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

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

Study of aging properties of a wire chamber operating with high-pressure hydrogen

The project for a precision measurement of the µp-capture rate (µCAP experiment) is based on an application of a multi-wire proportional chamber (MWPC) operating in ultra-pure hydrogen at 10 bar pressure. A special test setup was constructed at PNPI to investigate the MWPC performance under the expected experimental conditions. The aging studies of the MWPCs were performed with intense irradiation from an alpha-source (Am 241 ) and a beta-source (Sr 90 ). After 45 days of continuous irradiation by alpha-particles no changes in the currents, in the signal shapes, and in the counting rates were observed. It was demonstrated that the MWPCs can operate without degradation at least up to accumulated charges of 0.1 C/cm wire. These irradiation conditions are much more severe than in the real experiment. During the study of the MWPC we have observed an appearance of short duration signals with amplitudes an order of magnitude larger than those of normal signals from the alpha-particles. The number of such signals ("streamers") strongly depend on HV. We shall continue these tests in the future with the goal of obtaining more detailed information about aging properties of MWPCs operating with high-pressure hydrogen

Study of aging properties of a wire chamber operating with high-pressure hydrogen

Abstract The project for a precision measurement of the mp-capture rate (mCAP experiment) is based on an application of a multi-wire proportional chamber (MWPC) operating in ultra-pure hydrogen at 10 bar pressure. A special test setup was constructed at PNPI to investigate the MWPC performance under the expected experimental conditions. The aging studies of the MWPCs were performed with intense irradiation from an a-source ð 241 AmÞ and a b-source ð 90 SrÞ: After 45 days of continuous irradiation by a-particles no changes in the currents, in the signal shapes, and in the counting rates were observed. It was demonstrated that the MWPCs can operate without degradation at least up to accumulated charges of 0:1 C=cm wire. These irradiation conditions are much more severe than in the real experiment. During the study of the MWPC we have observed an appearance of short duration signals with amplitudes an order of magnitude larger than those of normal signals from the a-particles. The number of such signals (''streamers'') strongly depend on HV. We shall continue these tests in the future with the goal of obtaining more detailed information about aging properties of MWPCs operating with high-pressure hydrogen.

Синтез и физико-химические свойства адсорбентов на основе Li1,33Mn1,67O4

Adsorbents based on binary lithium-manganese oxides with the spinel structure of Li1.33Mn1.67O4 were synthesized by using solid-phase, sol-gel, and hydrothermal methods. The effect of the synthesis methods and calcination temperature on the crystal structure, phase composition, textural characteristics, and morphology of prepared adsorbents was established. It was found that the samples obtained by solid-phase and sol-gel methods and calcined at 600 °C were single-phase (Li1.33Mn1.67O4) while the Mn2O3 trace phase was also obtained only in hydrothermal synthesis. The increase in the average crystallite size and the decrease in the specific surface and the total volume of pores were observed during temperature rise in the range from 400 to 800 °C. The samples prepared by sol-gel and hydrothermal methods after at 600 °C calcination had the highest adsorption efficiency of Li+ ions.С использованием твердофазного, золь-гель и гидротермального методов синтезированы адсорбенты на основе двойных оксидов лития-марганца шпинельной структуры Li1,33Mn1,67O4. Установлено влияние способа синтеза и температуры последующей термообработки на кристаллическую структуру, фазовый состав, текстурные свойства и морфологию полученных адсорбентов. Выявлено, что образцы, полученные твердофазным и золь-гель методами и прокаленные при 600 °С, являются однофазными (Li1,33Mn1,67O4), а примесная фаза Mn2O3 образуется только при гидротермальном синтезе. С ростом температуры прокаливания от 400 до 800 °С наблюдается увеличение среднего размера кристаллитов, снижение удельной поверхности и общего объема пор. Полученные золь-гель и гидротермальным методами образцы после прокаливания при 600 °С показали наиболее высокую эффективность сорбции ионов Li+

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force- and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the well-known Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force- and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations