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Microwave ablation is a minimally invasive technique using microwave energy to heat and destroy abnormal cells in tumors, in which temperature monitoring is critical to achieve the desired thermal therapy effect while protecting surrounding healthy tissue. This article proposes for the first time using a surface plasmon resonance (SPR)-based temperature sensor for the real-time monitoring of tissue temperature changes during microwave ablation. The SPR sensor has the advantages of simple structure, low cost, large measurement range, and satisfactory sensitivity. The SPR sensor adopted a multimode fiber (MMF)–thin-core fiber (TCF)–MMF structure, yielding a sensitivity of $-1.781 \pm 0.031$ nm/°C in the range of $22~^{\circ }$ C– $94~^{\circ }$ C. Furthermore, a commercially available fiber Bragg grating (FBG) array sensor was used as a reference, confirming the effectiveness of the proposed SPR sensor in the application.

The propagation of localised (in space-time) waves is analysed in the context of the dynamic theory of incompressible hyperelastic solids subject to body forces corresponding to a dual power-law substrate potential. A broad class of exact solutions is obtained which, under the assumption of slow modulation, incorporates Helmholtz-type solitary waves. The linear stability of these solutions is studied under the assumption that the speed of propagation of the wave is small enough compared to the speed at which transverse waves travel in the linear regime and in the absence of external actions.

Due to the formal resemblance of some models for the Cauchy stress tensor of elastic solids and viscous fluids, some classes of exact solutions for the equations governing the flows in Navier–Stokes fluids have been generalized to linear and nonlinear elastodynamics. In this paper, we study the conditions under which two special classes of generalized Beltrami flows, the vortices in lattice form and Kelvin’s cat’s eye solutions, are solutions of the equations governing the motions in a linearly elastic transversely isotropic solid.

In modern biomedical technology, the fabrication of high-performance sensors for dopamine detection is an important issue because dopamine is a major neurotransmitter and abnormal level of its concentration in the human body is accountable for several neurological diseases. Here, we report a highly sensitive and selective surface plasmon resonance (SPR) sensor modified with small copper oxide nanoparticles (CuO NPs) for experimentally detecting dopamine. Fiber optic sensing probes were fabricated by depositing a 50-nm-thick gold film over the unclad portion of a multimode optical fiber using magnetron sputtering and then further modified with synthesized CuO NPs (~7 nm). Detection of dopamine with the designed SPR sensor was achieved for a wide range of concentrations from very low concentrations with a limit of detection at 1.11 nM and up to 50 nM. The maximum sensitivity was achieved as 0.787 nm/nM and the limit of quantification was at 1.43 nM. To evaluate the selectivity of the studied sensor, experiments were also performed with ascorbic acid and uric acid, which usually coexist with dopamine in the biological fluids. Moreover, sensing characteristics, such as repeatability, linearity, and response time, were studied in detail. Taken together, these findings show that CuO NPs are excellent candidates as SPR sensitizer effectively improving the sensing performance of dopamine.

Laser ablation (LA) holds great promise for the localized treatment of pancreatic tumors. However, there are still many technical aspects that require improvements before largely applying this technique in clinical practice. This work shed light on the following subjects: the thermal response of the pancreas to LA using a diffusing applicator and delivering different laser wavelengths (i.e., 808 and 1064 nm); the development of a pancreas-specific numerical model with temperature-dependent tissue properties based on non-Fourier heat conduction for predicting the temperature distribution. To experimentally study the pancreas thermal response and to tune the model parameters, 80 fiber Bragg grating (FBG) sensors, embedded in arrays with millimetric spatial resolution, were implanted in ex vivo pancreas undergoing LA to obtain the real-time and 2-D temperature distribution. Based on the temperature measured by the FBG sensors, results show that the laser wavelength affects the pancreas thermal response: at 2 mm from the applicator, LA at 808 nm resulted in a thermally affected area 5%–15% larger than at 1064 nm, whereas no notable difference was observed at 6 mm. The temperature distribution and laser-induced lesion obtained from the non-Fourier numerical model were found to closely match the experimental results when the phase lag of the temperature gradient was five times that of the heat flux vector.

