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A new class of constitutive equation is proposed for isotropic thermoelastic solids, wherein the Hencky strain tensor is assumed to be a function of the Cauchy stress tensor, via a Gibbs potential. The solid is assumed to be incompressible in the referential state, but the volume can change due to differences in the temperature relative to a reference temperature. The change in volume only depends on temperature. Some restrictions are found for the Gibbs potential, resulting in a constitutive equation for isotropic solids, wherein the volume depends on temperature. Using the resulting constitutive equation, some boundary value problems are studied, considering some relatively simple distributions for the temperature, deformations and stresses. [ABSTRACT FROM AUTHOR]

AN IMPLICIT CONSTITUTIVE RELATION IS PROPOSED FOR ELASTIC BODIES, when the gradient of the displacement is assumed to be very small, and as a result the strains are small. The resulting constitutive relation is a non-linear relationship between the linearized strain and the stress. The model is used to fit data for rock and concrete. Some boundary value problems are studied within the context of homogeneous deformations, and also a problem with inhomogeneous deformations is analyzed, namely the inflation of a circular annulus. The predictions of this new implicit constitutive relation are compared with the predictions of the constitutive equations for linearized elastic bodies. [ABSTRACT FROM AUTHOR]

The sum of lognormal variables has been a topic of interest in several fields of research such as engineering, biology and finance, among others. For example, in the field of telecommunications, the aggregate interference of radio frequency signals is modeled as a sum of lognormal variables. To date, there is no closed expression for the probability distribution function (PDF) of this sum. Several authors have proposed approximations for this PDF, with which they calculate the mean and variance. However, each method has limitations in its range of parameters for mean, variance and number of random variables to be added. In other cases, long approximations as power series are used, which makes the analytical treatment impractical and reduces the computational performance of numerical operations. This paper shows an alternative method for calculating the mean and variance of the sum of lognormal random variables from a computational performance approach. Our method has been evaluated extensively by Monte Carlo simulations. As a result, this method is computationally efficient and yields a low approximation error computation for a wide range of mean values, variances and number of random variables. [ABSTRACT FROM AUTHOR]

In Part I, an implicit constitutive relation was proposed to describe stress softening of solids. In this second part, we use the constitutive relation developed earlier to study different boundary value problems, namely the homogeneous compression of a cylinder without radial stresses, the homogeneous compression of a cylinder with radial stress (triaxial test), the simple shear of a slab, and the inflation of a cylindrical annulus, when the displacement gradients are small. [ABSTRACT FROM AUTHOR]

For a relatively new class of linearization of implicit constitutive relations, wherein the linearized strain tensor is assumed to be a function of the Cauchy stress tensor, we write the balance of linear momentum and the time differentiated constitutive relation as a first order system, and we examine conditions for the hyperbolicity of such a system; this procedure is carried out for one and three dimensions. For the one dimensional case we use the characteristic polynomial and find conditions so that our system is hyperbolic. For three dimensions we find conditions so that our system can be put in a symmetric hyperbolic form. • We write the equations as a first order system. • For the one dimensional case we use the characteristic polynomial and find conditions so that our system is hyperbolic. • For three dimensions we find conditions so that our system can be put in a symmetric hyperbolic form. [ABSTRACT FROM AUTHOR]

An implicit constitutive relation is proposed to describe stress softening exhibited by solids, using as a basis the second law of thermodynamics, and appropriate choices for the specific Helmholtz potential and the rate of entropy production function. The implicit constitutive relation that is developed is a generalization of the earlier one-dimensional model developed by Rajagopal and Srinivasa (Int J Plast 71:1–9, 2015). One subclass is studied, wherein the stress is the controlling variable, which permits the study of a body that softens with the stress. [ABSTRACT FROM AUTHOR]

