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Hyperelastic Material
A hyperelastic or Green elastic materialR.W. Ogden, 1984, ''Non-Linear Elastic Deformations'', , Dover. is a type of constitutive model for ideally elastic material for which the stress–strain relationship derives from a strain energy density function. The hyperelastic material is a special case of a Cauchy elastic material. For many materials, linear elastic models do not accurately describe the observed material behaviour. The most common example of this kind of material is rubber, whose stress- strain relationship can be defined as non-linearly elastic, isotropic and incompressible. Hyperelasticity provides a means of modeling the stress–strain behavior of such materials. The behavior of unfilled, vulcanized elastomers often conforms closely to the hyperelastic ideal. Filled elastomers and biological tissues are also often modeled via the hyperelastic idealization. In addition to being used to model physical materials, hyperelastic materials are also used as ficti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gent (hyperelastic Model)
The Alan N. Gent, Gent hyperelastic material model is a phenomenological model of rubber elasticity that is based on the concept of limiting chain extensibility. In this model, the strain energy density function is designed such that it has a mathematical singularity, singularity when the first invariant of the left Cauchy-Green deformation tensor reaches a limiting value I_m. The strain energy density function for the Gent model is Gent, A.N., 1996, '' A new constitutive relation for rubber'', Rubber Chemistry Tech., 69, pp. 59-61. : W = -\cfrac \ln\left(1 - \cfrac\right) where \mu is the shear modulus and J_m = I_m -3. In the limit where J_m \rightarrow \infty, the Gent model reduces to the Neo-Hookean solid model. This can be seen by expressing the Gent model in the form : W =- \cfrac\ln\left[1 - (I_1-3)x\right] ~;~~ x := \cfrac A Taylor series expansion of \ln\left[1 - (I_1-3)x\right] around x = 0 and taking the limit as x\rightarrow 0 leads to : W = \cfrac (I_1-3 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arruda–Boyce Model
In continuum mechanics, an Arruda–Boyce model Arruda, E. M. and Boyce, M. C., 1993, A three-dimensional model for the large stretch behavior of rubber elastic materials,, J. Mech. Phys. Solids, 41(2), pp. 389–412. is a hyperelastic constitutive model used to describe the mechanical behavior of rubber and other polymeric substances. This model is based on the statistical mechanics of a material with a cubic representative volume element containing eight chains along the diagonal directions. The material is assumed to be incompressible. The model is named after Ellen Arruda and Mary Cunningham Boyce, who published it in 1993. The strain energy density function for the incompressible Arruda–Boyce model is given byBergstrom, J. S. and Boyce, M. C., 2001, Deformation of Elastomeric Networks: Relation between Molecular Level Deformation and Classical Statistical Mechanics Models of Rubber Elasticity, Macromolecules, 34 (3), pp 614–626, . : W = Nk_B\theta\sqrt\left beta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mooney–Rivlin Solid
In continuum mechanics, a Mooney–Rivlin solidMooney, M., 1940, ''A theory of large elastic deformation'', Journal of Applied Physics, 11(9), pp. 582–592.Rivlin, R. S., 1948, ''Large elastic deformations of isotropic materials. IV. Further developments of the general theory'', Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 241(835), pp. 379–397. is a hyperelastic material model where the strain energy density function W\, is a linear combination of two invariants of the left Cauchy–Green deformation tensor \boldsymbol. The model was proposed by Melvin Mooney in 1940 and expressed in terms of invariants by Ronald Rivlin in 1948. The strain energy density function for an incompressible Mooney–Rivlin material is :W = C_ (\bar_1-3) + C_ (\bar_2-3), \, where C_ and C_ are empirically determined material constants, and \bar I_1 and \bar I_2 are the first and the second invariant of \bar \boldsymbol B = (\det \bol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Drucker Stability
Drucker stability (also called the Drucker stability postulates) refers to a set of mathematical criteria that restrict the possible nonlinear stress- strain relations that can be satisfied by a solid material. The postulates are named after Daniel C. Drucker. A material that does not satisfy these criteria is often found to be unstable in the sense that application of a load to a material point can lead to arbitrary deformations at that material point unless an additional length or time scale is specified in the constitutive relations. The Drucker stability postulates are often invoked in nonlinear finite element analysis. Materials that satisfy these criteria are generally well-suited for numerical analysis, while materials that fail to satisfy this criterion are likely to present difficulties (i.e. non-uniqueness or singularity) during the solution process. Drucker's first stability criterion Drucker's first stability criterion (first proposed by Rodney Hill and also cal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Der Waals (hyperelatic Model)
Van der Waals or Van der Waal may refer to: People * Fransje van der Waals (born 1950), Dutch medical physician * Grace VanderWaal (born 2004), American singer-songwriter * Henk van der Waal (born 1960), Dutch poet * Joan van der Waals (1920–2022), Dutch physicist * Johannes Diderik van der Waals (1837–1923), Dutch physicist * (1912–1950), Dutch spy, in German service during World War II (see Dutch resistance) Physics There are a series of subjects named after Johannes Diderik van der Waals: * Van der Waals force * Van der Waals equation * Van der Waals molecule * Van der Waals radius * Van der Waals surface Other uses * Van der Waals (crater) Van der Waals is a Lunar craters, lunar impact crater on the Far side (Moon), far side of the Moon. It is a heavily eroded feature with an irregular outer rim. The edge is lowest along the southern side where it is little more than a circular cre ..., named after the physicist * Mona Vanderwaal, ''Pretty Little Liars'' charact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rubber Elasticity