Embedding optical fibers with fiber Bragg grating (FBG) sensors in 3-D-printed samples can effectively facilitate the systematic use of smart materials in many fields, such as civil, biomedical, and soft robotics applications. The aim of this study is to analyze different combinations of filament materials and FBG coatings and to assess their metrological characteristics. Eighteen samples are fabricated and tested under different mechanical and thermal conditions. The repeated tests allow to perform an evaluation of the measurement repeatability for each sample, along with an analysis of the sample’s sensitivity. The filaments employed are acrylonitrile butadiene styrene (ABS), polylactic acid (PLA), and thermoplastic polyurethane (TPU). The fiber coatings are acrylate, Ormocer,Registered trademark. and polyimide. Results indicate that the fiber coating has no sigificative influence on the performance of the sensors. The tests for temperature sensitivity highlight a good performance of ABS (116 pm/°C) and TPU samples (32 pm/°C) up to 60 °C, whereas the fabricated PLA samples (139 pm/°C for polyimide, 55 pm/°C for acrylate, and 14 pm/°C for Ormocer1) cannot be used above 40 °C. The tests for strain sensitivity in axial elongation show an average sensitivity of 3.049 nm/mm for ABS, 1.991 nm/mm for PLA, and 3.726 nm/mm for TPU. The bending tests show that all specimen materials have different sensitivities to elongation (2.994 nm/mm for ABS, 0.668 nm/mm for PLA, and 0.149 nm/mm for TPU). Only for acrylate in PLA samples, an effective difference for bending sensitivity resulted (1.241 nm/mm for the acrylate coating versus 2.366 nm/mm for the other coatings).

•Impromptu speaking is an essential leadership skill that can improve with practice.•This is feasible within a residency program's existing protected educational time.•Previous leadership training does impact the degree of improvement in these skills.

This work proposes the quasi-distributed real-time monitoring and control of laser ablation (LA) of liver tissue. To confine the thermal damage, a pre-planning stage of the control strategy based on numerical simulations of the bioheat-transfer was developed to design the control parameters, then experimentally assessed. Fiber Bragg grating (FBG) sensors were employed to design the automatic thermometry system used for temperature feedback control for interstitial LA. The tissue temperature was maintained at a pre-set value, and the influence of different sensor locations (on the direction of the beam propagation and backward) on the thermal outcome was evaluated in comparison with the uncontrolled case. Results show that the implemented computational model was able to properly describe the temperature evolution of the irradiated tissue. Furthermore, the realized control strategy allowed for the accurate confinement of the laser-induced temperature increase, especially when the temperature control was actuated by sensors located in the direction of the beam propagation, as confirmed by the calculated fractions of necrotic tissues (e.g., 23 mm^3 and 53 mm^3 for the controlled and uncontrolled LA, respectively).

Endoscopic submucosal dissection allows for “en bloc” removal of early gastrointestinal neoplasms. However, it is technically demanding and time-consuming. Alternatives could rely on energy-based techniques. We aimed to evaluate a predictive numerical model of thermal damage to preoperatively define optimal laser settings allowing for a controlled ablation down to the submucosa, and the ability of confocal endomicroscopy to provide damage information. A Nd:YAG laser was applied onto the gastric mucosa of 21 Wistar rats on 10 spots (total 210). Power settings ranging from 0.5 to 2.5W were applied during 1–12 s, with a consequent energy delivery varying from 0.5 to 30 J. Out of the 210 samples, a total of 1050 hematoxilin–eosin stained slides were obtained. To evaluate thermal injury, the ratio between the damage depth (DD) over the mucosa and the submucosa thickness (T) was calculated. Effective and safe ablation was considered for a DD/Tratio ≤ 1 (only mucosal and submucosal damage). Confocal endomicroscopy was performed before and after ablation. A numerical model, using human physical properties, was developed to predict thermal damage. No full-thickness perforations were detected. On histology, the DD/Tratio at 0.5 J was 0.57 ± 0.21, significantly lower when compared to energies ranging from 15 J (a DD/T ratio = 1.2 ± 0.3; p< 0.001) until 30 J (a DD/Tratio = 1.33 ± 0.31; p< 0.001). Safe mucosal and submucosal ablations were achieved applying energy between 4 and 12 J, never impairing the muscularis propria. Confocal endomicroscopy showed a distorted gland architecture. The predicted damage depth demonstrated a significant positive linear correlation with the experimental data (Pearson’s r0.85; 95% CI 0.66–0.94). Low-power settings achieved effective and safe mucosal and submucosal ablation. The numerical model allowed for an accurate prediction of the ablated layers. Confocal endomicroscopy provided real-time thermal damage visualization. Further studies on larger animal models are required.