In this communication a generalized strain approach is proposed to model constitutive equations for nonlinear residually stressed magneto-electric coupled viscoelastic solids with short term memory. This approach is a change with respect to the work that has been done, in the last decades, on the mechanics of nonlinear solids. The generalized strain model uses spectral invariants, where they have a clear physical meaning and hence are attractive for use in experiments. A specific form for a constitutive equation containing single-variable functions is presented, which are easy to deal with, if compared to multivariable functions. The effects of viscosity, residual stress and magneto-electric fields are studied via the results of boundary value problems, and some of these results are compared with experimental data. • A generalized strain approach is proposed to obtain constitutive equations. • A nonlinear residually stressed magneto-electric coupled viscoelastic solid is built. • The generalized strain model uses spectral invariants, all with physical meaning. • The effects of viscosity, residual stress and magneto-electric fields are studied. [ABSTRACT FROM AUTHOR]

In this prospective, randomised, blinded clinical study, we compared the sedative, antinociceptive and cardiorespiratory effects of intranasal (IN) dexmedetomidine at 5 μg/kg (diluted with 0.03 mL/kg NaCl 0.9%, DEX) with or without methadone (0.3 mg/kg; DEXMET), through a mucosal atomization device to one nostril in twenty healthy client-owned dogs. At 5-min intervals over 45 min, sedation score, onset, cardiopulmonary variables, mechanical nociceptive thresholds (MNTs) were assessed, also ease of administration, adverse effects, and response to IV catheterization. Statistical analysis employed t-test, the Mann-Whitney U, repeated measures ANOVA and Chi-square tests as appropriate (P < 0.05). Higher sedation ocurred in DEXMET (7 [5–10]) compared to DEX (5 [2–7]) from 15 to 30 min (P < 0.01, median [interquartile range]). Heart rate was lower in DEXMET (P < 0.01; 65% reduction vs. 41% in DEX, P = 0.001). The MNTs were higher in DEXMET than DEX from 15 to 45 min (P < 0.01), peaking at T30 (17.1 ± 3.8, DEXMET and 8.5 ± 5.4 N, DEX). No differences were observed in mean arterial blood pressure and respiratory rate. Intranasal administration was considered easy for 8 dogs per group. Reverse sneezing (8 dogs; P < 0.001), sialorrhea and retching (4 and 2 dogs, respectively) occurred in DEXMET. Response to catheterisation was lower in DEXMET than DEX (P = 0.039; 2 and 7 dogs, respectively). In conclusion, intranasal methadone (0.3 mg/kg) increased the sedative and antinociceptive effects produced by dexmedetomidine (5 μg/kg) in healthy dogs and resulted in lower heart rate. • Methadone potentiated sedative effect of intranasal (IN) dexmedetomidine. • Methadone IN produced greater antinociceptive effects than dexmedetomidine alone. • Lower heart rate was observed when both drugs were administered IN. [ABSTRACT FROM AUTHOR]

Ridsdalea philippinensis (Rubiaceae), a new species from the karst forest in El Nido (Palawan, Philippines), is described and illustrated. It is unique among Malesian Ridsdalea species in having a corolla tube that is distinctly inflated at the apex, a character state also displayed by R. sootepensis and R. thailandica from Laos and Thailand. Amongst others, R. philippinensis, however, differs from both of these species in having smaller flowers and anthers that do not emerge from the corolla tube. An updated key for Philippine Ridsdalea is also presented. [ABSTRACT FROM AUTHOR]

Gastric tumors, especially gastric adenocarcinomas, are rare in childhood and adolescence, as a result of which there is limited information. Therefore, management is typically extrapolated from adult patients. We report the case of a 10-year-old girl referred to our institution with systemic symptoms and pyloric syndrome. An infiltrating antro-pyloric lesion without evidence of metastasis was found. Histopathological analysis confirmed the presence of an undifferentiated diffuse gastric adenocarcinoma with signet ring cells. Diagnostic laparoscopy was carried out, which demonstrated signs of peritoneal carcinomatosis, so palliative chemotherapy was proposed. [ABSTRACT FROM AUTHOR]

