Rigid Inclusion Research Articles

Exact elastoplastic analysis of a rotating cylinder with a rigid inclusion under mechanical loading and unloading

AbstractAn elastoplastic rotating cylinder with a rigid inclusion under plane strain condition is investigated. The analysis is based on infinitesimal strain theory, Tresca's yield condition, and its associated flow rule and perfectly plastic material behavior. Both loading and unloading are considered. It is established that secondary plastic flow may occur during unloading after a previous rotation, and the exact solutions for all stages of deformation are obtained. The results are illustrated by the distributions of the displacement, stress and plastic strain in a cylinder rotating at different speeds.

EXACT SOLUTION OF CIRCULAR INCLUSION PROBLEMS BY A BOUNDARY INTEGRAL METHOD

As an excellent numerical method, boundary element method (BEM) has been widely applied in various scientific and engineering problems. In this paper, a new boundary integral method is obtained based on Somigliana's equation and the properties of Green's function by referring to the idea of boundary element method. It can be used to find the analytic solution of linear elastic problems. The boundary integral method can also be obtained from Betti's reciprocity theorem. By using this new method, the classical problem of elastic circular inclusion under a uniform tensile field at infinity is solved. Firstly, the perfect bonding between inclusion and matrix is set up, and the displacement and stress at interface are expanded according to Fourier series. According to the symmetry of the problem and the orthogonality of trigonometric function, the hypothesis is simplified and the number of undetermined coefficients is reduced. Secondly, the appropriate trial functions are selected (these trial functions satisfy the condition of displacement single value and the control equation of linear elasticity without body force). And the boundary integral method is used to calculate the displacement and stress at the interface. Then the displacement and stress in the domain are solved using similar tricks. The exact analytical solution of the problem is obtained, which is exactly the same with the results in literatures. When the elastic modulus of the inclusion is zero or tends to infinity, it degenerates to the analytical solution of the problem of circular hole or rigid inclusion. The solution process shows that if the problem has boundary conditions at infinity, trial functions should meet the boundary condition at infinity. If the domain of the problem contains the coordinate origin, the displacement and stress of trial functions at the origin should be limited. The results show that the method is effective.

Increased gastrointestinal symptom frequency in diabetes mellitus even with good glycemic control

Background and Aim: Gastrointestinal problems are reportedly more frequent in patients with diabetes mellitus (DM) compared to the general population and are a cause of reduced quality of life (QOL). Even though studies have suggested that parameters such as glycemic control and disease duration are responsible for upper gastrointestinal (GI) symptoms in DM, there is little compelling evidence to show a direct relationship given the fact that various other studies report no relationship. These conflicts may be caused by the lack of standardization of patient populations, evaluation methods and other causes. Our aim was to determine and compare the frequency of GI symptoms and GI-related QOL in recently diagnosed DM patients and healthy controls in order to evaluate this relationship with minimization of confounding factors.Material and methods: A total of 59 patients newly diagnosed with DM and 92 age- and sex-matched controls were included in this study. Demographic characteristics, chronic diseases, GI symptoms (as measured by 8-MGSI score) and GI-related QOL (irritable bowel syndrome quality of life, IBS-QOL) scores were evaluated. Linear regression analysis was performed to determine factors that independently influenced IBS-QOL.Results: The patient and control groups were similar with regard to all characteristics except for chronic diseases. The scores for 8-MGSI and IBS-QOL were significantly worse in patients with DM. Regression analyses showed that IBS, DM and dyspepsia were independent factors that influences IBS-QOL scores.Conclusion:The results of our study show that the effect of DM on GI symptoms is not a function of disease duration or glycemic control; DM presence itself seems to have adverse effects on the GI system through mechanisms that are yet unknown. The explanation of these mechanisms rely on experimental research and prospective studies with rigid patient inclusion criteria.

