Continuum model of dispersion caused by an inherent material characteristic length

1995 ◽  
Vol 77 (8) ◽  
pp. 4054-4063 ◽  
Author(s):  
M. B. Rubin ◽  
P. Rosenau ◽  
O. Gottlieb
Keyword(s):  
Continuum Model ◽  
Characteristic Length ◽  
Material Characteristic

Two types of scale effects on the nonlinear forced vibration of axially moving nanobeams

2020 ◽  
Vol 34 (10) ◽  
pp. 2050095
Author(s):  
Jing Wang ◽  
Jianqiang Sun
Keyword(s):  
Mechanical Properties ◽  
Frequency Response ◽  
Continuum Mechanics ◽  
Forced Vibration ◽  
Characteristic Length ◽  
Scale Effects ◽  
Material Characteristic ◽  
Main Resonance ◽  
Amplitude Frequency Response ◽  
Axially Moving

Various non-classical continuum mechanics models appearing in previous studies cannot perfectly explain the mechanical properties of micro- and nanomaterials. Establishing a reasonable continuum mechanics model that comprehensively reflects the scale effect on material deformation is of great practical significance for objectively explaining the variation law of mechanical properties of micro- and nanomaterials under the combined action of different scale effects. Based on nonlocal strain gradient theory, a new scale-dependent model is proposed for axially moving nanobeams. In this study, an asymptotic expansion is performed using the multiscale time method to obtain the amplitude-frequency response curve of the equilibrium solutions for the forced vibration problem. Afterwards, the effects of various system parameters, especially the scale parameters, on the resonance curve are examined. Finally, the effects of nonlocal parameters and material characteristic length parameters on the amplitude-frequency response curves are investigated through typical numerical examples. The numerical results show that the nonlocal parameters promote the emergence of the main resonance, whereas the material characteristic length parameters suppress the emergence of the main resonance. Moreover, these parameters also affect the response amplitude and the skewness and jumping point of the amplitude-frequency characteristic curve.

Theoretical Effects of Rigid Particle Additives in Noncyclic Squeeze Films

1983 ◽  
Vol 105 (1) ◽  
pp. 105-112 ◽  
Author(s):  
Prawal Sinha ◽  
Chandan Singh
Keyword(s):  
Effective Viscosity ◽  
Characteristic Length ◽  
Three Dimensional ◽  
Molecular Size ◽  
Squeeze Film ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Material Characteristic ◽  
Rigid Particle ◽  
Fluid Theory

The micropolar fluid theory, a possible non-Newtonian model for fluids with rigid particle additives in which the average molecular size may be comparable to the material characteristic length, is applied to a two-dimensional problem of squeeze film of a ball in a spherical seat and to some three-dimensional noncyclic squeeze film problems, assuming the characteristic coefficients to be constant, in an effort to study the effects of rigid particle additives for the three-dimensional micropolarity model. Increase in effective viscosity due to the presence of additives is established theoretically. It is also shown that the theoretical effects of the additives on three-dimensional lubrication are identical to the two-dimensional problems, at least qualitatively.

scholarly journals A Bernoulli equation for potential flow of incompressible materials with an inherent material characteristic length

2013 ◽  
Vol 469 (2151) ◽  
pp. 20120641 ◽  
Author(s):  
M. B. Rubin
Keyword(s):  
Circular Cylinder ◽  
Constitutive Equations ◽  
Potential Flow ◽  
Size Dependence ◽  
Characteristic Length ◽  
Inviscid Fluid ◽  
Bernoulli Equation ◽  
Material Characteristic ◽  
Velocity Gradients ◽  
Incompressible Materials

A general simple continua can be enhanced by constitutive equations which depend on the acceleration and velocity gradients to model the effects of a material characteristic length. This paper shows that for irrotational flows of a class of incompressible materials this model yields a Bernoulli equation. Consequently, for this class of materials and flows, it is possible to satisfy the balance of linear momentum exactly, including the effect of a material characteristic length which introduces size dependence of solutions. An example of a rigid circular cylinder moving through an inviscid fluid is considered to demonstrate dependence of the motion on the size of the cylinder.