In this paper, we use an implicit generalization of the celebrated Kelvin–Voigt solid constitutive equation to study the problem of circumferential shearing of a cylindrical annulus of viscoelastic material. This generalization of the Kelvin–Voigt model allows one to take into consideration the possibility of the body undergoing shear thinning or shear thickening and allows the material moduli to depend on the mechanical pressure. Most importantly, the constitutive relation is a relation in the true mathematical sense in that neither the stress, nor the strain nor the symmetric part of the velocity gradient can be expressed explicitly in terms of the other quantities, thereby making the balance of linear momentum and the constitutive relation requiring solution simultaneously, unlike the case of the Kelvin–Voigt model where we can substitute the constitutive expression for the stress into the equilibrium equations to obtain an equation for the displacement field. [ABSTRACT FROM AUTHOR]

A constitutive equation is provided for nonlinear transversely isotropic elastic solids, wherein the linearized strain tensor is assumed to be a function of the Cauchy stress tensor; this elastic constitutive equation belongs to a subclass of a more general set of implicit constitutive relations proposed in the recent years. The proposed constitutive equation is valid for both compressible and incompressible bodies and can be simply modified, to exclude the mechanical influence of compressed fibres and to model inextensible fibres. A crude specific constitutive model is proposed to compare with a uniaxial experimental data on Marcellus shale. Some simple boundary value problems are analyzed. [ABSTRACT FROM AUTHOR]

In this communication a spectral constitutive equation for nonlinear viscoelastic-electroactive bodies with short-term memory response is developed, using the total stress formulation and the electric field as the electric independent variable. Spectral invariants, each one with a clear physical meaning and hence attractive for use in experiment, are used in the constitutive equation. A specific form for constitutive equation containing single-variable functions is presented, which are easy to analyze compared to multivariable functions. The effects of viscosity and an electric field are studied via the results of boundary value problems for cases considering homogeneous distributions for the strains and the electric field, and some these results are compared with experimental data. [ABSTRACT FROM AUTHOR]

Some universal solutions are studied for a new class of elastic bodies, wherein the Hencky strain tensor is assumed to be a function of the Kirchhoff stress tensor, considering in particular the case of assuming the bodies to be isotropic and incompressible. It is shown that the families of universal solutions found in the classical theory of nonlinear elasticity, are also universal solutions for this new type of constitutive equation. [ABSTRACT FROM AUTHOR]

In the present article, a spectral model is developed for residually stressed electro-elastic bodies. The model uses a total energy function that depends on the right stretch tensor, residual stress tensor and one of the electric variables. Some boundary value results with cylindrical symmetry are given. Results for the inflation of a hollow sphere, where the residual stress is assumed to depend only on the radial position, are also given. The constitutive formulation contains spectral invariants that have an immediate physical interpretation which is useful in a rigorous construction of a specific form of the total energy function via an appropriate experiment [ABSTRACT FROM AUTHOR]

In this paper we study the response of bodies that are residually stressed within the context of a new class of constitutive relations, wherein the strains are assumed to be functions of the stresses. Such bodies are said to have residual stresses if there are stresses within the bodies even though the bodies are unstrained in the configuration of interest in the absence of external traction. Problems within the context of the norm of the gradient of the displacement field being small are considered, with regard to the determination of the residual stresses in an anisotropic cylindrical annulus with two preferred directions, and the nature of residual stresses within an anisotropic slab. The residual stresses in a body that is subject to incremental stresses are also studied. [ABSTRACT FROM AUTHOR]