Interactions of Anisotropic Inclusions on a Fluid Membrane

Biological cells and membranes need to be properly shaped to fulfill many fundamental functions. This shaping is often aided by the aggregation of membrane-bound proteins that both sense the membrane curvature and shape it. Therefore, these protein inclusions interact with each other through the deformation of the membrane that they influence, and a key question is to understand the law that governs their interaction. Whereas the theoretical case of isotropic proteins is well understood, an important feature of many such proteins is their anisotropic interaction with the membrane. Here, we derive an interaction law for rigid circular membrane inclusions which impose an anisotropic contact angle on the surrounding membrane. We include the effects of both membrane bending and tension. Using asymptotic analysis, we identify two distinguished limits corresponding to weak anisotropy/weak tension and strong anisotropy/strong tension, respectively. The resulting laws exhibit a bistability in the equilibrium separation of inclusions. Inclusions with very weak anisotropy equilibrate with large separation, those with very strong anisotropy equilibrate with small separation, while there is a range of anisotropies for which both equilibria are stable. Our results provide a theoretical mechanism for the global aggregation of inclusions seen both in experiments and simulations.

Performance Evaluation of Rigid Inclusion Foundations in the Reduction of Settlements

Performance Evaluation of Rigid Inclusion Foundations in the Reduction of Settlements

Diffraction of normal SH-wave from a semi-infinite rigid inclusion in an elastic layer

Diffraction of normal SH-wave from a semi-infinite rigid inclusion in an elastic layer

Optimal Control of Parameters for Elastic Body with Thin Inclusions

In this paper, an equilibrium problem for 2D non-homogeneous anisotropic elastic body is considered. It is assumed that the body has a thin elastic inclusion and a thin rigid inclusion. A connection between the inclusions at a given point is characterized by a junction stiffness parameter. The elastic inclusion is delaminated, thus forming an interfacial crack with the matrix. Inequality-type boundary conditions are imposed at the crack faces to prevent interpenetration. Existence of solutions is proved; different equivalent formulations of the problem are discussed; junction conditions at the connection point are found. A convergence of solutions as the junction stiffness parameter tends to zero and to infinity as well as the rigidity parameter of the elastic inclusion tends to infinity is investigated. An analysis of limit models is provided. An optimal control problem is analyzed with the cost functional equal to the derivative of the energy functional with respect to the crack length. A solution existence of an inverse problem for finding the junction stiffness and rigidity parameters is proved.

Numerical modelling and comparison of the temporal evolution of mantle and tails surrounding rigid elliptical objects in simple shear regime under stick and slip boundary conditions

Structures associated with rigid inclusions are a rich source of evidence to understand the local deformation regime. The behaviour of rigid objects in modelled here as being immersed in a linear Newtonian fluid with either (i) a stick boundary condition (continuity of stress and velocity across the boundary) or (ii) a slip boundary condition (continuity of boundary normal stress and velocity across the boundary with zero shear stress at the boundary). Of particular interest are the types of structures developed in a concentric region adjacent to the object termed the mantle. A model of the displacement of points around the inclusion comprises a set of ordinary differential equations which are solved numerically. A comprehensive set of simulations for a variety of mantle sizes, object aspect ratios, initial orientations as well as different boundary conditions has been performed. A comparison between natural examples and model output indicates a level of consistency. The resulting structures differ in detail and in a broader sense. In general δ-type structures only develop when stick boundary conditions are in operation. In contrast, σ-type structures at high strain are restricted to slip boundary conditions. Slip conditions also tend to be the source of complex mantle types involving more than one generation of mantle structures or wings. Furthermore, our model indicates that using asymmetry of orientation of objects relative to the shear direction may be problematic when used alone, particularly if stick boundary conditions prevail but that together with mantle structures there is less chance of confusion.

Cloaking of a circular cylindrical elastic inclusion from antiplane elastic waves and resonance effects

