Unbounded Body Research Articles

A new fractional viscoelastic model for an infinitely thermoelastic body with a spherical cavity including Caputo-Fabrizio operator without singular kernel

Many applications and contexts including materials science, metallurgy, and solid-state physics, are concerned with the study of the behavior of viscoelastic materials. In addition, any composite or complex construction containing embedded polymers exhibits viscoelastic behavior under static and dynamic stress conditions. Wide types of linear/nonlinear constitutive models have been proposed to define the viscoelastic deformation process of viscoelastic materials in order to explore their mechanical behavior. However, it has been shown that the constitutive relationship in the integer-order of stress-strain available in conventional viscoelastic models may fail in some types of situations and do not match well with empirical evidence. In this paper, a novel mathematical model is provided that uses Caputo-Fabrizio fractional-order derivatives to describe the viscoelastic phenomena and is consistent with thermodynamic principles. The Caputo-Fabrizio kernel has many features, such as nonlocality and non-singularity in addition to the exponential form. The suggested model is used to study the dynamic reactions of an unbounded body with a spherical cavity made of viscoelastic material subjected to time-varying heat. Using the Laplace transform technique, numerical calculations of many physical fields are obtained and explored in depth.

Dying on television versus dying in intensive care units following withdrawal of life support: how normative frames may traumatise the bereaved.

While treatment is often withdrawn from patients in intensive care units (ICUs), few people outside the healthcare profession have witnessed a death under such circumstances. Family members who have made the decision to withdraw treatment may have expectations about the dying process, what constitutes a good death and how they should behave in an ICU based on popular prime-time television series. An inductive comparative thematic coding strategy is therefore used to examine how death following treatment withdrawal as depicted in a US medical drama (Grey's Anatomy) differs from realities observed for 6months fieldwork at an ICU in Canada. Three common frames (privacy, emotional control and memorialising) help patients' intimates normalise the unfamiliar experience and guide their behaviour during the event. However, discrepancies between media representations and experiences in the ICU, especially around the frames of timing of death and the physicality of the unbounded body (incontinence and agonal breathing), can traumatise them. The bereaved may be left viewing ventilator withdrawal and dying as chaotic processes and believing their loved one suffered through a bad death. Understanding these normative and discrepant frames should help healthcare professionals better prepare the public to witness death.

The effect of modified Ohm’s and Fourier’s laws in generalized magneto-thermo viscoelastic spherical region

This paper is dealing the modified Ohm’s law, including the temperature gradient and charge thickness impacts, and the generalized Fourier’s law, including the current density impact, the conditions of generalized thermo-viscoelasticity for a thermally, isotropic and electrically leading unbounded body with a spherical cavity is given. The detailing is applied to the generalized thermo elasticity dependent on Green–Naghdi (G-N II) and (G-N III) theory, where there is an underlying magnetic field corresponding to the plane limit, because of the utilization of the magnetic field, it results an incited magnetic and electric fields in the medium. The state space investigation is applied to acquire the temperature, displacement, stresses, induced electric field, instigated magnetic field and current density. Application is utilized to our concern to get the arrangement in the total structure. The considered variables are introduced graphically and discussions are made.

Scaled boundary finite element method with circular defining curve for geo-mechanics applications

This paper presents an efficient and accurate numerical technique based upon the scaled boundary finite element method for the analysis of two-dimensional, linear, second-order, boundary value problems with the domain completely described by a circular defining curve. The scaled boundary finite element formulation is established in a general framework allowing single-field and multi-field problems, bounded and unbounded bodies, distributed body source, and general boundary conditions to be treated in a unified fashion. The conventional polar coordinates together with a properly selected scaling center are utilized to achieve the exact description of the circular defining curve, exact geometry of the domain, and exact spatial differential operators. The computational performance of the implemented procedure is then fully investigated for various scenarios within the context of geo-mechanics applications.
 Keywords:
 exact geometry; geo-mechanics; multi-field problems; SBFEM; scaled boundary coordinates.

Cidadania, corpo e punição: expansão e violação de direitos civis de adolescentes internados na antiga Febem/SP

Resumo Este artigo discute a garantia de direitos civis e a proteção contra agressões físicas para adolescentes em cumprimento de medida de internação. A relação entre direitos civis e proteção do corpo dos adolescentes é aqui entendida a partir do conceito de cidadania disjuntiva e da noção de corpo incircunscrito, que remetem aos processos contraditórios de constituição da cidadania no Brasil. Com base em pesquisa qualitativa realizada em prontuários e pastas de adolescentes que deram entrada na antiga Febem de São Paulo, entre 1990 e 2006, e focando o que esses documentos permitem dizer sobre a violência física nas unidades de internação, o artigo apresenta como essa violência revela um paradoxo entre expansão e violação de direitos civis, tornando possível que investimentos na garantia desses direitos ocorram ao mesmo tempo em que sua violação permaneça na forma de castigos físicos.