The aim of this study was to compare the effects on mean arterial pressure (MAP) and ventilation of propofol total IV anaesthesia (TIVA) and isoflurane as anaesthetic maintenance in healthy dogs undergoing orthopaedic surgery, with epidural anaesthesia. Dogs were premedicated IM with dexmedetomidine (4 μg/kg) and methadone (0.3 mg/kg), induced with IV propofol (0.65–5 mg/kg) and randomly assigned to be maintained with isoflurane (group I) or propofol (group P). Isoflurane end-tidal concentration (EtISO) and propofol infusion rate were adjusted during the surgery to maintain a suitable anaesthetic depth. All dogs received bupivacaine (1 mg/kg) and morphine (0.1 mg/kg) in the lumbosacral epidural space (total volume 0.2 mL/kg). MAP was recorded every 5 min during the procedure. Statistical analysis was performed using parametric (Student’s t test) and nonparametric (Mann–Whitney U -test, chi-square) tests, as appropriate. Anaesthetic maintenance in groups I and P was accomplished by providing a mean EtISO of 1.12 ± 0.15% and a mean propofol infusion rate of 15.0 ± 4.7 mg/kg/h, respectively. MAP was significantly higher in group P than in group I (92 ± 17 mmHg versus 78 ± 10 mmHg; P = 0.021). Eleven dogs in group P and two dogs in group I reached an EtCO 2 > 7.3 kPa, requiring mechanical ventilation ( P = 0.001). In combination with epidural anaesthesia, propofol TIVA improved MAP and is a suitable alternative to isoflurane in orthopaedic surgery of the hind limb in healthy dogs. Nevertheless, since it was associated with increased respiratory depression, mechanical ventilation should be available. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear constitutive relation is proposed to model the behaviour of sandstone. The model is based on a relatively new class of constitutive relations proposed recently in the literature, which cannot be classified as Cauchy or Green elastic bodies. A specific expression for the constitutive relation is proposed on the basis of some experimental data for the compression of a sample of rock, and several boundary value problems are analysed, considering homogeneous distributions of strains, as well as a problem wherein one has a non-homogeneous distribution of strains. Finally, the behaviour of the P- and S-waves is studied for a sample of rock under compression, and it is discovered that the wave speed depends on the compressive load, a result supported by experiments. [ABSTRACT FROM AUTHOR]

The heterogeneity of distribution of ordinary matter in the universe at a small scale, allows us to suppose the essential component of the cosmic fabric as a network of finite tissue affected by the presence of masses in the space-time continuum. Thus, massive astrophysical objects, such as black holes, product of the explosion of massive stars through supernovas which do not succeed at compressing to neutron stars, deform continuous space-time or cosmic tissue into a plane of simultaneity like the one described in Einstein's theory of special relativity by an observer who accompanies the black hole during its contraction. From the results obtained from the mass/radius relation of the object with the proposed metric, it is verified that it effectively corresponds to a static black hole, whose classical escape velocity "quasi" reaches the speed of light at a radius greater than that of Schwarzschild, so that time will never stop for any object that crosses its horizon of events and the illusion of time dilation for an external observer. From calculations made in general relativity with the energy-momentum tensor, the thermo-physical properties of the static black hole obtained from the proposed metric were measured, the results of which agree with those of other authors. Given the calculations of the time of evaporation and temperature, it is clear that the Hawking radiation of the event horizon is negligible for this massive black hole, so that the measurement of its shadow by a telescope as the telescope of the event horizon (Event Horizon Telescope, EHT, for its acronym in English) would be a great find. [ABSTRACT FROM AUTHOR]

In this paper we are interested in developing constitutive equations for fiber-reinforced nonlinearly viscoelastic solids. It has been shown that constitutive equations for such bodies can be expressed in terms of a complete minimal set of 18 classical invariants associated with deformation and fiber orientation. In this paper, we give an alternative formulation using a set of spectral invariants. It is shown via the use of spectral invariants that only 11 of the 18 classical invariants are independent. We analyze the spectral invariants for two illustrative deformation gradients: (i) simple tension, and (ii) simple shear. [ABSTRACT FROM AUTHOR]

In this paper we generalize the recent implicit models that have been put into place to describe the elastic response of bodies when thermal effects come into play. The implicit constitutive relations for thermoelastic response presented here provide a very natural way to overcome a serious problem associated with the celebrated model due to Fourier, namely infinite speed of the propagation of temperature. We also study some boundary value problems within the context of the implicit equations that we have developed. We carry out a linearization based on the classical assumption that the displacement gradient is small and obtain constitutive relations that allow the linearized strain to be a non-linear function of the stress and temperature. [ABSTRACT FROM AUTHOR]