Cloaking of a circular cylindrical elastic inclusion embedded in a homogeneous linear isotropic elastic medium from antiplane elastic waves is studied. The transformation or change-of-variables method is used to determine the material properties of the cloak and the homogenization theory of composites is used to construct a multilayered cloak consisting of many bi-material cells. The large system of algebraic equations associated with this problem is solved by using the concept of multiple scattering with wave expansion coefficient matrices. Numerical results for cloaking of an elastic inclusion and a rigid inclusion are compared with the case of a cavity. It is found that while the cloaking patterns for the three cases are similar, the major difference is that standing waves are generated in the elastic inclusion and the multilayered cloak cannot prevent the motion inside the elastic inclusion, even though the cloak seems nearly perfect. Waves can penetrate into and cause vibrations inside the elastic inclusion, where the amplitude of standing waves depend on the material properties of the inclusion but are very much reduced when compared to the case when there is no cloak. For a prescribed mass density, the displacements inside the elastic cylinder decrease as the shear modulus increases. Moreover, the cloaking of the elastic inclusion over a range of wavenumbers is also investigated. There is significant low frequency scattering even if the cloak consists of a large number of layers. When the wavenumber increases, the multilayered cloak is not effective if the cloak consists of an insufficient number of layers. Resonance effects that occur in cloaking of elastic inclusions are also discussed.

Experimental evaluation of the strain intensity factor at the rigid line inclusion tip embedded in an epoxy matrix using digital image correlation

The strain intensity factor for a rigid line inclusion tip is experimentally determined using the digital image correlation (DIC) technique using multi-parameter displacement field equations. The multi-parameter displacement field equations for a rigid line inclusion are derived based on the Airy’s stress function approach and are reported here in an elegant manner. The unknown coefficients in the multi-parameter equation, inclusion tip location, rigid body translations and rotation are determined using a linear least squares method in an over-deterministic manner. A rigid line inclusion specimen is prepared using 0.1 mm steel strip embedded in an epoxy matrix. Experiments are performed for two inclusion configurations when the embedding matrix is subjected to a remote tensile field. In the first configuration, the inclusion is placed along the tensile loading direction. In the second configuration, the inclusion is kept inclined to the loading direction. The experimentally obtained strain intensity factor agrees well with the analytical estimates with an error less than 6% for the seven parameter solution for both the configuration, thereby confirming the accuracy of the proposed methodology.

Rupture and Damage at Dilatant Geological Interfaces

The work discusses the processes that can be present at fractures and defects at geological interfaces. The introductory comment clearly indicates that the computational approaches offer the most appropriate methods for examining complex contact problems at geomaterial interfaces. There are, however, certain types of contact problems that are amenable to analytical treatment. The paper examines the problem of a circular dilatant-frictional patch located at an otherwise frictionless interface. The dilatancy processes are induced at the circular patch by the relative shear of the elastic regions. The paper presents a mathematical approach for the study of the problem where results from the solution of integral equations applicable for the internal indentation of a penny-shaped crack by a rigid inclusion and the internal pressurization of an annular crack are combined with a work-dissipation relationship to examine the mechanics of the interactions at the dilatant zone.

Stress State of an Inhomogeneous Elastic Layer Made of Heterogeneous Materials with a Coin-Like Rigid Inclusion under Torsion

Problems on cracks and inclusions closely relate to problems of determination of the stress-strain state of homogeneous and inhomogeneous elastic solids that contain stress concentrators. Due to their theoretical and practical importance to the issues of construction structures, machines and their parts in machinery, in the calculation of hydro-technical structures as well as in various other spheres of applied mechanics, these problems have become a subject of investigation for many authors. This paper studies the problem of determination of the stress-strain state of a piecewise homogeneous elastic layer under torsion. The upper and lower surfaces of the compound layer are loaded with tangential forces and the interface of the heterogeneous layers contains a thin absolutely rigid coin-like inclusion. It is required to determine stress jumps on the boundary of the inclusion as well as intensity coefficients of the stresses (ICS).

On the Stress State of a Heterogeneous Plate Made of a Material with a Step Change in Elastic Characteristics in the Presence of an Inclusion System and Temperature Influence

In the formulation of thermoelasticity and in the framework of the conventional theory of thermal stresses, the problem on the stress state of an elastic piecewise-homogeneous plane or an infinite plate at non-uniform steady-state heating is considered. On the interface of dissimilar materials, the compound plane is reinforced by a collinear system of absolutely rigid thin inclusions and is subjected to mechanical and thermal influences. First, to determine the temperature distribution in a piecewise-homogeneous plane the corresponding boundary value problem of the theory of steady-state heat conduction is solved using the integral Fourier transform. Solving this problem is reduced to solving a singular integral equation (SIE) that allows an exact solution. Further, the elastic displacements of points of the compound plane, caused by mechanical and temperature influence, are determined by the known methods of thermoselasticity. Based on these results, solving the problem of the contact interaction between the system of inclusions and a compound plane is again reduced to solving SIE, which also allows an exact solution. A special case is considered.