Periodic Crack Systems in a Transversally Isotropic Solid

Three-dimensional problems are studied on periodic chains of elliptic cracks oriented along one of the coordinate axes lying in a plane that is perpendicular to the isotropy planes of a transversely isotropic elastic unbounded body. Using the integral Fourier transform, the problems are reduced to integro-differential equations, whose kernels are presented in the form of series and do not contain quadratures. To solve the problem, the regular asymptotic method by V. M. Alexandrov was used with the introduction of the main dimensionless parameter characterizing the relative distance of neighboring cracks from each other. The limits of applicability of the method depend on the anisotropy parameters and the location of the cracks; the method is effective for cracks relatively distant from each other. Asymptotics are obtained for the stress intensity factor related to the case of a single crack. Parameters of asymptotic solutions are calculated for different transversely isotropic materials.

Scaled boundary finite element method with exact defining curves for two-dimensional linear multi-field media

This paper presents an efficient and accurate numerical technique based upon the scaled boundary finite element method for the analysis of two-dimensional, linear, second-order, boundary value problems with a domain completely described by a circular defining curve. The scaled boundary finite element formulation is established in a general framework allowing single-field and multi-field problems, bounded and unbounded bodies, distributed body source, and general boundary conditions to be treated in a unified fashion. The conventional polar coordinates together with a properly selected scaling center are utilized to achieve the exact description of the circular defining curve, exact geometry of the domain, and exact spatial differential operators. Standard finite element shape functions are employed in the discretization of both trial and test functions in the circumferential direction and the resulting eigenproblem is solved by a selected efficient algorithm. The computational performance of the implemented procedure is then fully investigated for various scenarios to demonstrate the accuracy in comparison with standard linear elements.

Analytic center cutting plane methods for variational inequalities over convex bodies

An analytic center cutting plane method is an iterative algorithm based on the computation of analytic centers. In this paper, we propose some analytic center cutting plane methods for solving quasimonotone or pseudomonotone variational inequalities whose domains are bounded or unbounded convex bodies.

Eigen Value Approach to Generalized Thermoelastic Interactions in an Unbounded Body with Circular Cylindrical Cavity without Energy Dissipation

The theory of generalized thermoelasticity in the context of the Green-Naghdi model -II (thermoelasticity without energy dissipation) is studied for an infinite circular cylindrical cavity subjected to two different cases of thermoelastic interactions when the radial stress is zero for (a) maintaining constant temperature and (b) temperature is varying exponentially with time. The Laplace transform from time variable is used to the governing equations to formulate a vector matrix differential equation which is then solved by the eigen value approach. Numerical computations for the displacement component, temperature distribution and components of thermal stress have been made and presented graphically.

On the Magnetic Shield for a Vlasov–Poisson Plasma

We study the screening of a bounded body $\Gamma$ against the effect of a wind of charged particles, by means of a shield produced by a magnetic field which becomes infinite on the border of $\Gamma$. The charged wind is modeled by a Vlasov-Poisson plasma, the bounded body by a torus, and the external magnetic field is taken close to the border of $\Gamma$. We study two models: a plasma composed by different species with positive or negative charges, and finite total mass of each species, and another made of many species of the same sign, each having infinite mass. We investigate the time evolution of both systems, showing in particular that the plasma particles cannot reach the body. Finally we discuss possible extensions to more general initial data. We show also that when the magnetic lines are straight lines, (that imposes an unbounded body), the previous results can be improved.

Thermoelastic Interactions in an Infinite Orthotropic Continuum of a Variable Thermal Conductivity with a Cylindrical Hole

In this work, the generalized thermoelasticity theory with phase lags is used to solve a thermoelastic problem for an orthotropic infinite unbounded body containing a cylindrical cavity by approximate techniques. The thermal conductivity of the present body is assumed to vary linearly with the temperature. The surface of the cylinder is traction free and subjected to a uniform step temperature. The general solutions for the temperature, displacement, and thermal stresses are obtained by the method of Laplace transforms. The effects of dual phase lags and the variable thermal conductivity parameter on the studied fields for a cobalt material are discussed.

Spatial and temporal behavior in the theory of thermoelasticity for solids with double porosity

ABSTRACTIn this article, we study the spatial and the temporal behavior of solutions to the initial boundary value problem associated with the linear theory of thermoelastic materials with a double porosity structure. We consider two appropriate time-weighted integral measures and we deduce some exponential estimates that describe the spatial behavior of solutions. For bounded bodies, we obtain estimates of Saint-Venant type, while for unbounded bodies we deduce some alternatives of Phragmén–Lindelöf type. The temporal behavior of solutions is described using the Cesáro means of various parts of the total energy.