In the literature, residual stress problems are generally formulated using classical invariants despite most of them having an unclear physical meaning and not having experimental advantages. In this article, we give an alternative formulation for residual stress problems using a set of spectral invariants. These invariants have a clear physical meaning which may facilitate the design of a residual stress experiment. For the case of an energy function that depends on the right Cauchy tensor and the residual stress tensor, we show that only nine of the classical invariants are independent, not 10 as commonly assumed. Details of the spectral formulation are given and several boundary value problems are illustrated. [ABSTRACT FROM AUTHOR]

Although carbon nanotubes/aluminum (CNT/Al) composites are promising materials in the production of structural components, their mechanical behavior under overaging conditions has not been considered. In this paper the effect of CNTs on the microstructural and mechanical behavior of a 2024 aluminum alloy (Al2024) synthesized by mechanical alloying (MA) and powder metallurgy routes is discussed, as well as the effect of aging heat treatments at different temperatures and aging times. The mechanical behavior of composites was screened by hardness measurements as function of aging time. After 96 h of aging time, composites showed mechanical stability in their hardness performance. Images from transmission electron microscopy showed that the mechanical stability of composites was due to a homogeneous dispersion of CNTs in the aluminum matrix and a subsequent alteration in the kinetics of precipitation is due to their presence in the aluminum matrix. Even though strengthening precipitation took place during aging, this was not the main strengthening mechanism observed in composites. [ABSTRACT FROM AUTHOR]

Several boundary value problems are solved for a new class of constitutive equation, where the left Cauchy-Green stretch tensor is given as a non-linear function of the Cauchy stress tensor. Some constitutive inequalities and restrictions are proposed as well. [ABSTRACT FROM AUTHOR]

New sets of spectral invariants are proposed to study the behaviour of electro-elastic bodies composed of a matrix filled with one or two (in general non-orthogonal) families of ‘fibres’, where both the matrix and the fibres can react to the presence of electric fields. [ABSTRACT FROM AUTHOR]

The consequences of the constraint of incompressibility is studied for a new class of constitutive relation for elastic bodies, for which the left Cauchy-Green tensor is a function of the Cauchy stress tensor. The requirement of incompressibility is imposed directly in the constitutive relation, and it is not necessary to assume a priori that the stress tensor should be divided into two parts, a constraint stress and a constitutively specified part, as in the classical theory of nonlinear elasticity. [ABSTRACT FROM AUTHOR]

The objectives of this study were to determine: (1) the sedative effects of dexmedetomidine in combination with methadone, midazolam, or both, and (2) the propofol dose required to achieve endotracheal intubation in healthy dogs. Seven healthy Beagle dogs were included in a prospective experimental, crossover, randomised and masked design. All dogs received four treatments IM, with at least 1 week between sessions, as follows: dexmedetomidine 5 µg/kg (D) alone, or combined with methadone 0.3 mg/kg (DMe), midazolam 0.3 mg/kg (DMi), or both (DMeMi). The degree of sedation was evaluated using a numerical scale (maximum 15 points). The dose of propofol required for intubation was also calculated for each group. Recovery time and quality were determined. Statistical analysis was performed using parametric (ANOVA) and nonparametric tests (Friedman, Cochran Q), as appropriate. The degree of sedation obtained with DMe and DMeMi (13, [7–14]; 13, [6–14], respectively) was significantly higher than in the control group (2, [1–4]; P  = 0.023, P  = 0.006, respectively). The required dose of propofol was lower in all groups (DMi, 1.5 ± 0.5 mg/kg, P  = 0.002; DMe, 1.2 ± 0.5 mg/kg, P  <   0.001; DMeMi, 0.9 ± 0.3 mg/kg) than in the control group (2.9 ± 0.9 mg/kg; P  <   0.001). Recovery quality was not different between groups ( P  = 0.137). In healthy dogs, the addition of midazolam did not enhance the sedative effects of dexmedetomidine or a dexmedetomidine–methadone combination at the doses studied, and propofol requirements were reduced. The sedative effect of dexmedetomidine was enhanced with methadone, and the required dose of propofol was reduced. [ABSTRACT FROM AUTHOR]