Investigation of behavior of footings over rigid inclusion-reinforced soft soil: experimental and numerical approaches

The aim of this study is to investigate the behavior of a footing lying directly upon a rigid inclusion-reinforced soft soil. Both experimental and numerical approaches were conducted. The studied cases include single rigid inclusion tests, a footing over nonrigid inclusion-reinforced soil, and a footing over rigid inclusion-reinforced soil. The vertical loading tests on single rigid inclusions and the footing over unreinforced soil showed the behavior of the multi-layered soil, thus allowing for the determination of soil parameters for the numerical analyses. The tests on the footing over reinforced soil were, furthermore, carried out with different loading cases (centered and eccentric vertical loads and horizontal loads). Special attention was paid to the influence of the complex loading cases on the footing over a reinforced soil system by the measurement of the inclusion head pressure, the vertical and lateral footing settlements, and the lateral inclusion displacements. The measured pressure on the inclusion seemed to increase linearly with the vertical loading on the footing. A good agreement between the numerical analysis results and measurement data has been found for the loading phases while underprediction appears for a few loading cycles, probably due to the simplified soil constitutive model adopted.

Creep and plastic flow in a rotating cylinder with a rigid inclusion

Creep and plastic flow in a rotating cylinder with a rigid inclusion

Prediction of resin pocket geometry around rigid fiber inclusion in composite laminate by hot-pressing of prepregs

In this paper, two analytic methods are presented to predict the geometry of resin pockets formed around rigid fiber inclusions at the interlayer of unidirectional prepregs. The bending strain energy is calculated on fiber scale in one method, while it is calculated on layer scale in the other method. For the fiber scale method, several fibers in thickness direction are tied together to account for the bending stiffness increase caused by the interaction between fibers. And for the layer scale method, a single ply is divided into several sublayers to account for the bending stiffness decrease caused by the sliding between adjacent fibers. Both analytic methods can provide the closed-form solution for the resin pocket width, and the analytic results agree well with experimental results. The physical consistency of two methods is proved. It is found that the resin pocket size depends mainly on ply angles of the plies close to the inclusion, and the stacking sequence has some effect.

Numerical study on the effect of rigid inclusions on existing railroads

SummaryRailroad track problems have been exacerbated by the continuous increase in freight loads and train traffic. The need to implement soil improvement technique in a relatively short window‐time (ie, to minimize train‐traffic disruption) is a key aspect to be considered when adopting a convenient remedial solution to control settlements in railroads constructed on problematic subgrades. Rigid inclusions are selected in this paper because they are reliable solutions relatively easy to implement. Furthermore, they can be used in different ground conditions and are suitable for short construction times (eg, do not require a curing time, as in grouting methods). Typical (analytical) methods for the design of rigid inclusions are adopted in this paper to define an optimal distribution of piles for the case of existing railroads. The selected layout is then analyzed in detail by means of a 3‐D dynamic finite element simulator using both, elastoplastic and elastic models. The performance of rigid inclusions is studied considering different operational scenarios, with dynamic and static loads, as well as involving subgrades with different plasticity index values. It is found that the predictions from the analytical design methods for rigid inclusion tend to be unconservative when compared against the finite element results. As for the numerical solutions, the most unfavorable stress condition is associated with the dynamic elastoplastic finite element solution. It is estimated that the rigid inclusions will contribute to a reduction in the ground settlements of around 15% to 20%, depending on the subgrade plasticity index.

