scholarly journals A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure

2016 ◽  
Vol 472 (2192) ◽  
pp. 20160438 ◽  
Author(s):  
Michael B. Muhlestein ◽  
Michael R. Haberman
Keyword(s):  
Degrees Of Freedom ◽  
Effective Properties ◽  
Matrix Material ◽  
Momentum Density ◽  
Velocity Fields ◽  
Elastic Matrix ◽  
Relaxation Processes ◽  
Homogenization Technique ◽  
Elastic Metamaterials ◽  
Anisotropic Elastic

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field. Assuming dynamic subwavelength inhomogeneities only interact through their volume-averaged fields implies the macroscopic stress and momentum density fields are functions of both the microscopic strain and velocity fields, and may be related to the macroscopic strain and velocity fields through localization tensors. The macroscopic and microscopic fields are combined to yield a homogenization scheme that predicts the local effective stiffness, density and coupling tensors for an effective Willis-type constitutive equation. It is shown that when internal degrees of freedom of the inhomogeneities are present, Willis-type coupling becomes necessary on the macroscale. To demonstrate the utility of the homogenization technique, the effective properties of an isotropic elastic matrix material containing isotropic and anisotropic spherical inhomogeneities, isotropic spheroidal inhomogeneities and isotropic dynamic spherical inhomogeneities are presented and discussed.

scholarly journals A Dynamical Study of Fusion Hindrance with Nakajima-Zwanzig Projection Method

2021 ◽  
Author(s):  
Yasuhisa Abe ◽  
David Boilley ◽  
Quentin Hourdillé ◽  
Caiwan Shen
Keyword(s):  
Cross Sections ◽  
Degrees Of Freedom ◽  
Operator Method ◽  
Initial Distribution ◽  
Physical Parameters ◽  
Relaxation Processes ◽  
Fast Variable ◽  
Dynamical Study ◽  
Injection Point ◽  
Slow Variables

Abstract A new framework is proposed for the study of collisions between very heavy ions which lead to the synthesis of Super-Heavy Elements (SHE), to address the fusion hindrance phenomenon. The dynamics of the reaction is studied in terms of collective degrees of freedom undergoing relaxation processes with different time scales. The Nakajima-Zwanzig projection operator method is employed to eliminate fast variable and derive a dynamical equation for the reduced system with only slow variables. There, the time evolution operator is renormalised and an inhomogeneous term appears, which represents a propagation of the given initial distribution. The term results in a slip to the initial values of the slow variables. We expect that gives a dynamical origin of the so-called “injection point s” introduced by Swiatecki et al in order to reproduce absolute values of measured cross sections for SHE. A formula for the slip is given in terms of physical parameters of the system, which confirms the results recently obtained with a Langevin equation, and permits us to compare various incident channels.

scholarly journals Image-based semi-multiscale finite element analysis using elastic subdomain homogenization

Meccanica ◽  
2021 ◽  
Author(s):  
J. Jansson ◽  
K. Salomonsson ◽  
J. Olofsson
Keyword(s):  
Finite Element ◽  
Analytical Method ◽  
Effective Properties ◽  
Reference Model ◽  
Computational Time ◽  
Component Level ◽  
Element Analysis ◽  
Model Fidelity ◽  
Multiscale Finite Element ◽  
Anisotropic Elastic

AbstractIn this paper we present a semi-multiscale methodology, where a micrograph is split into multiple independent numerical model subdomains. The purpose of this approach is to enable a controlled reduction in model fidelity at the microscale, while providing more detailed material data for component level- or more advanced finite element models. The effective anisotropic elastic properties of each subdomain are computed using periodic boundary conditions, and are subsequently mapped back to a reduced mesh of the original micrograph. Alternatively, effective isotropic properties are generated using a semi-analytical method, based on averaged Hashin–Shtrikman bounds with fractions determined via pixel summation. The chosen discretization strategy (pixelwise or partially smoothed) is shown to introduce an uncertainty in effective properties lower than 2% for the edge-case of a finite plate containing a circular hole. The methodology is applied to a aluminium alloy micrograph. It is shown that the number of elements in the aluminium model can be reduced by $$99.89\%$$ 99.89 % while not deviating from the reference model effective material properties by more than $$0.65\%$$ 0.65 % , while also retaining some of the characteristics of the stress-field. The computational time of the semi-analytical method is shown to be several orders of magnitude lower than the numerical one.