Recently, there has been an interest in the development of implicit constitutive relations between the stress and the deformation gradient, to describe the response of elastic bodies as such constitutive relations are capable of describing physically observed phenomena, in which classical models within the construct of Cauchy elasticity are unable to explain. In this paper, we study the consequences of the constraint of incompressibility in a subclass of such implicit constitutive relations. [ABSTRACT FROM AUTHOR]

Recently, there has been interest in the study of a new class of constitutive relation, wherein the linearized strain tensor is assumed to be a function of the stresses. In this communication, some boundary value problems are solved using the finite element method and the solid material being described by such a constitutive relation, where the stresses can be arbitrarily 'large', but strains remain small. Three problems are analyzed, namely the traction of a plate with hyperbolic boundaries, a plate with a point load, and the traction of a plate with an elliptic hole. The results for the stresses and strains are compared with the predictions that are obtained by using the constitutive equation of the classical linearized theory of elasticity. [ABSTRACT FROM AUTHOR]

In this paper, we study the consequences of the constraint of inextensibility with regard to a class of constitutive relations, where the strain is given as a function of the stress. Such constitutive equations belong to a wider class of implicit constitutive relations, which have been proposed recently in the literature. [ABSTRACT FROM AUTHOR]

The class of elastic bodies, that is bodies incapable of dissipation in whatever motion that they undergo, has been significantly enlarged recently (see Rajagopal 2003, On implicit constitutive theories. Appl. Math., 48, 279-319; Rajagopal 2007, The elasticity of elasticity. Z. Angew. Math. Phys. 58, 309-317; Rajagopal, K. R. & Srinivasa, A. R. 2007, On the response of non-dissipative solids. Proc. R. Soc. Lond. A, 463, 357-367). The new classes include fully implicit constitutive relations for the stress and the deformation gradient, and the interesting sub-class wherein the Cauchy-Green tensor or the linearized strain tensor bears a non-linear relationship to the stress. While a fully thermodynamic treatment of such elastic bodies, when defined through implicit constitutive relations between the Piola stress and the Green-St. Venant strain, within a 3D framework has been carried out (see Rajagopal, K. R. & Srinivasa, A. R. 2007, On the response of non-dissipative solids, Proc. R. Soc. Lond. A, 463, 357-367), other possible implicit relationships between other stress and kinematic measures have not been investigated. This paper is devoted to the determination of the consequences of thermodynamics on the new class of elastic bodies, when they are expressed through implicit relations for different stress and stretch/strain measures. [ABSTRACT FROM AUTHOR]

We report results concerning the treatment of elastic bodies described by implicit constitutive relations which are not solvable, in the sense of expressing the stresses as functions of the strains or vice versa. Motivated by the theory of generalized hyperelastic materials, which applies also to polyatomic crystals, the field equations to be solved for a body described by a non-solvable implicit constitutive relation in the above sense are lied down. In addition to the momentum equation, auxiliary variables come into play. These variables are accompanied by an equation governing them. We specialize to the case of an isotropic constitutive relation and give some conditions in order for a broad subclass of an isotropic body to be a generalized material. Then, we lay down the field equations for such a body. [ABSTRACT FROM AUTHOR]

In Part II of the paper, we study the response of a spherical annular region of the same strain limiting elastic body considered in Part I, wherein the linearized strain is a nonlinear function of the stress. We study the response of the annular region due to a normal radial inflation, and as in Part I, we find the response to be strikingly different from that of the classical linearized elastic solid. [ABSTRACT FROM AUTHOR]