Topology optimization design for total sound absorption in porous media

Acoustic porous layers used for noise reduction have the unique functionality of dissipating sound energy. It is very difficult for finite length porous layers to realize total sound absorption if they are filled only with homogeneous materials. Rigid inclusions inserted in a porous medium will certainly alter the acoustic field, realizing total sound absorption at some frequencies, but finding their optimal distributions by trial and error is intractable, especially for multiple target frequencies. The aim of this study is to develop a finite element-based numerical method to distribute rigid inclusions inside a porous layer having a fixed thickness for the total sound absorption. Without any special treatment for initial layout, multiply divided rigid inclusions are distributed systematically in an optimized porous layer by the present density-based topology optimization formulation. Considering single target frequency problems, we initially assess the effectiveness of the developed formulation with regard to achieving total sound absorption. In these problems, various resonance mechanisms, such as the Helmholtz resonance and the quarter-wavelength resonances, are generated inside the porous layer by the distributed rigid inclusions. Subsequently, we solve problems considering multiple target frequencies. The numerical results show that different types of resonances occur appropriately in the optimized porous–rigid layer to achieve total sound absorption simultaneously for all the different target frequencies considered here.

NIMG-73. NEUROLOGICAL ASSESSMENT IN NEURO-ONCOLOGY (NANO) CORRELATES WITH INTEGRATED PREDICTIVE RADIOGRAPHIC BIOMARKERS OF PROGRESSED HIGH GRADE ASTROCYTIC TUMORS (IPROMPT): A PROPOSED SUPPLEMENT TO RANO

Abstract This year nearly 86,000 persons in the US will be diagnosed with a primary brain tumor. Glioblastoma (GBM) is the deadliest and most common of these tumors in adults with overall survival around 15mos. Disease progression is inevitable, and effective second-line therapies are few. Delays in identifying progressed GBM risks neurologic decline, continuation of ineffective therapies, and increased tumor-mutational-burden, potentially rendering treatment less-effective. Brain tumor imaging can be ambiguous and is an active topic in neuro-oncology as there are currently no validated approaches to assessment of tumor treatment response. We present a single institution database including 622 gross-totally-resected GBMs (2006–2018) to evaluate changes in T2/FLAIR signal intensity (T2FSI), diffusion restriction, and contrast enhancement both in and around the resection cavity (RC) to determine earliest indicators of tumor progression. Analysis of NANO score was completed to correlate with predicted tumor progression. This is an early data release of an ongoing two-phased retrospective/prospective study with findings that support a novel integration of radiographic sequences and NANO to supplement established RANO criteria in earlier detection of GBM progression. Of 622 confirmed GBMs, 158 fit the rigorous criteria – included here are 58 cases. We report 70% (n=41) of patients show RC T2FSI correlating with restricted diffusion and increasing NANO score (0.5–1.4) as early as 3.8mos prior to and at time of radiographic progression, respectively. Previous studies have reported similar T2FSI but without associated NANO, less rigid inclusion criteria, and limited MRI sequences. We also report imaging phenomena, not previously described, such as FLAIR migration and FLAIR coring timed closely with progression. The proposed technique uses routine MRI, therefore readily standardized in clinical practice. With further validation, this novel integration of imaging and neurologic assessment might serve to supplement existing response criteria in GBM and improve clinician confidence in earlier detection of progression.

Approximation Method for Evaluation of Strains and Forces in LTP Reinforcement of Embankments on Columns

This article presents a method of approximate finding of forces and strains resulting from the so-called membrane effect in the reinforcement of the transmission layer of embankments located on a soft soil improved by columns (rigid inclusions). The model task needed to determine the characteristic values in geosynthetic reinforcement supported on rigid columns was formulated. The reinforcement is treated as an isotropic membrane, in which the strains are determined using the formula for the length of the curve, i.e. it deviates from the assumptions of the small strain theory. Spatial problems are reduced to equivalent one-dimensional static tasks for analysis using the isotropic membrane theory. The closed form solution of this task exists only in the case of uniform load. For other types of loads, it is necessary to approximate the formula for the length of the curve occurring in the expression defining the strains in the membrane, e.g. using the Taylor series, and then solving the strongly non-linear equation in which the membrane tension force is unknown. The article presents the analysis of the effect of the length curve approximation with usage of the Taylor series on the accuracy of the results obtained. The presented analysis is very important from the point of view of standard engineering calculations needed to design the reinforcement of the transmission layer in the case of embankments located on soft soil reinforced with rigid inclusions.