Elastic modulus of lightweight concrete with pvc aggregate was studied by kou et al. The modulus of elasticity, also known as youngs modulus, is a material property and a measure of its stiffness under compression or tension. The elastic properties of cracked rocks depend on a number of facts. This extends to a piezoelectric quasicrystalline medium the traditional notion of a screw dislocation in a linear solely elastic solid material by the introduction of the concept of an extended burgers vector that has discontinuities in the components, u.
A variational formulation has been recently proposed by the authors xu x. The modulus of elasticity formula is simply stress divided by strain. Elastic solid article about elastic solid by the free. A strict approach to the study of effective elastic moduli of an isotropic medium containing a set of flat parallel cracks is proposed. Effective moduli, nonlinear deformation and strength of a. Stress impact on elastic anisotropy of triclinic porous. Study of effective elastic moduli of cracked solid. Elastic modulus is sometimes called youngs modulus after thomas young who published the concept back in 1807. Generalized maxwell model for microcracked viscoelastic. The elastic moduli of a solid permeated with an isotropic distribution of flat cracks have been calculated from the energy of a single crack by use of a selfconsistent approximation. In this paper, effective moduli of cracked solid material were investigated.
Some other versions of the emm were proposed by kerner 1956 and christensen and loo 1979 in order to improve the predictions of the emm. Differences between static and dynamic elastic moduli of a. Elastic moduli synonyms, elastic moduli pronunciation, elastic moduli translation, english dictionary definition of elastic moduli. To further complicate the matter, however, i now need to twist the rubber band.
It is defined as the ratio of tensile stress to tensile strain. They varied the width of the fgm insert from one having a smaller slope so as to be equivalent to a homogeneous beam, and decreased it to a limit wherein the beam behaves as a bimaterial. For the love of physics walter lewin may 16, 2011 duration. For a linear elastic material, the elastic modulus in a certain direction is defined as the stress value in that direction that causes a unit strain in the same direction. Dynamic bulk and shear moduli due to grainscale local. Assumptions are made to extend this calculation to multiaxial creep. Solid objects will deform when adequate forces are applied to them. Effective elastic moduli of cracked solid and application. For this reason the influence of the elastic moduli of an anisotropic material on crack rotation are studied. Calculations on the basis of the selfconsistent method are made for the elastic moduli of bodies containing randomly distributed flat cracks, with or without fluid in their interiors. The effective elastic moduli of a cracked solid depend on a scalar variable, termed material damage, representing the local microcrack density. Parameters are identified which adapt the elliptic crack results to.
Effective elastic moduli of an isotropic medium weakened. Discover the solidworks plastic part design demo from the solidworks 3d design demo library. The effect of microcracks on the elastic moduli of brittle materials. To complete these works, this paper develops a model to estimate viscoelastic properties of materials that are constituted of two phases. Accurate modeling of elastic properties of cracked rocks in the earths shallow crust has long been an important topic in the field of geophysics. Introduction a medium containing numerous cracks behaves differently compared to the homogeneous medium. Elastic energy is the mechanical potential energy stored in the configuration of a material or physical system as it is subjected to elastic deformation by work performed upon it. Cracked solid cell model elasticity crack orientation complex potential multipole expansion effective moduli abstract this paper addresses the problem of calculating effective elastic properties of a solid containing multiple cracks with prescribed orientation statistics. For instance, elastic moduli of cracked materials obtained by this version of the emm budiansky and oconnell, 1976 tends to zero when the density of cracks is not very large. Using this formulation, explicit expressions have been obtained for the upper bounds of the elastic moduli in the case of penny. Their results indicate that elastic modulus is reduced with an increase in pvc content. General concepts are outlined for arbitrary cracks and explicit derivations together with numerical results are given for elliptic cracks. On the elastic and viscous properties of media containing.
