Homogenization of weakly coercive integral functionals in three-dimensional linear elasticity

International audienceThis paper deals with the homogenization through Γ-convergence of weakly coercive integral energies with the oscillating density L(x/ε)∇v : ∇v in three-dimensional elasticity. The energies are weakly coercive in the sense where the classical functional coercivity satisfied by the periodic tensor L (using smooth test functions v with compact support in R 3) which reads as Λ(L) > 0, is replaced by the relaxed condition Λ(L) ≥ 0. Surprisingly, we prove that contrary to the two-dimensional case of [2] which seems a priori more constrained, the homogenized tensor L 0 remains strongly elliptic, or equivalently Λ(L 0) > 0, for any tensor L = L(y1) satisfying L(y)M : M + D : Cof(M) ≥ 0, a.e. y ∈ R 3 , ∀ M ∈ R 3×3 , for some matrix D ∈ R 3×3 (which implies Λ(L) ≥ 0), and the periodic functional coercivity (using smooth test functions v with periodic gradients) which reads as Λper(L) > 0. Moreover, we derive the loss of strong ellipticity for the homogenized tensor using a rank-two lamination, which justifies by Γ-convergence the formal procedure of [8]

Microencapsulation Yield Assessment Using TGA

In this study, microcapsules containing different contents of different kinds of fragrances and with a regular spherical shape, 2,0–8,0 µm diameter, were synthesized in various core:shell ratios. Mint and cuir fragrances were successfully encapsulated in poly(urea-formaldehyde) (PUF) shell via in-situ polymerization. This was confirmed by optical microscope, scanning electron microscope (SEM) and Fourier transform infrared spectroscopy (FTIR) studies. By observation from thermogravimetric analysis (TGA), it was found a relation between thermal gravimetric curves and the amount of fragrance encapsulated, which was later contrasted by ultraviolet-visible spectroscopy. In this way, comparatively, the yield percentage values can be quantitatively defined with a sufficient degree of accuracy by TGA methodPostprint (author's final draft

Gamma-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficients

The present paper deals with the asymptotic behavior of equi-coercive sequences {Fn} of nonlinear functionals defined over vector-valued functions in W1,p 0 (Ω)M , where p > 1, M ≥ 1, and Ω is a bounded open set of RN , N ≥ 2. The strongly local energy density Fn(·, Du) of the functional Fn satisfies a Lipschitz condition with respect to the second variable, which is controlled by a positive sequence {an} which is only bounded in some suitable space L r(Ω). We prove that the sequence {Fn} Γ-converges for the strong topology of Lp(Ω)M to a functional F which has a strongly local density F(·, Du) for sufficiently regular functions u. This compactness result extends former results on the topic, which are based either on maximum principle arguments in the nonlinear scalar case, or adapted div-curl lemmas in the linear case. Here, the vectorial character and the nonlinearity of the problem need a new approach based on a careful analysis of the asymptotic minimizers associated with the functional Fn. The relevance of the conditions which are imposed to the energy density Fn(·, Du), is illustrated by several examples including some classical hyper-elastic energies.Ministerio de Economía y CompetitividadInstitut de Recherche Mathématique de Renne

The value of air plethysmography in predicting clinical outcome after surgical treatment of chronic venous insufficiency

Purpose: The role of air plethysmography (APG) as a predictor of clinical outcome after surgery in venous disease is yet to be defined. The purpose of this study was to investigate the value of APG in predicting clinical outcome after venous surgery for chronic venous insufficiency (CVI). Methods: Seventy-three extremities in 71 patients with Class 3 through 6 CVI were assessed preoperatively with CEAP (c linical, e tiologic, a natomic, p athophysiologic) criteria, standing reflux duplex ultrasound scan, and APG with measurements of preoperative venous filling index (VFI), venous volumes, ejection fraction, and residual volume fraction. After surgical treatment of the affected limbs, repeat APG studies were obtained within 6 weeks. Established venous reporting standards were used for follow-up to calculate clinical symptom scores (CSSs) in each patient. Results: Superficial venous reflux occurred alone in 24 limbs or in conjunction with perforator incompetence in 26 limbs. Deep and superficial reflux, with or without perforator incompetence, was found in 16 limbs, and seven limbs had isolated deep insufficiency. Follow-up was available in 60 of 71 patients (mean period, 44.3 months). Postoperative APG demonstrated significant hemodynamic changes after surgery as measured with VFI, venous volumes, ejection fraction, and residual volume fraction. Mean CSSs decreased from 7.35 ± 0.56 preoperatively to 1.79 ± 0.32 at late follow-up after surgery (P Conclusions: Normalization of the VFI after venous surgery for CVI is predictive of a good clinical outcome. This APG measurement may be a useful parameter to predict adequacy of surgery in patients with venous insufficiency. (J Vasc Surg 2000;32:961-8.