Spectral Stiffness Microplane Model for Quasibrittle Composite Laminates—Part II: Calibration and Validation

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
Alessandro Beghini ◽  
Gianluca Cusatis ◽  
Zdeněk P. Bažant
Keyword(s):  
Experimental Data ◽  
Composite Laminates ◽  
World Wide ◽  
Characteristic Length ◽  
Present Theory ◽  
Material Characteristic ◽  
Microplane Model ◽  
Softening Behavior ◽  
Crack Band ◽  
Biaxial Tests

The spectral stiffness microplane (SSM) model developed in the preceding Part I of this study is verified by comparisons with experimental data for uniaxial and biaxial tests of unidirectional and multidirectional laminates. The model is calibrated by simulating the experimental data on failure stress envelopes analyzed in the recent so-called “World Wide Failure Exercise,” in which various existing theories were compared. The present theory fits the experiments as well as the theories that were best in the exercise. In addition, it can simulate the post-peak softening behavior and fracture, which is important for evaluating the energy-dissipation capability of composite laminate structures. The post-peak softening behavior and fracture are simulated by means of the crack band approach which involves a material characteristic length.

Energy-Based Strength Theory for Soft Elastic Membranes

2019 ◽  
Vol 86 (7) ◽  
Author(s):  
Reza Pourmodheji ◽  
Shaoxing Qu ◽  
Honghui Yu
Keyword(s):  
Experimental Data ◽  
Critical Load ◽  
Biaxial Loading ◽  
Characteristic Length ◽  
Styrene Butadiene Rubber ◽  
Butadiene Rubber ◽  
Material Characteristic ◽  
Principal Stresses ◽  
Growth Modes ◽  
Failure Conditions

In the previous studies by the authors and others, it was demonstrated that there are two possible defect growth modes and a characteristic material length for any soft material. For a pre-existing defect smaller than the material characteristic length, the energy is dissipated all around the defect as it grows and the critical load for the growth is independent of the defect size. For defects larger than the characteristic length, the growth is by cracking and the energy is dissipated along a plane. Thus, the critical load for the growth is size dependent and can be predicted by fracture mechanics. In this study, we apply the same energy-based argument to the failure of thin membranes, with the focus on the first growth mode that gives the maximum critical load. We assume that strain localization due to damage is the precursor to rupture, and hence, we model the corresponding zone as a through-thickness hole, with its size smaller than the material characteristic length. The defect grows when the elastic energy relaxed by the growth is enough to provide the energy needed for internal microstructure changes. This leads us to the size-independent failure conditions for membranes under the biaxial load. The conditions are expressed in terms of either two principal stretches or two principal stresses for two different types of materials. For verification, we test the theory using the published experimental data on natural and styrene-butadiene rubber. By using the experimental data from equal biaxial loading, we predict the critical principal stretch ratios and critical stresses for different biaxialities. The predictions agree well with the experimental results.

scholarly journals Etude de l’influence des défauts de petite taille sur le comportement à rupture avec le modèle de Dugdale régularisé

2008 ◽  
pp. 481-493
Author(s):  
Hichème Ferdjani ◽  
Med Zaim Khelifi ◽  
Jean-Jacques Marigo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Characteristic Length ◽  
The Finite Element Method ◽  
Material Characteristic ◽  
Limit Loads ◽  
Cohesive Forces ◽  
Petite Taille ◽  
Dugdale’S Model

The goal of this work is to prove that, within the framework of Fracture Mechanics with the regularized Dugdale’s model of cohesive forces, the defects the size of which are small compared to the material characteristic length are practically without influence on the limit loads of structures. For that, we treat two examples : the case of a precracked plate, then the case of a plate with a circular hole. The calculations are made with the finite element method.

A Continuum Model for Void Nucleation by Inclusion Debonding

1987 ◽  
Vol 54 (3) ◽  
pp. 525-531 ◽  
Author(s):  
A. Needleman
Keyword(s):  
Cohesive Zone ◽  
Continuum Model ◽  
Cohesive Zone Model ◽  
Characteristic Length ◽  
Void Nucleation ◽  
Finite Geometry ◽  
Zone Model ◽  
Unified Framework ◽  
Full Account ◽  
Spherical Inclusions

A cohesive zone model, taking full account of finite geometry changes, is used to provide a unified framework for describing the process of void nucleation from initial debonding through complete decohesion. A boundary value problem simulating a periodic array of rigid spherical inclusions in an isotropically hardening elastic-viscoplastic matrix is analyzed. Dimensional considerations introduce a characteristic length into the formulation and, depending on the ratio of this characteristic length to the inclusion radius, decohesion occurs either in a “ductile” or “brittle” manner. The effect of the triaxiality of the imposed stress state on nucleation is studied and the numerical results are related to the description of void nucleation within a phenomenological constitutive framework for progressively cavitating solids.

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