Moreover, figure 2 shows experimentally observed ratios between the third. An analytical approach is discussed for a cracked solid containing randomly oriented inclusions by using elastic potential and a standard tensorial basis. Calculator for exploring relations among the elastic constants. An apparatus for the measurement of elastic modulus in a nonsolid ceramic material comprising. I was under the impression that nitinol can have different youngs modulus associated with either the austenite or martensite formation of the material. Studies of elastic wave attenuation in cracked solid media have been studied for at least 30 years, since the work of mal, 1,2. Static and dynamic elastic moduli of calcare massiccio mudstonelimestone, the typical seismogenic rock in the italian apennines, are measured using a standard uniaxial static compression test, a dual cantilever forced oscillation test and. Variational formulation on effective elastic moduli of. Imagine those two dowel posts protruding from a board at 90 degree angles, one at each end of the board. The damage evolves as a function of the ongoing deformation, leading to degradation and recovery of the effective elastic moduli and accumulation of inelastic strain beyond. Solidworks plastic part design 3d design demo library. Youngs modulus e describes tensile elasticity, or the tendency of an object to deform along an axis when opposing forces are applied along that axis.
This calculator converts any two given elastic constants of an isotropic material to other commonly used elastic constants. At their functional core, all of these stretchy, formfitting accoutrements rely on a material known as elastic. Request pdf variational formulation on effective elastic moduli of randomly cracked solids formulation of variational bounds for properties of inhomogeneous media constitutes one of the most. Solidworks simulation incorporates the baileynorton power law to calculate the uniaxial creep strain in terms of stress, time and temperature for the primary and secondary ranges. Scaling relations of earthquakes and aseismic deformation. If the material is elastic, the object will return to its initial shape and size when these forces are removed. In particular a linear elastic problem for a straight mode i crack, located on a symmetry axis of an orthotropic plane is considered. A new technique is presented for modelling the elastic constants of cracked structures with application to systems with weak concentrations of paralle.
Elastic moduli definition of elastic moduli by the free. Explicit bounds on elastic moduli of solids containing. The idea of the approach is to use a generalized periodic structural model and to reduce model boundaryvalue problems formulated based on it to a system of linear algebraic equations. Stress is applied to force per unit area, and strain is proportional change in length.
The assumption that the voids can be represented by spheroids, which can account for a wide variety of pore shapes and are characterized by their aspect ratio, a, offers the possibility of an analytical. One of the ways to increase the resistance of a structure to catastrophic fracture is to force a main line crack to deviate from its path. Because elastic returns to its original length or shape after being stretched, it has numerous. At time t 0, the program automatically computes g 0 or k 0 from the elastic modulus and poissons ratio. Simulation of elastic moduli of porous materials crewes research report volume 2001 85 31 23 12 33 22 11 1 1 1 31 23 12 33 22 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1. There are two major theoretical approaches in the literature addressing the problem of. Elastic energy occurs when objects are impermanently compressed, stretched or generally deformed in any manner.
Dispersion and anisotropy of elastic waves in cracked. Finiteelement modeling of a damaged pipeline repaired using the wrap of a composite material. Elastic moduli of a cracked solid international journal. As a noun not to be confused with the adjective meaning springy or resilient, elastic refers to any textile cord, tape or fabric woven with strips of natural or synthetic rubber. In their model, solid grains and soft pores are assumed to make up a modified solid phase, while stiff pores are assumed to occupy the main pore space in which fluid pressure is. A sphereequivalency approach for calculating the elastic. Understanding motion simulation motion simulation provides complete, quantitative information about the kinematicsincluding position, velocity, and acceleration, and the dynamicsincluding joint reactions, inertial forces, and power requirements, of all the components of a moving mechanism. Elastic constants includes youngs modulus, shear modulus, poissons raito, bulk modulus, and lames constnat. Elastic modulus in the global x, y, and z directions. A sphereequivalency approach of elastic wave scattering was used to model the elastic moduli of an isotropic solid containing aligned cracks. General concepts are outlined for arbitrary cracks and explicit derivations together with numerical results are given for. There are two major theoretical approaches in the literature addressing the problem of effective elastic moduli of cracked rocks.
Dependence of a crack growth path on the elastic moduli of. Alternatively, elastic velocities can be measured and moduli extracted for zero porosity aggregates. Generalized kelvin model for microcracked viscoelastic materials. Elasticity theory primarily develops formalisms for the mechanics of solid bodies and materials. To incorporate the additional calculation of creep strain, use the check box in the material editor window and include the 4 required constants. An elastic modulus e can be determined for any solid material and represents a constant ratio of stress and strain a stiffness a material is elastic if it is able to return to its original shape or size immediately after being stretched or squeezed. To do so, the representative unit cell approach has been used. The elastic properties of cracked rocks depend on a number of factors.
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