Understanding the effect of processed- and mastication-induced common bean characteristics to engineer its digestive starch functionality

Common beans are nutritious and sustainable commodities in which nutrients are bio-encapsulated in natural barriers. Processing is impeccable to increase their palatability, but also to increase embedded macronutrients digestibilities. In an ongoing PhD work, we investigated how different variables at the level of processing and digestion (e.g. in vivo mastication) affect structural and in vitro starch digestion kinetics of common beans. In a first part 1, we studied the effect of conventional cooking on macro- and microstructural characteristics. We observed that cooking time was an important factor to influence the hardness and microstructural composition of the beans. From short to long cooking times, microstructural properties shifted from free starch granules over cell clusters to free, closed cells. These structures were the result of processing and a simple mechanical desintegration with mortle and pestle. Secondly2, we investigated the effect of in vivo mastication on the tissue structural breakdown pattern. Within the mastication panel, different mastication characteristics were observed but free, closed cells were detected to be the characteristic microstructure of bean tissue when cooked within the palatable range. Finally3,4, we investigated the natural barrier role (e.g. cell wall, protein matrix) on in vitro starch digestion kinetics. We proved that starch digestion in bean cells is a multistep process, in which digestive enzymes need to cross the cell wall barrier, reach their substrate and metabolites produced need to leave the cell in order to be considered bio-accessible3. We also observed that by cooking beans at different intensities, different structural characteristics of proteins can be observed, which can be one of the reasons why beans being cooked with different processing intensities clearly show different digestibilities4. Pallares Pallares, A. (1) (2018). Food Res. Int. ; (2) (2019). Submitted to Br. J. Nut. ; (3) (2018). Food and Funct.; (4) (2019). Submitted to Food Funct.status: publishe

In vitro starch hydrolysis of common bean process-induced structures

Common beans have natural structural barriers playing a fundamental role in the fate of starch upon consumption. In this study, the influence of process-induced modifications of natural barriers on the in vitro starch hydrolysis of common bean cotyledons was investigated. Initially, water-soaked common beans were subjected to three different processes, each as a function of time: a thermal treatment (HT, 95⁰C, 0.1MPa), a high-pressure treatment (HP, 20⁰C, 600MPa), and a combined high-temperature high-pressure treatment (HTHP, 95⁰C, 600MPa). After processing, cotyledons were isolated and the time-dependent evolution of hardness (whole cotyledons) and microstructural properties (after mechanical degradation) was determined. Subsequently, for a number of mechanically disrupted samples with specific microstructural characteristics, the time-dependent evolution of in vitro small intestinal starch hydrolysis (expressed as percentage of digested starch) was determined. It was detected that HP samples were mostly characterized by free, non-swollen starch granules, whilst in samples obtained by HT and HTHP there was major presence of cell clusters at early processing times and free cells at longer times. However, HTHP samples had higher microstructural heterogeneity than HT samples. A fractional conversion model properly described the time-dependent evolution of in vitro starch hydrolysis. From the joint confidence regions of the estimated kinetic parameters, the presence of statistically significant differences among the samples became clear. In general, rate constants of all samples were similar, whilst the final values of digested starch exhibited major differences. The predicted final digested starch decreased with an increase in the level of starch bio-encapsulation (from free gelatinized starch to cell clusters) and a decrease in the degree of starch gelatinization. In samples with the same level of starch bio-encapsulation (free cells), the observed differences might be attributed either to a different degree of starch gelatinization or to a distinct cell wall porosity induced by a longer processing time.status: publishe

Processing as a tool to manage digestive barriers in plant-based foods: recent advances

status: publishe