Rubber elasticity is the ability of solid rubber to be stretched up to a factor of 10 from its original length, and return to close to its original length upon release. This process can be repeated many times with no apparent Material failure theory, degradation to the rubber. Rubber, like all materials, consists of Molecule, molecules. Rubber's Elasticity (physics), elasticity is produced by Molecular dynamics, molecular processes that occur due to its molecular structure. Rubber's molecules are Polymer, polymers, or large, chain-like molecules. Polymers are produced by a process called polymerization. This process builds polymers up by sequentially adding short molecular backbone units to the chain through Chemical reaction, chemical reactions. A rubber polymer follows a random winding path in three dimensions, intermingling with many other rubber polymers. Natural rubbers, such as polybutadiene and polyisoprene, are extracted from plants as a fluid colloid and then solidified ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marlow (hyperelastic Model)
Marlow may refer to: Places Australia *Marlow, New South Wales, a suburb on the Central Coast Germany *Marlow, Germany United Kingdom *Little Marlow, Buckinghamshire *Marlow, Buckinghamshire **Marlow Bridge, an old suspension bridge over the River Thames ** Marlow RUFC, a rugby union club in Buckinghamshire **Marlow F.C., a football club in Buckinghamshire **Marlow United F.C., a football club in Buckinghamshire **Marlow Regatta, an international rowing event ** Marlow Town Regatta and Festival, a local rowing event and festival *Marlow, Herefordshire United States *Marlow, Missouri *Marlow, New Hampshire *Marlow, Oklahoma *Marlow, Tennessee *Marlow Heights, Maryland Other uses * Marlow (surname), including list of persons and fictional characters with the name *Marlow Industries, an American electronics manufacturer *Marlow (TV series) See also *Marlowe (other) Marlowe may refer to: Name * Marlowe (name), including list of people and characters with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yeoh (hyperelastic Model)
image:Yeoh model comp.png, 300px, Yeoh model prediction versus experimental data for natural rubber. Model parameters and experimental data froPolymerFEM.com] The Yeoh hyperelastic material model is a phenomenological model for the deformation of nearly incompressible, nonlinear Elasticity (physics), elastic materials such as rubber. The model is based on Ronald Rivlin's observation that the elastic properties of rubber may be described using a strain energy density function which is a power series in the strain invariants I_1, I_2, I_3 of the Cauchy-Green deformation tensors. The Yeoh model for incompressible rubber is a function only of I_1. For compressible rubbers, a dependence on I_3 is added on. Since a polynomial form of the strain energy density function is used but all the three invariants of the left Cauchy-Green deformation tensor are not, the Yeoh model is also called the reduced polynomial model. Yeoh model for incompressible rubbers Strain energy density functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial (hyperelastic Model)
The polynomial hyperelastic material model is a phenomenological model of rubber elasticity. In this model, the strain energy density function is of the form of a polynomial in the two invariants I_1,I_2 of the left Cauchy-Green deformation tensor. The strain energy density function for the polynomial model is Rivlin, R. S. and Saunders, D. W., 1951, '' Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber.'' Phi. Trans. Royal Soc. London Series A, 243(865), pp. 251-288. : W = \sum_^n C_ (I_1 - 3)^i (I_2 - 3)^j where C_ are material constants and C_=0. For compressible materials, a dependence of volume is added : W = \sum_^n C_ (\bar_1 - 3)^i (\bar_2 - 3)^j + \sum_^m \frac(J-1)^ where : \begin \bar_1 & = J^~I_1 ~;~~ I_1 = \lambda_1^2 + \lambda_2 ^2+ \lambda_3 ^2 ~;~~ J = \det(\boldsymbol) \\ \bar_2 & = J^~I_2 ~;~~ I_2 = \lambda_1^2 \lambda_2^2 + \lambda_2^2 \lambda_3^2 + \lambda_3^2 \lambda_1^2 \end In the limit w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soft Tissue
Soft tissue connective tissue, connects and surrounds or supports internal organs and bones, and includes muscle, tendons, ligaments, Adipose tissue, fat, fibrous tissue, Lymphatic vessel, lymph and blood vessels, fasciae, and synovial membranes. Soft tissue is Tissue (biology), tissue in the body that is not hard tissue, hardened by the processes of ossification or calcification such as bones and teeth. It is sometimes defined by what it is not – such as "nonepithelial, extraskeletal mesenchyme exclusive of the reticuloendothelial system and glia". Composition The characteristic substances inside the extracellular matrix of soft tissue are the collagen, elastin and ground substance. Normally the soft tissue is very hydrated because of the ground substance. The fibroblasts are the most common cell responsible for the production of soft tissues' fibers and ground substance. Variations of fibroblasts, like chondroblasts, may also produce these substances. Mechanical character ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phenomenological Model
A phenomenological model is a scientific model that describes the empirical relationship of phenomena to each other, in a way which is consistent with fundamental theory, but is not directly derived from theory. In other words, a phenomenological model is not derived from first principles. A phenomenological model forgoes any attempt to explain why the variables interact the way they do, and simply attempts to describe the relationship, with the assumption that the relationship extends past the measured values. Regression analysis is sometimes used to create statistical models that serve as phenomenological models. Examples of use Phenomenological models have been characterized as being completely independent of theories, though many phenomenological models, while failing to be derivable from a theory, incorporate principles and laws associated with theories. The liquid drop model of the atomic nucleus, for instance, portrays the nucleus as a liquid drop and describes it as havin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