Arterial blood supply deficiency and venous congestion both play a role in anastomotic complications. Our aim was to evaluate a software-based analysis of the fluorescence signal to recognize the patterns of bowel ischemia. In 18 pigs, two clips were applied on the inferior mesenteric artery (group A: n= 6) or vein (group V: n= 6) or on both (group A–V: n= 6). Three regions of interest (ROIs) were identified on the sigmoid: P = proximal to the first clip; C = central, between the two clips; and D = distal to the second clip. Indocyanine Green was injected intravenously. The fluorescence signal was captured by means of a near-infrared laparoscope. The time-to-peak (seconds) and the maximum fluorescence intensity were recorded using software. A normalized fluorescence intensity unit (NFIU: 0-to-1) was attributed, using a reference card. The NFIU’s over-time variations were computed every 10 min for 50 min. Capillary lactates were measured on the sigmoid at the 3 ROIs. Various machine learning algorithms were applied for ischemia patterns recognition. The time-to-peak at the ischemic ROI C was significantly longer in group A versus V (20.1 ± 13 vs. 8.43 ± 3.7; p= 0.04) and in group A–V versus V (20.71 ± 11.6 vs. 8.43 ± 3.7; p= 0.03). The maximal NIFU at ROI C, was higher in the V group (1.01 ± 0.21) when compared to A (0.61 ± 0.11; p= 0.002) and A–V (0.41 ± 0.2; p= 0.0005). Capillary lactates at ROI C were lower in V (1.3 ± 0.6) than in A (1.9 ± 0.5; p= 0.0071), and A–V (2.6 ± 1.5; p= 0.034). The K nearest neighbor and the Linear SVM algorithms provided both an accuracy of 75% in discriminating between A versus V and 85% in discriminating A versus A–V. The accuracy dropped to 70% when the ML had to identify the ROI and the type of ischemia simultaneously. The computer-assisted dynamic analysis of the fluorescence signal enables the discrimination between different bowel ischemia models.

We consider the superimposition of two shear waves on a pseudo-plane motion of the first kind with elliptical streamlines. If the shear waves satisfy some special assumptions it is possible to establish a recurrence relation among the Rivlin–Ericksen tensors associated with the flow at hand. This remarkable kinematical result allows to determine new exact solutions for a large class of materials and to generalize some well known solutions modelling special flows (such as the celebrated Berker’s solution for a Navier–Stokes fluid in an orthogonal rheometer).

Over the last few decades, minimally invasive treatments have garnered much interest as alternatives to surgical resection. Among others, laser ablation has gained a broad clinical acceptance in the treatment of a certain number of solid tumors (e.g., liver, lung, and prostate). In this context, the knowledge of temperature during the treatment may be useful to better control the amount of damaged tissue and to subsequently improve clinical outcomes. The objective of this paper is to assess the feasibility of two multipoint probes for temperature monitoring during laser ablation. The probes consist of a needle made up of a carbon fiber tube. Each probe embeds an array of seven fiber Bragg grating sensors. Experiments performed in in vivo animal models (pig livers) show that the probe can reach deep-seated organs and offer the possibility to monitor tissue temperature in seven different positions. This information may be crucial to guide clinicians in the optimization of treatment settings and to improve the accuracy of theoretical models, which will pilot future studies to design new heating devices and to develop patient-specific treatments.

Nonlinear Schrödinger equations with spatial modulation associated with integrable Hamiltonian systems of Ermakov-Ray-Reid type are introduced. An algorithmic procedure is presented which exploits invariants of motion to construct exact wave packet representations with potential applications in a wide range of physical contexts such as, ‘inter alia’, the analysis of Bloch wave and matter wave solitonic propagation and pulse transmission in Airy modulated NLS models. A particular Ermakov reduction for Mooney-Rivlin materials is set in the broader context of transverse wave propagation in a class of higher-order hyperelastic models of incompressible solids.

Nonlinear Schrödinger equations with spatial modulation associated with integrable Hamiltonian systems of Ermakov-Ray-Reid type are introduced. An algorithmic procedure is presented which exploits invariants of motion to construct exact wave packet representations with potential applications in a wide range of physical contexts such as, ‘inter alia’, the analysis of Bloch wave and matter wave solitonic propagation and pulse transmission in Airy modulated NLS models. A particular Ermakov reduction for Mooney-Rivlin materials is set in the broader context of transverse wave propagation in a class of higher-order hyperelastic models of incompressible solids.

ABSTRACTIncomplete APOBEC3G/F neutralization by a defective HIV-1Vif protein can promote genetic diversification by inducing G-to-A mutations in the HIV-1 genome. The HIV-1 Env V3 loop, critical for coreceptor usage, contains several putative APOBEC3G/F target sites. Here, we determined if APOBEC3G/F, in the presence of Vif-defective HIV-1 virus, can induce G-to-A mutations at V3 positions critical to modulation of CXCR4 usage. Peripheral blood mononuclear cells (PBMC) and monocyte-derived macrophages (MDM) from 2 HIV-1-negative donors were infected with CCR5-using 81.A-VifWTvirus (i.e., with wild-type [WT] Vif protein), 81.A-VifE45G, or 81.A-VifK22E(known to incompletely/partially neutralize APOBEC3G/F). The rate of G-toA mutations was zero or extremely low in 81.A-VifWT- and 81.A-VifE45G-infected PBMC from both donors. Conversely, G-to-A enrichment was detected in 81.A-VifK22E-infected PBMC (prevalence ranging from 2.18% at 7 days postinfection [dpi] to 3.07% at 21 dpi in donor 1 and from 10.49% at 7 dpi to 8.69% at 21 dpi in donor 2). A similar scenario was found in MDM. G-to-A mutations occurred at 8 V3 positions, resulting in nonsynonymous amino acid substitutions. Of them, G24E and E25K strongly correlated with phenotypically/genotypically defined CXCR4-using viruses (P= 0.04 and 5.5e−7, respectively) and increased the CXCR4 N-terminal binding affinity for V3 (WT, −40.1 kcal/mol; G24E, −510 kcal/mol; E25K, −522 kcal/mol). The analysis of paired V3 and Vif DNA sequences from 84 HIV-1-infected patients showed that the presence of a Vif-defective virus correlated with CXCR4 usage in proviral DNA (P= 0.04). In conclusion, incomplete APOBEC3G/F neutralization by a single Vif amino acid substitution seeds a CXCR4-using proviral reservoir. This can have implications for the success of CCR5 antagonist-based therapy, as well as for the risk of disease progression.

We find the strain energy function for isotropic incompressible solids exhibiting a linear relationship between shear stress and amount of shear, and between torque and amount of twist, when subject to large simple shear or torsion deformations. It is inclusive of the well-known neo-Hookean and the Mooney–Rivlin models, but also can accommodate other terms, as certain arbitrary functions of the principal strain invariants. Effectively, the extra terms can be used to account for several non-linear effects observed experimentally but not captured by the neo-Hookean and Mooney–Rivlin models, such as strain stiffening effects due to limiting chain extensibility.

A phenomenological model based on the three-dimensional theory of nonlinear elasticity is developed to describe the phenomenon of overstretching in the force-extension curve for double-stranded DNA (dsDNA). By using the concept of a material with multiple reference configurations a single formula is obtained to fit the force-extension curve.

A phenomenological model based on the three-dimensional theory of nonlinear elasticity is developed to describe the phenomenon of overstretching in the force-extension curve for double-stranded DNA (dsDNA). By using the concept of a material with multiple reference configurations a single formula is obtained to fit the force-extension curve.

In this article, we propose a microstructure-based continuum model to describe the material behavior of spider silks. We suppose that the material is composed of a soft fraction with entropic elasticity and a hard, damageable fraction. The hard fraction models the presence of stiffer, crystal-rich, oriented regions and accounts for the effect of softening induced by the breaking of hydrogen bonds. To describe the observed presence of crystals with different size, composition, and orientation, this hard fraction is modeled as a distribution of materials with variable properties. The soft fraction describes the remaining regions of amorphous material and is here modeled as a wormlike chain. During stretching, we consider the effect of bond-breaking as a transition from the hard- to the soft-material phase. As we demonstrate, a crucial effect of bond-breaking that accompanies the softening of the material is an increase in contour length associated with chains unraveling. The model describes also the self-healing properties of the material by assuming partial bond reconnection upon unloading. Despite its simplicity, the proposed mechanical system reproduces the main experimental effects observed in cyclic loading of spider silks. Moreover, our approach is amenable to two- or three-dimensional extensions and may prove to be a useful tool in the field of microstructure optimization for bioinspired materials.