Shock discontinuity zone effect: the main factor in the explosive decomposition detonation process

1992 ◽  
Vol 339 (1654) ◽  
pp. 355-364 ◽  
Keyword(s):  
Degrees Of Freedom ◽  
Thermal Ionization ◽  
Relaxation Processes ◽  
Explosive Decomposition ◽  
Time Duration ◽  
Active Particles ◽  
Condensed Explosives ◽  
Discontinuity Zone ◽  
Electronically Excited ◽  
Non Equilibrium

A new qualitative conception of the detonation mechanism in condensed explosives has been developed on the basis of experimental and numerical modelling data. According to the conception the mechanism consists of two stages: non-equilibrium and equilibrium. The mechanism regularities are explosive characteristics and they do not depend on explosive charge structure (particle size, nature of filler in the pores, explosive state, liquid or solid, and so on). The tremendous rate of loading inside the detonation wave shock discontinuity zone ( ca. 10 -13 s) is responsible for the origin of the non-equilibrium stage. For this reason, the kinetic part of the shock compression energy is initially absorbed only by the translational degrees of freedom of the explosive molecules. It involves the appearance of extremely high translational temperatures for the polyatomic molecules. In the course of the translational-vibrational relaxation processes (that is, during the first non-equilibrium stage of ca. 10 -10 s time duration) the most rapidly excited vibrational degrees of freedom can accumulate surplus energy, and the corresponding bonds decompose faster than behind the front at the equilibrium stage. In addition to this process, the explosive molecules become electronically excited and thermal ionization becomes possible inside the translational temperature overheat zone. The molecules thermal decomposition as well as their electronic excitation and thermal ionization result in some active particles (radicals, ions) being created. The active particles and excited molecules govern the explosive detonation decomposition process behind the shock front during the second equilibrium stage. The activation energy is usually low, so that during this stage the decomposition proceeds extremely rapidly. Therefore the experimentally observed dependence of the detonation decomposition time for condensed explosives is rather weak.

THREE-DIMENSIONAL COSSERAT CONTINUUM MODELING OF FRACTURED ROCK MASSES

2010 ◽  
Vol 02 (03n04) ◽  
pp. 217-234
Author(s):  
IOANNIS STEFANOU ◽  
JEAN SULEM
Keyword(s):  
Mechanical Properties ◽  
Discrete System ◽  
Degrees Of Freedom ◽  
Fractured Rock ◽  
Three Dimensional ◽  
Cosserat Continuum ◽  
Point Of View ◽  
Rock Masses ◽  
Homogenization Technique ◽  
Rock Structure

The behavior of rock masses is influenced by the existence of discontinuities, which divide the rock in joint blocks making it an inhomogeneous anisotropic material. From the mechanical point of view, the geometrical and mechanical properties of the rock discontinuities define the mechanical properties of the rock structure. In the present paper we consider a rock mass with three joint sets of different dip angle, dip direction, spacing and mechanical properties. The dynamic behavior of the discrete system is then described by a continuum model, which is derived by homogenization. The homogenization technique applied here is called generalized differential expansion homogenization technique and has its roots in Germain's (1973) formulation for micromorphic continua. The main advantage of the method is the avoidance of the averaging of the kinematic quotients and the derivation of a continuum that maps exactly the degrees of freedom of the discrete system through a one-to-one correspondence of the kinematic measures. The derivation of the equivalent continuum is based on the identification for any virtual kinematic field of the power of the internal forces and of the kinetic energy of the continuum with the corresponding quantities of the discrete system. The result is an anisotropic three-dimensional Cosserat continuum.

scholarly journals Multi-Scale Probabilistic Analysis for the Mechanical Properties of Plain Weave Carbon/Epoxy Composites Using the Homogenization Technique

2020 ◽  
Vol 10 (18) ◽  
pp. 6542
Author(s):  
Ji-Won Jin ◽  
Byung-Wook Jeon ◽  
Chan-Woong Choi ◽  
Ki-Weon Kang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Effective Properties ◽  
Level Structure ◽  
Tensile Tests ◽  
Epoxy Composites ◽  
Plain Weave ◽  
Homogenization Technique ◽  
Simulation Based ◽  
Micro Level

Probabilistic analyses of carbon fabric composites were conducted using the Monte Carlo simulation based on a homogenization technique to evaluate the mechanical properties of composites and their stochastic nature. First, the homogenization analysis was performed for a micro-level structure, which fiber and matrix are combined. The effective properties obtained from this analysis were compared with the results from the rule of mixture theory to verify the homogenization analysis. And, tensile tests were conducted to clearly evaluate the result and the reliability was verified by comparing the results of the tensile tests and homogenization analysis. In addition, the Monte Carlo simulation was performed based on homogenization analyses to consider the uncertainties of the micro-level structure combined of fiber and matrix. Next, the results of this simulation were applied to the macro-level structure combined of the tow and matrix to perform the Monte Carlo simulation based on the homogenization technique. Finally, the sensitivity analysis was conducted to identify the effect of constituents of the carbon plain weave composite and the linear correlation of the micro- and macro-level structures combined of the fiber/matrix and tow/matrix, respectively. The findings of this study verified that the effective properties of the plain weave carbon/epoxy composite and their uncertainties depended on the properties of the carbon fiber and epoxy, which are the basic constituents of plain weave carbon/epoxy composites.