Effective balance equations for elastic composites subject to inhomogeneous potentials

We derive the new effective governing equations for linear elastic composites subject to a body force that admits a Helmholtz decomposition into inhomogeneous scalar and vector potentials. We assume that the microscale, representing the distance between the inclusions (or fibers) in the composite, and its size (the macroscale) are well separated. We decouple spatial variations and assume microscale periodicity of every field. Microscale variations of the potentials induce a locally unbounded body force. The problem is homogenizable, as the results, obtained via the asymptotic homogenization technique, read as a well-defined linear elastic model for composites subject to a regular effective body force. The latter comprises both macroscale variations of the potentials, and nonstandard contributions which are to be computed solving a well-posed elastic cell problem which is solely driven by microscale variations of the potentials. We compare our approach with an existing model for locally unbounded forces and provide a simplified formulation of the model which serves as a starting point for its numerical implementation. Our formulation is relevant to the study of active composites, such as electrosensitive and magnetosensitive elastomers.

Electro–magneto interaction in fractional Green-Naghdi thermoelastic solid with a cylindrical cavity

A unified mathematical model of Green–Naghdi’s thermoelasticty theories (GN), based on fractional time-derivative of heat transfer is constructed. The model is applied to solve a one-dimensional problem of a perfect conducting unbounded body with a cylindrical cavity subjected to sinusoidal pulse heating in the presence of an axial uniform magnetic field. Laplace transform techniques are used to get the general analytical solutions in Laplace domain, and the inverse Laplace transforms based on Fourier expansion techniques are numerically implemented to obtain the numerical solutions in time domain. Comparisons are made with the results predicted by the two theories. The effects of the fractional derivative parameter on thermoelastic fields for different theories are discussed.

Qualitative properties in strain gradient thermoelasticity with microtemperatures

This paper is devoted to the strain gradient theory of thermoelastic materials whose microelements possess microtemperatures. The work is motivated by an increasing use of materials which possess thermal variation at a microstructure level. In the first part of this paper we deduce the system of basic equations of the linear theory and formulate the boundary-initial-value problem. We establish existence, uniqueness, and continuous dependence results by the means of semigroup theory. Then, we study the one-dimensional problem and establish the analyticity of solutions. Exponential stability and impossibility of localization are consequences of this result. In the case of the anti-plane problem we derive uniqueness and instability results without assuming the positivity of the mechanical energy. Finally, we study equilibrium theory and investigate the effects of a concentrated heat source in an unbounded body.

Thermoelastic interactions without energy dissipation in an unbounded body with a cylindrical cavity

ABSTRACTIn this work, we apply Green and Naghdi's generalized thermoelasticity theory to a one-dimensional problem of an infinitely long cylindrical cavity. Laplace transform techniques are used to solve the problem. A comparison of generalized thermoelasticity theory with one relaxation time is made. Numerical results are computed and represented graphically for the temperature,displacement, and stress distributions.

Spatial Behavior in Linear Theory of Thermoviscoelasticity with Voids

In the present article we study the spatial behavior of the solutions to the initial boundary value problem associated with the linear theory of thermoviscoelastic materials with voids. We prove a set of properties for an appropriate time-weighted surface power function, which allows us to obtain an idea of the domain of influence in linear thermoviscoelasticity with voids. Some spatial estimates of the Saint–Venant type, for bounded bodies, and Phragmén–Lindelöf type, for unbounded bodies, are obtained. Such estimates are characterized by time-dependent as well as time-independent decay and growth rates.

Effect of temperature dependency on constrained orthotropic unbounded body with a cylindrical cavity due to pulse heat flux

Effect of temperature dependency on constrained orthotropic unbounded body with a cylindrical cavity due to pulse heat flux

Stationary heat conduction processes in bodies of randomly inhomogeneous structure

This work is devoted to the mathematical modeling of stationary heat conduction processes in randomly inhomogeneous multiphase structures. An integro-differential equation with a random kernel, whose solution is constructed in the form of a Neumann series, is put in correspondence with the boundary-value problem of heat conduction. We establish the conditions of absolute and uniform convergence of this series, in particular, the condition of boundedness of the body volume. It is shown that, for unbounded bodies, the condition of boundedness of the domain occupied by inclusions is necessary for convergence of the Neumann series.

On the Micromorphic Thermoelasticity without Energy Dissipation

The linear dynamic theory of micromorphic thermoelasticity without energy dissipation is considered. First, we establish a reciprocity relation which involves thermoelastic processes at different instants. We show that this relation can be used to establish a uniqueness theorem and a reciprocal theorem. The uniqueness result is derived with no definiteness assumption on elastic constitutive coefficients. The reciprocal theorem avoids both the use of the Laplace transform and the incorporation of initial conditions into the equations of motion. Then, a variational theorem for the first boundary-initial value problem is established. The effect of a concentrated heat supply in an unbounded body is also investigated.