Single molecule DNA experiments provide interesting data that allow a better understanding of the mechanical interactions between the strands and the nucleotides of this molecule. In some sense, these experiments complement the classical ones about DNA thermal denaturation. It is well known that the original Peyrard–Bishop (PB) model by means of a harmonic stacking potential and a nonlinear substrate potential has been able to predict the existence of a critical temperature of full denaturation of the molecule. In the present paper, driven by the findings of single molecule experiments, we substitute the original harmonic intra-strand stacking potential with a Duffing type potential. By elementary and analytical arguments, we show that with this choice it is possible to obtain a sharp transition in the classical domain wall solution of the PB model and the compactification of the classical solitary wave solutions of other models for the dynamics of DNA. We discuss why these solutions may improve our knowledge of the DNA dynamics in several directions.

In this paper, we review critically some basic models derived from the statistics of long-chain molecules and then discuss the status of such models within the three-dimensional nonlinear theory of elasticity. We draw attention to some deficiencies of certain worm-like chain (WLC) models when viewed within the three-dimensional continuum mechanics framework. Modifications of the WLC models motivated by such considerations and avoiding these deficiencies are then discussed and shown to correspond well with data generated by the exact WLC model.

Abstract Constitutive models are proposed for compressible isotropic hyperelastic materials that reflect limiting chain extensibility. These are generalizations of the model proposed by Gent for incompressible materials. The goal is to understand the effects of limiting chain extensibility when the compressibility of polymeric materials is taken into account. The basic homogeneous deformation of simple tension is considered and simple closed-form relations for the deformation characteristics are obtained for slightly compressible materials. An explicit first-order approximation is obtained for the lateral contraction and for the Poisson function in terms of the axial extension which is shown to be valid for each of two specific compressible versions of the Gent model. One of the main results obtained is that the effect of limiting chain extensibility is to stiffen the material relative to the neo-Hookean compressible case.

In this paper we develop a theory to describe the Mullins effect in rubber–like solids, based on the notion of limiting chain extensibility associated with the Gent model of rubber elasticity. We relate the theory to the mechanisms of network alteration and to the pseudo–elasticity theory of the Mullins effect. The inherently anisotropic nature of the Mullins effect is also discussed.

The purpose of this research is to investigate the basic issues that arise when generalized plane strain deformations are superimposed on anti-plane shear deformations in isotropic incompressible hyperelastic materials. Attention is confined to a subclass of such materials for which the strain-energy density depends only on the first invariant of the strain tensor. The governing equations of equilibrium are a coupled system of three nonlinear partial differential equations for three displacement fields. It is shown that, for general plane domains, this system decouples the plane and anti-plane displacements only for the case of a neo-Hookean material. Even in this case, the stress field involves coupling of both deformations. For generalized neo-Hookean materials, universal relations may be used in some situations to uncouple the governing equations. It is shown that some of the results are also valid for inhomogeneous materials and for elastodynamics.

Abstract:  Certain aspects of the mechanical response of arterial walls can be described using nonlinear elasticity theory. Uniaxial tests on vascular walls reveal nonlinear stress–strain behavior, with higher extensibility in the low stretch range and progressively lower extensibility with increasing stretch. This phenomenon is well known in the framework of rubber-like materials where it is called a strain-hardening or strain-stiffening effect. Constitutive models of incompressible hyperelasticity that take this into account include power-law models and limiting chain extensibility models. Our purpose in this paper is to bring to the attention of the biomechanics community some essential features of one such model of the latter type due to Gent. This model is compared with isotropic versions of biomechanical constitutive models by Takamizawa–Hayashi and Fung; the latter is a limiting version of a power-law material. Two particular problems are considered for which experimental data on arterial wall deformations are available. The first concerns small oscillations superposed on a large static stretch of a vertical string of arterial tissue. It is shown that the exponential model of Fung and the Gent model match well with the experimental data. The second problem is the extension of an internally pressurized circular cylindrical tube. It is shown that an inversion phenomenon observed experimentally for the human iliac artery can be described within a membrane theory by the Gent model whereas this cannot be described using the exponential model. The foregoing considerations are carried out for isotropic elastic materials in the absence of residual stress. Extensions to include anisotropy are also indicated.

