Application of the method of multiple scales to unravel energy exchange in nonlinear locally resonant metamaterials

In this paper, the effect of weak nonlinearities in 1D locally resonant metamaterials is investigated via the method of multiple scales. Commonly employed to the investigate the effect of weakly nonlinear interactions on the free wave propagation through a phononic structure or on the dynamic response of a Duffing oscillator, the method of multiple scales is here used to investigate the forced wave propagation through locally resonant metamaterials. The perturbation approach reveals that energy exchange may occur between propagative and evanescent waves induced by quadratic nonlinear local interaction

Model reduction in computational homogenization for transient heat conduction

International audienceThis paper presents a computationally efficient homogenization method for transient heat conduction problems. The notion of relaxed separation of scales is introduced and the homogenization framework is derived. Under the assumptions of linearity and relaxed separation of scales, the microscopic solution is decomposed into a steady-state and a transient part. Static condensation is performed to obtain the global basis for the steady-state response and an eigenvalue problem is solved to obtain a global basis for the transient response. The macroscopic quantities are then extracted by averaging and expressed in terms of the coefficients of the reduced basis. Proof-of-principle simulations are conducted with materials exhibiting high contrast material properties. The proposed homogenization method is compared with the conventional steady-state homogenization and transient computational homogenization methods. Within its applicability limits, the proposed homogenization method is able to accurately capture the microscopic thermal inertial effects with significant computational efficiency

A multi-scale framework to predict damage initiation at martensite/ferrite interface

Martensite/ferrite (M/F) interface damage largely controls failure of dual-phase (DP) steels. In order to predict the failure and assess the ductility of DP steels, accurate models for the M/F interfacial zones are needed. Several M/F interface models have been proposed in the literature, which however do not incorporate the underlying microphysics. It has been recently suggested that (lath) martensite substructure boundary sliding dominates the M/F interface damage initiation and therefore should be taken into account. Considering the computationally infeasibility of direct numerical simulations of statistically representative DP steel microstructures, while explicitly resolving the interface microstructures and the sliding activity, a novel multi-scale approach is developed in this work. Two scales are considered: the DP steel mesostructure consisting of multiple lath martensite islands embedded in a ferrite matrix, and the microscopic M/F interfacial zone unit cell resolving the martensite substructure. Based on the emerging microscopic damage initiation pattern, an effective indicator for the M/F interface damage initiation is determined from the interface microstructural unit cell response, along with the effective sliding in this unit cell. Relating these two effective quantities for different interface microstructural configurations leads to an effective mesoscale model relating the interface damage indicator to the sliding activity of the martensite island in terms of the mesoscopic kinematics. This microphysics-based M/F interface damage indicator model, which could not be envisioned a-priori, is fully identified from a set of interfacial unit cell simulations, thus enabling the efficient prediction of interface damage initiation at the mesoscale. The capability of the developed effective model to predict the mesoscopic M/F interface damage initiation is demonstrated on an example of a realistic DP steel mesostructure

Revisiting the martensite/ferrite interface damage initiation mechanism:The key role of substructure boundary sliding

Martensite/ferrite (M/F) interface damage plays a critical role in controlling failure of dual-phase (DP) steels and is commonly understood to originate from the large phase contrast between martensite and ferrite. This however conflicts with a few, recent observations, showing that considerable M/F interface damage initiation is often accompanied by apparent martensite island plasticity and weak M/F strain partitioning. In fact, martensite has a complex hierarchical structure which induces a strongly heterogeneous and orientation-dependent plastic response. Depending on the local stress state, (lath) martensite is presumed to be hard to deform based on common understanding. However, when favourably oriented, substructure boundary sliding can be triggered at a resolved shear stress which is comparable to that of ferrite. Moreover, careful measurements of the M/F interface structure indicate the occurrence of sharp martensite wedges protruding into the ferrite and clear steps in correspondence with lath boundaries, constituting a jagged M/F interfacial morphology that may have a large effect on the M/F interface behaviour. By taking into account the substructure and morphology features, which are usually overlooked in the literature, this contribution re-examines the M/F interface damage initiation mechanism. A systematic study is performed, which accounts for different loading conditions, phase contrasts, residual stresses/strains resulting from the preceding martensitic phase transformation, as well as the possible M/F interfacial morphologies. Crystal plasticity simulations are conducted to include inter-lath retained austenite (RA) films enabling the substructure boundary sliding. The results show that the substructure boundary sliding, which is the most favourable plastic deformation mode of lath martensite, can trigger M/F interface damage and hence control the failure behaviour of DP steels. The present finding may change the way in which M/F interface damage initiation is understood as a critical failure mechanism in DP steels

Enriched Computational Homogenization Schemes Applied to Pattern-Transforming Elastomeric Mechanical Metamaterials