There is considerable evidence that shows that for a large class of materials the relationship between the stress and the strain is nonlinear even in the range of strain that is considered small enough for the classical linearized theory of elasticity to be applicable (see Saito et al. in Science 300:464-467, ; Li et al. in Phys Rev Lett 98:105503, ; Talling et al. in Scr Mater 59:669-672, ; Withey et al. in Mater Sci Eng A 493:26-32, ; Zhang et al. in Scr Mater 60:733-736, ). A proper description of the experiments requires an alternative theory which when linearized would allow the possibility of such a nonlinear relationship between the stress and the strain. Recently, such a theory of elastic bodies has been put into place (see Rajagopal in Appl Math 48:279-319, ; Bustamante in Proc R Soc A 465:1377-1392, ; Rajagopal in Math Mech Solids 16:536-562, ). In this paper, we consider a special class of bodies that belong to the new generalization of response relations for elastic bodies that have a nonlinear relationship between the linearized strain and the stress. We use the special class of bodies that exhibit limited small strain to study two boundary value problems, the first concerning the telescopic shearing and inflation of a tube and the second being the extension, inflation and circumferential shearing of a tube. The results that we obtain for the models under consideration are markedly different from the predictions of the classical linearized elastic model with regard to the same boundary value problems. [ABSTRACT FROM AUTHOR]

Implicit constitutive relations that characterize the response of elastic bodies have greatly enhanced the arsenal available at the disposal of the analyst working in the field of elasticity. This class of models were recently extended to describe electroelastic bodies by the present authors. In this paper, we extend the development of implicit constitutive relations to describe the behaviour of elastic bodies that respond to magnetic stimuli. The models that are developed provide a rational way to describe phenomena that have hitherto not been adequately described by the classical models that are in place. After developing implicit constitutive relations for magnetoelastic bodies undergoing large deformations, we consider the linearization of the models within the context of small displacement gradients. We then use the linearized model to describe experimentally observed phenomena which the classical linearized magnetoelastic models are incapable of doing. We also solve several boundary value problems within the context of the models that are developed: extension and shear of a slab, and radial inflation and extension of a cylinder. [ABSTRACT FROM AUTHOR]

In this work a new set of principal axis invariants is proposed in order to study the problem of considering large magneto-elastic deformations, for bodies that are isotropic in the un-deformed configuration when no external magnetic induction is applied. The new set of invariants has clear physical meanings and may have an experimental advantage over the standard invariants used in many previous works in this area. The principal axis invariant formulation is also shown to be more general. Some simple boundary value problems are solved, such as the simple shear, and the biaxial extension of a slab, where with the use of these new invariants, it is possible to study in a much simpler manner the effect of different types of deformations on the response of the material. An illustrated simple specific constitutive equation is proposed which compares well with experiment. [ABSTRACT FROM AUTHOR]

For a new class of elastic bodies, where the linearized strain tensor is given as a function of the Cauchy stress tensor, the problem of considering unsteady motions is studied. A system of partial differential equations that only depends on the stress tensor is found from the equation of motion, which is a system of six partial differential equations for the six components of the stress tensor. A simple boundary value problem is solved for a 1D bar using exact and numerical methods. [ABSTRACT FROM PUBLISHER]

In the past, to model fibre stiffness of finite-radius fibres, previous finite-strain (nonlinear) models were mainly based on the theory of non-linear strain-gradient (second-gradient) theory or Kirchhoff rod theory. We note that these models characterize the mechanical behaviour of polar transversely isotropic solids with infinitely many purely flexible fibres with zero radius. To introduce the effect of fibre bending stiffness on purely flexible fibres with zero radius, these models assumed the existence of couple stresses (contact torques) and non-symmetric Cauchy stresses. However, these stresses are not present on deformations of actual non-polar elastic solids reinforced by finite-radius fibres. In addition to this, the implementation of boundary conditions for second gradient models is not straightforward and discussion on the effectiveness of strain gradient elasticity models to mechanically describe continuum solids is still ongoing. In this paper, we develop a constitutive equation for a non-linear non-polar elastic solid, reinforced by embedded fibers, in which elastic resistance of the fibers to bending is modelled via the classical branches of continuum mechanics, where the development of the theory of stresses is based on non-polar materials; that is, without using the second gradient theory, which is associated with couple stresses and non-symmetric Cauchy stresses. In view of this, the proposed model is simple and somewhat more realistic compared to previous second gradient models. [ABSTRACT FROM AUTHOR]