Effective properties of composite materials containing voids

1993 ◽  
Vol 440 (1909) ◽  
pp. 461-473 ◽  
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Effective Properties ◽  
Young's Modulus ◽  
Matrix Material ◽  
Practical Importance ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Two Dimensional ◽  
Isotropic Composite

Recent results of theoretical and practical importance prove that the two-dimensional (in-plane) effective (average) Young’s modulus for an isotropic elastic material containing voids is independent of the Poisson’s ratio of the matrix material. This result is true regardless of the shape and morphology of the voids so long as isotropy is maintained. The present work uses this proof to obtain explicit analytical forms for the effective Young’s modulus property, forms which simplify greatly because of this characteristic. In some cases, the optimal morphology for the voids can be identified, giving the shapes of the voids, at fixed volume, that maximize the effective Young’s modulus in the two-dimensional situation. Recognizing that two-dimensional isotropy is a subset of three-dimensional transversely isotropic media, it is shown in this more general case that three of the five properties are independent of Poisson’s ratio, leaving only two that depend upon it. For three-dimensionally isotropic composite media containing voids, it is shown that a somewhat comparable situation exists whereby the three-dimensional Young’s modulus is insensitive to variations in Poisson’s ratio, v m , over the range 0 ≤ v m ≤ ½, although the same is not true for negative values of v m . This further extends the practical usefulness of the two-dimensional result to three-dimensional conditions for realistic values of v m .

scholarly journals Alginate Nanoformulation: Influence of Process and Selected Variables

2020 ◽  
Vol 13 (11) ◽  
pp. 335
Author(s):  
Hazem Choukaife ◽  
Abd Almonem Doolaanea ◽  
Mulham Alfatama
Keyword(s):  
Drug Delivery ◽  
Biomedical Applications ◽  
Effective Properties ◽  
Matrix Material ◽  
Cost Effective ◽  
Biological Properties ◽  
Layer By Layer ◽  
Therapeutic Outcomes ◽  
Manufacturing Techniques ◽  
Formulation Parameters

Nanocarriers are defined as structures and devices that are constructed using nanomaterials which add functionality to the encapsulants. Being small in size and having a customized surface, improved solubility and multi-functionality, it is envisaged that nanoparticles will continue to create new biomedical applications owing to their stability, solubility, and bioavailability, as well as controlled release of drugs. The type and physiochemical as well as morphological attributes of nanoparticles influence their interaction with living cells and determine the route of administration, clearance, as well as related toxic effects. Over the past decades, biodegradable polymers such as polysaccharides have drowned a great deal of attention in pharmaceutical industry with respect to designing of drug delivery systems. On this note, biodegradable polymeric nanocarrier is deemed to control the release of the drug, stabilize labile molecules from degradation and site-specific drug targeting, with the main aim of reducing the dosing frequency and prolonging the therapeutic outcomes. Thus, it is essential to select the appropriate biopolymer material, e.g., sodium alginate to formulate nanoparticles for controlled drug delivery. Alginate has attracted considerable interest in pharmaceutical and biomedical applications as a matrix material of nanocarriers due to its inherent biological properties, including good biocompatibility and biodegradability. Various techniques have been adopted to synthesize alginate nanoparticles in order to introduce more rational, coherent, efficient and cost-effective properties. This review highlights the most used and recent manufacturing techniques of alginate-based nanoparticulate delivery system, including emulsification/gelation complexation, layer-by-layer, spray drying, electrospray and electrospinning methods. Besides, the effects of the main processing and formulation parameters on alginate nanoparticles are also summarized.

scholarly journals Translation of a Coated Rigid Spherical Inclusion in an Elastic Matrix: Exact Solution, and Implications for Mechanobiology

2019 ◽  
Vol 86 (5) ◽  
Author(s):  
Xin Chen ◽  
Moxiao Li ◽  
Shaobao Liu ◽  
Fusheng Liu ◽  
Guy M. Genin ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Exact Solution ◽  
Analytical Solution ◽  
Spherical Inclusion ◽  
Matrix Material ◽  
Elastic Matrix ◽  
Protein Ligands ◽  
First Case ◽  
The Matrix ◽  
Matrix Modulus

The displacement of relatively rigid beads within a relatively compliant, elastic matrix can be used to measure the mechanical properties of the matrix. For example, in mechanobiological studies, magnetic or reflective beads can be displaced with a known external force to estimate the matrix modulus. Although such beads are generally rigid compared to the matrix, the material surrounding the beads typically differs from the matrix in one or two ways. The first case, as is common in mechanobiological experimentation, is the situation in which the bead must be coated with materials such as protein ligands that enable adhesion to the matrix. These layers typically differ in stiffness relative to the matrix material. The second case, common for uncoated beads, is the situation in which the beads disrupt the structure of the hydrogel or polymer, leading to a region of enhanced or reduced stiffness in the neighborhood of the bead. To address both cases, we developed the first analytical solution of the problem of translation of a coated, rigid spherical inclusion displaced within an isotropic elastic matrix by a remotely applied force. The solution is applicable to cases of arbitrary coating stiffness and size of the coating. We conclude by discussing applications of the solution to mechanobiology.

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