Elastomeric mechanical metamaterials exhibit unconventional mechanical behaviour owing to their complex microstructures. A clear transition in the effective properties emerges under compressive loading, which is triggered by local instabilities and pattern transformations of the underlying cellular microstructure. Such transformations trigger a non-local mechanical response resulting in strong size effects. For predictive modelling of engineering applications, the effective homogenized material properties are generally of interest. For mechanical metamaterials, these can be obtained in an expensive manner by ensemble averaging of the direct numerical simulations for a series of translated microstructures, applicable especially in the regime of small separation of scales. To circumvent this expensive step, computational homogenization methods are of benefit, employing volume averaging instead. Classical first-order computational homogenization, which relies on the standard separation of scales principle, is unable to capture any size and boundary effects. Second-order computational homogenization has the ability to capture strain gradient effects at the macro-scale, thus accounting for the presence of non-localities. Another alternative is micromorphic computational homogenization scheme, which is tailored to pattern-transforming metamaterials by incorporating prior kinematic knowledge. In this contribution, a systematic study is performed, assessing the predictive ability of computational homogenization schemes in the realm of elastomeric metamaterials. Three representative examples with distinct mechanical loading are employed for this purpose: uniform compression and bending of an infinite specimen, and compression of a finite specimen. Qualitative and quantitative analyses are performed for each of the load cases where the ensemble average solution is set as a reference.Comment: 32 pages, 19 figures, 1 table, abstract shortened to fulfil 1920 character limi

Increased Rate of Hospitalization for Diabetes and Residential Proximity of Hazardous Waste Sites

BACKGROUND: Epidemiologic studies suggest that there may be an association between environmental exposure to persistent organic pollutants (POPs) and diabetes. OBJECTIVE: The aim of this study was to test the hypothesis that residential proximity to POP-contaminated waste sites result in increased rates of hospitalization for diabetes. METHODS: We determined the number of hospitalized patients 25–74 years of age diagnosed with diabetes in New York State exclusive of New York City for the years 1993–2000. Descriptive statistics and negative binomial regression were used to compare diabetes hospitalization rates in individuals who resided in ZIP codes containing or abutting hazardous waste sites containing POPs (“POP” sites); ZIP codes containing hazardous waste sites but with wastes other than POPs (“other” sites); and ZIP codes without any identified hazardous waste sites (“clean” sites). RESULTS: Compared with the hospitalization rates for diabetes in clean sites, the rate ratios for diabetes discharges for people residing in POP sites and “other” sites, after adjustment for potential confounders were 1.23 [95% confidence interval (CI), 1.15–1.32] and 1.25 (95% CI, 1.16–1.34), respectively. In a subset of POP sites along the Hudson River, where there is higher income, less smoking, better diet, and more exercise, the rate ratio was 1.36 (95% CI, 1.26–1.47) compared to clean sites. CONCLUSIONS: After controlling for major confounders, we found a statistically significant increase in the rate of hospitalization for diabetes among the population residing in the ZIP codes containing toxic waste sites

Retardation of plastic instability via damage-enabled microstrain delocalization

Multi-phase microstructures with high mechanical contrast phases are prone to microscopic damage mechanisms. For ferrite-martensite dual-phase steel, for example, damage mechanisms such as martensite cracking or martensite-ferrite decohesion are activated with deformation, and discussed often in literature in relation to their detrimental role in triggering early failure in specific dual-phase steel grades. However, both the micromechanical processes involved and their direct influence on the macroscopic behavior are quite complex, and a deeper understanding thereof requires systematic analyses. To this end, an experimental-theoretical approach is employed here, focusing on three model dual-phase steel microstructures each deformed in three different strain paths. The micromechanical role of the observed damage mechanisms is investigated in detail by in-situ scanning electron microscopy tests, quantitative damage analyses, and finite element simulations. The comparative analysis reveals the unforeseen conclusion that damage nucleation may have a beneficial mechanical effect in ideally designed dual-phase steel microstructures (with effective crack-arrest mechanisms) through microscopic strain delocalization

ДИСПЕРСНОСТЬ И МОРФОЛОГИЯ ГИДРОЗОЛЯ ДИОКСИДА ТИТАНА

Hydrous titanium dioxide has been obtained by hydrolysis of titanium tetrachloride in aqueous solution both with and without alcohol. Method of atomic force microscopy has been used in order to investigate morphology of air dried samples of  hydrous titanium dioxide. The paper shows  formation of conglomerates in case of hydrolysis without addition of isobutyl alcohol. According to turbidimetric data particle radius of hydrosol has varied in the suspension within the range of (135 ± 5) nm that is in good correlation with atomic force microscopy data. Гидратированный диоксид титана получен гидролизом тетрахлорида титана в водной среде как в присутствии спирта, так и без него. Методом атомно-силовой микроскопии изучена морфология высушенных на воздухе образцов гидратированного диоксида титана. Показано образование конгломератов в случае проведения гидролиза без добавления изобутилового спирта. По данным турбидиметрии, радиус частиц гидрозоля в суспензии изменялся в пределах (135 ± 5) нм, что находится в хорошей корреляции с данными атомно-силовой микроскопии

Model for End‐Stage Liver Disease‐Lactate and Prediction of Inpatient Mortality in Patients With Chronic Liver Disease

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/163652/3/hep31199.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163652/2/hep31199_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163652/1/hep31199-sup-0001-Supinfo.pd