. During hospitalization, a brain magnetic resonance imaging (MRI) examination detected high signal intensity from diffusion-weighted imaging (DWI) of the bilateral frontal grey matter-white matter junction. Electrophysiological tests revealed the main site of injury was at the myelin sheath in the motor nerves. A skin biopsy revealed eosinophilic spherical inclusion bodies in the nuclei of small sweat gland cells, fibroblasts and fat cells, whilst immunohistochemistry revealed that p62 and ubiquitin antibodies were positive. From genetic analyses, the patient was not a carrier of the fragile X mental retardation 1 (FMR1) permutation, but repeated GGC sequences in the NOTCH2NLC gene confirmed an NIID diagnosis. Through antipsychotic and nutritional support therapy, the patient’s symptoms were completely relieved within 3 weeks. Conclusions This report of an NIID case with both stroke-like onset and encephalitic attacks provides new information for NIID diagnoses, and a comprehensive classification of clinical characteristics.

About Limit Transitions in Spatial Homogenization Problems for Two-Component Dielectric Composites with Extremal Moduli for One of Phases

The spatial problem of calculating the effective permittivity of two-component composite, consisting of a base material filling a spherical layer and one spherical inclusion, is considered. The homogenization problem is solved by effective moduli method with calculation of the energy characteristics in the composite medium and in its individual phases. In the obtained solution, the limit transitions are made for two extreme cases: pores or inclusions with zero dielectric constant and conductive inclusions with infinitely high dielectric constant. The solutions of these problems are compared with the solutions of homogenization problems for a medium with void and for a medium with conductive inclusion boundary. In problems with one basic material, the properties of inclusions were taken into account only by the corresponding boundary conditions on the interface. It is shown that calculations of the effective permittivity by energy criterion give correct results in all the cases considered, while the calculations by the average permittivity for a composite with a conductive inclusion boundary may be erroneous.