Molecular constitutive models for rubber based on non-Gaussian statistics generally involve the inverse Langevin function. Such models are widely used since they successfully capture the typical strain-hardening at large strains. Limiting chain extensibility constitutive models have also been developed on using phenomenological continuum mechanics approaches. One such model, the Gent model for incompressible isotropic hyperelastic materials, is particularly simple. The strain-energy density in the Gent model depends only on the first invariant I1of the Cauchy–Green strain tensor, is a simple logarithmic function of I1and involves just two material parameters, the shear modulus μ and a parameter Jmwhich measures a limiting value for I1−3 reflecting limiting chain extensibility. In this note, we show that the Gent phenomenological model is a very accurate approximation to a molecular based stretch averaged full-network model involving the inverse Langevin function. It is shown that the Gent model is closely related to that obtained by using a Padè approximant for this function. The constants μ and Jmin the Gent model are given in terms of microscopic properties. Since the Gent model is remarkably simple, and since analytic closed-form solutions to several benchmark boundary-value problems have been obtained recently on using this model, it is thus an attractive alternative to the comparatively complicated molecular models for incompressible rubber involving the inverse Langevin function.

The purpose of this research is to investigate the mechanical response in anti-plane shear of a class of incompressible isotropic hyperelastic materials for which the strain-energy density depends only on the first invariant of the strain tensor. Our concern is with the subclass of these materials that exhibits hardening at large deformations. In the molecular theory of elasticity, these models are called non-Gaussian, since they introduce a distribution function which is not Gaussian for the end-to-end distance of the polymeric chain. Two classes of these materials are considered, namely those with limiting chain extensibility and power-law models. The governing partial differential equation of equilibrium in anti-plane shear (a single second-order quasilinear partial differential equation) is obtained for specific constitutive models of the above type. Some solutions are derived using group symmetry reduction methods. Applications to crack problems and spatial decay of end effects are described. The results are applicable to rubber-like and biological materials.

We consider the propagation of finite amplitude plane transverse waves in a class of homogeneous isotropic incompressible viscoelastic solids. It is assumed that the Cauchy stress may be written as the sum of an elastic part and a dissipative viscoelastic part. The elastic part is of the form of the stress corresponding to a Mooney–Rivlin material, whereas the dissipative part is a linear combination of A1, A12and A2, where A1, A2are the first and second Rivlin–Ericksen tensors. The body is first subject to a homogeneous static deformation. It is seen that two finite amplitude transverse plane waves may propagate in every direction in the deformed body. It is also seen that a finite amplitude circularly polarized wave may propagate along either n+or n−, where n+, n−are the normals to the planes of the central circular section of the ellipsoid x⋅B−1x=1. Here Bis the left Cauchy–Green strain tensor corresponding to the finite static homogeneous deformation.

The Cauchy stress tensor, T_ij, is considered for an elastic material which is subject to any internal isotropic constraint, apart from the constraint of incompressibility. For a given strain, it is seen that if in a given basis one of the eigenvectors of the stress tensor has a zero component, say the αth component, and if the arbitrary scalar term in the stress may be chosen so that T_αβ(α≠β) shear stress component is zero, then the stress tensor has a double eigenvalue. This means that there is a great simplification in the stress field. The given strain may be maintained experimentally by a simple tension superimposed upon a hydrostatic stress field. Examples are presented for Bell-constrained and Ericksen-constrained materials.

Abstract: The purpose of this research is to investigate the simple torsion problem for a solid circular cylinder composed of isotropic hyperelastic incompressible materials with limiting chain extensibility. Three popular models that account for hardening at large deformations are examined. These models involve a strain-energy density which depends only on the first invariant of the Cauchy–Green tensor. In the limit as a polymeric chain extensibility tends to infinity, all of these models reduce to the classical neo-Hookean form. The main mechanical quantities of interest in the torsion problem are obtained in closed form. In this way, it is shown that the torsional response of all three materials is similar. While the predictions of the models agree qualitatively with experimental data, the quantitative agreement is poor as is the case for the neo-Hookean material. In fact, by using a global universal relation, it is shown that the experimental data cannot be predicted quantitatively by any strain-energy density which depends solely on the first invariant. It is shown that a modification of the strain energies to include a term linear in the second invariant can be used to remedy this defect. Whether the modified strain-energies, which reflect material hardening, are a feasible alternative to the classic Mooney–Rivlin model remains an open question which can be resolved only by large strain experiments.

AbstractWe consider a Boltzmann-like mathematical model for a problem of outgassing and contamination in a region R. For simplicity we assume that this region is a slab composed by three compartments Ri,i= 1,2,3. The region R1is where the contaminant particles are produced, R2is the cavitywhere such particles migrate and interact with some host medium and R3is the target contaminated by the particles. The main feature of this new model is to consider a filter in the cavity and its consumption over the time. We prove that such a mathematical model has a unique positive strict solution, belonging to a suitable Banach space. Some numerical results for the well-mixed approximation of this model are presented.