Abstract: Recently, a very general and novel class of implicit bodies has been developed to describe the elastic response of solids. It contains as a special subclass the classical Cauchy and Green elastic bodies. Within the class of such bodies, one can obtain through a rigorous approximation, constitutive relations for the linearized strain as a nonlinear function of the stress. Such an approximation is not possible within classical theories of Cauchy and Green elasticity, where the process of linearization will only lead to the classical linearized elastic body. In this paper, we study numerically the states of stress and strain in a finite rectangular plate with an elliptic hole and a stepped flat tension bar with shoulder fillets, within the context of the new class of models for elastic bodies that guarantees that the linearized strain would stay bounded and limited below a value that can be fixed a priori, thereby guaranteeing the validity of the use of the model. This is in contrast to the classical linearized elastic model, wherein the strains can become large enough in the body leading to an obvious inconsistency. [Copyright &y& Elsevier]

Biomedical applications of superparamagnetic iron oxide particles have been of interest for quite a number of years. Recent developments show that multifunctionality can be efficiently achieved using polymers to coat the particles and to provide anchoring elements to their surface. This leads to the formation of nanobeads with a reduced number of particles trapped by the polymeric structure. While the magnetothermic behavior of isolated nanoparticles has been a subject of interest over the past several years, multicore magnetic nanobeads have thus far not received the same attention. The influence of structural and magnetic properties in the hyperthermia performance of a series of magnetic fluids designed for biomedical purposes is studied here. The fluids are made of maghemite multicore polymeric beads, with variable nanoparticle size and hydrodynamic size, dispersed in a buffer solution. The specific loss power (SLP) was measured from 5 to 100 kHz with a field intensity of 21.8 kA/m. SLP increases with increasing magnetic core size, reaching 32 W/g Fe2O3 at 100 kHz for 16.2 nm. Within the framework of the linear response theory, a graphical construction is proposed to describe the interplay of both size distributions and magnetic properties in the heating performance of such fluids in a given frequency range. Furthermore, a numerical model is developed to calculate the spare contribution of Néel and Brown relaxation mechanisms to SLP, which gives a fair reproduction of the experimental data. [ABSTRACT FROM AUTHOR]

The implicit function theorem is used to obtain some necessary and sufficient conditions, for which an implicit constitutive relation can be solved in terms of the stresses and strains, in the sense of expressing, for example, the strains in terms of the stresses or vice versa. For an isotropic body some exact solutions for the strains in term of the stresses are presented, using the theory of tensor equations of the form AX + XA = H. For the exact solutions considered, conditions for the existence and the uniqueness are given. [ABSTRACT FROM PUBLISHER]

Abstract: Incremental equilibrium equations and corresponding boundary conditions for an isotropic, hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure. A thick-walled spherical shell during inflation is analyzed using four different material models. Specifically, one and two terms in the Ogden energy formulation, the Gent model and an formulation recently proposed by Lopez-Pamies. We investigate the existence of local pressure maxima and minima and the dependence of the corresponding stretches on the material model and on shell thickness. These results are then used to investigate axisymmetric bifurcations of the inflated shell. The analysis is extended to determine the behavior of a thick-walled spherical shell subject to an external pressure. We find that the results of the two terms Ogden formulation, the Gent and the Lopez-Pamies models are very similar, for the one term Ogden material we identify additional critical stretches, which have not been reported in the literature before. [Copyright &y& Elsevier]