A unifying perspective: the relaxed linear micromorphic continuum

We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. Our relaxed model is still able to fully describe rotation of the microstructure and to predict non-polar size-effects. It is intended for the homogenized description of highly heterogeneous, but non polar materials with microstructure liable to slip and fracture. In contrast to classical linear micromorphic models our free energy is not uniformly pointwise positive definite in the control of the independent constitutive variables. The new relaxed micromorphic model supports well-posedness results for the dynamic and static case. There, decisive use is made of new coercive inequalities recently proved by Neff, Pauly and Witsch and by Bauer, Neff, Pauly and Starke. The new relaxed micromorphic formulation can be related to dislocation dynamics, gradient plasticity and seismic processes of earthquakes. It unifies and simplifies the understanding of the linear micromorphic models

Wave propagation in relaxed micromorphic continua: modelling metamaterials with frequency band-gaps

In this paper the relaxed micromorphic model proposed in [Patrizio Neff, Ionel-Dumitrel Ghiba, Angela Madeo, Luca Placidi, Giuseppe Rosi. A unifying perspective: the relaxed linear micromorphic continuum, submitted, 2013, arXiv:1308.3219; and Ionel-Dumitrel Ghiba, Patrizio Neff, Angela Madeo, Luca Placidi, Giuseppe Rosi. The relaxed linear micromorphic continuum: existence, uniqueness and continuous dependence in dynamics, submitted, 2013, arXiv:1308.3762] has been used to study wave propagation in unbounded continua with microstructure. By studying dispersion relations for the considered relaxed medium, we are able to disclose precise frequency ranges (band-gaps) for which propagation of waves cannot occur. These dispersion relations are strongly nonlinear so giving rise to a macroscopic dispersive behavior of the considered medium. We prove that the presence of band-gaps is related to a unique elastic coefficient, the so-called Cosserat couple modulus $\mu_{c}$, which is also responsible for the loss of symmetry of the Cauchy force stress tensor. This parameter can be seen as the trigger of a bifurcation phenomenon since the fact of slightly changing its value around a given threshold drastically changes the observed response of the material with respect to wave propagation. We finally show that band-gaps cannot be accounted for by classical micromorphic models as well as by Cosserat and second gradient ones. The potential fields of application of the proposed relaxed model are manifold, above all for what concerns the conception of new engineering materials to be used for vibration control and stealth technology

The relaxed linear micromorphic continuum: existence, uniqueness and continuous dependence in dynamics

We study well-posedness for the relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. In contrast to classical micromorphic models our free energy is not uniformly pointwise positive definite in the control of the independent constitutive variables. Another interesting feature concerns the prescription of boundary values for the micro-distortion field: only tangential traces may be determined which are weaker than the usual strong anchoring boundary condition. There, decisive use is made of new coercive inequalities recently proved by Neff, Pauly and Witsch and by Bauer, Neff, Pauly and Starke. The new relaxed micromorphic formulation can be related to dislocation dynamics, gradient plasticity and seismic processes of earthquakes.Comment: arXiv admin note: substantial text overlap with arXiv:1308.321

Microwave assisted pyrolysis of waste from short rotation coppice of poplar

Poplar short rotation coppice (SRC) plays an important role in biomass production because they are largely employed both in industry or used as solid fuel [1]. Recently there is a great interest in the below-ground biomass recovery (stump-root system) of poplar SRC because: a) it accounts for about 20% of the total plant dry weight [2] and the average poplar chips can yield 18 ton/ha of root biomass; b) it is easily accessible and harvested (sand-loamy soils); c) the root wood often has higher heating values than tops and branches, and may prove to be a better fuel [3]. Furthermore, the removal of the stump-roots systems does not require the payment of a concession, and using efficient recovery systems, the delivered cost might range from 28 to 66 €/ton[4]. The most common method to dispose waste from forestry biomass is combustion, which is an environmentally unfriendly process. Recently a remarkable interest has been focused on microwave assisted pyrolysis (MAP) of biomass due to the fast and efficient heating and the appealing characteristics of the products obtained [5]. Biomass are able to absorb microwave (MW) and even if a MW absorber is not strictly necessary, it may have some positive effects on the quality of products and pyrolysis time [6]. In this work MAP of residues from SRC of different poplar clones have been studied in a multimode batch oven.. MAP of stump-roots and leaves residues from different poplar clones were thoroughly investigated to produce high quantity and quality of bio-oils. They were obtained with high yield (up to 32.0%) and small water percentage (up to 17.5 %)and showed low density and viscosity and they were fluid at room temperature. Among bio-oils a sample with high acetic acid concentration (543.3 mg/mL) was obtained. Bio-oils were characterized with several analytical techniques: 1H-NMR, IR-ATR, density and viscosity measurements, and an original and innovative quatitative GC-MS method[7, 8]. These techniques let to make possible a detailed study on the bio-oils to define a correlation between their chemical and rheological properties with the parameters of the process. Please click Additional Files below to see the full abstract

Microwave assisted pyrolysis of kraft lignin at reduce pressure in a multimode oven

Lignin is the third-most abundant natural polymer after cellulose and hemicellulose[1] and the only renewable source of aromatics in nature. Moreover lignin is the most relevant waste from industry of paper and bioethanol[2]. Nowadays the common way to dispose it is combustion but the possibility to recovery aromatic moiety from thermochemical conversion of lignin has been received a grown attention. In this field the most promising approach is pyrolysis[3] and particularly interesting is use of microwave (MW) like heating source[4]. Microwave assisted pyrolysis (MAP) was successfully applied in the treatment of plastic materials[5, 6] and biomasses[7]. In this work MAP kraft lignin at reduced pressure was studied to magnify functionalized aromatic moieties recovery. For this reason, MAP processes were performed at different pressure (1 bar, 0.13 bar, 0.013 bar) with and without a fractionating system in a multimode MW batch reactor using carbon like MW absorber. Particularly this study was devoted to correlate quantity and composition of Bio-oils recovered with residence time into reactor. Bio-oils obtained were dark brown liquids and showed a low viscosity and density (close to 1cP and 1 g/mL respectively). The most relevant achievements were gained at residual pressure of 0.013 kPa whit a 37 wt% of Bio-oil collected without fractionating and at residual pressure of 0.013 kPa with fractionating when process was carried out in 9 min. Compositions of Bio-oils were evaluated through 1H-NMR, FT-IR ATR and A quatitative GC-MS method that allowed to evaluation concentration of Bio-oils compounds[8, 9]. Analysis showed high concentration of multisubstituted aromatic ring and few light hydrocarbons/organic acids (C1-C4) from advanced thermal degradation of lignin structure.Data collected showed that MAP at reduced pressure of kraft lignin was a reliable way to process it to recovery high quantity of complex mixture of aromatic compounds. Please click Additional Files below to see the full abstract