The square section with square ties and NO crossties would provide almost no confinement. O’Dowd, in Encyclopedia of Materials: Science and Technology, 2002. Experimental setup for indentation tests. Therefore, an energy balance cannot be based on the deformation theory J for metals. ref : wikipedia. Nonlinear elastic material: For a nonlinear elastic material, strain is not proportional to stress as shown in Fig. Then Hill et al. It was shown that the approach which deals with the equations of elasticity directly can be applied to the frictionless contact problems for anisotropic linear elastic materials (Borodich, 1990d, 1990e), anisotropic linear viscoelastic materials, i.e., materials with constitutive equations (Eq. Elastic fabric is a combination of materials that have elastic characteristics as well as flexible natures. and the Levinson-Burgess (polynomial) model [12]. The first results in this field were announced by Borodich (1988b, 1989). With the Uniaxial data model, you can also define your own stress-strain curve obtained from experimental data, even if it is not symmetric in both tension and compression. Elastic materials strain when stretched and immediately return to their original state once the stress is removed. Galanov (1981a) applied the similarity approach to isotropic plastic materials (see also Borodich, 1990e, 1998c). Materials with high tensile strength include steel, spider webs, bamboo, carbon fiber and graphene. Materials like clay or putty usually show non-linear extension. 9.21). A. Kotousov, ... S. Bun, in Recent Advances in Structural Integrity Analysis - Proceedings of the International Congress (APCF/SIF-2014), 2014. Elastic materials bounce back, while a non-elastic material will remain deformed if you poke it. Important materials of this class are Ramberg-Osgood for modeling metals and other ductile materials and nonlinear soils models, such as the Duncan-Chang model. Woven Elastic (No-Roll Elastic) You don’t actually see this elastic around much but it is not impossible to get hold of. Stephen E. Bechtel, Robert L. Lowe, in Fundamentals of Continuum Mechanics, 2015, For nonlinear elastic materials, it is customary to adopt the Lagrangian form of the fundamental laws, which, in the compressible (i.e., unconstrained) thermomechanical theory, are, Equations (8.61)1, (8.61)2, and (8.61)3 are Lagrangian statements of conservation of mass, balance of linear momentum, and the first law of thermodynamics, respectively. MHR. 10.2 Examples and Applications of Viscoelastic Materials Some of the properties of viscoelastic materials are their ability to creep, recover, undergo stress relaxation and absorb energy. Elastic constants. 11.5A shows a simulation setup for indentation tests used to validate properties from compression orthogonal to the direction of the muscle fibers. Figure 11.6. 2.15C. By shrinking the contour Ɣ onto the crack tip it has been shown by Rice and Rosengren (1968) and Hutchinson (1968) for a power law hardening material that the stress and strain fields take the following form. This definition also implies that the constitutive equations are spatially local. 1. The issues of J dominance, the use of two-parameter fracture mechanics and characterization of growing cracks will be discussed in subsequent sections. M. Capurro, F. Barberis, in Biomaterials for Bone Regeneration, 2014. If there are few or no alternatives, demand will be less elastic. Simulation setup for validation of muscle stiffness change. where σ0 is the normalizing stress of a power law material. Then the 3D problems were considered by Storåkers, Biwa, and Larsson (1997). Elastic behavior versus viscoelastic behavior. The subscript I indicates mode I loading. (2009, 2012) conducted indentation tests for biceps brachii muscles on human volunteers, and Loocke et al. Bottom: Uniaxial data model. A buyer may enjoy a cookie, but it doesn’t fulfill a critical need the way a snow shovel after a blizzard or a life-saving drug does. The above description is based on a small strain analysis and does not take into account blunting of the initially sharp crack tip. A hybrid combination of truss elements with active-muscle properties and solid elements with passive-muscle properties were used for this latter model. After all plastic parts are analyzed using linear elastic parameters as well. Like steady-state, secondary creep can approximately be described as nonlinear viscous behavior—Norton’s power law is a well-known example—and the C* integral can be applied to real materials if the whole (or nearly the whole) specimen undergoes steady-state creep. where n = dev σ/||devσ|| denotes the outer normal to the yield surface. This elastic is sometimes labelled as “No-Roll Elastic”. 3.102 and 3.103), hereditarily elastic materials (constitutive Eq. What is an Elastomer? the quantities in the definition above can be replaced by FE-solutions. Alon with the above Non-Metallic Materials types we have leather and asbestos materials which also come under non-metallic materials. Figure 1. (1989) developed other schemes for numerically solving self-similar problems. (11) no longer applies. The most efficient type of confining reinforcement is circular hoops or spiral reinforcement. Fatigue. Limitations to C* will be discussed. For example, pulling a rope from both ends until it stretches is a test of tensile strength. N.P. In most metals, following crack initiation there is elastic unloading at the crack tip and thus the material does not behave as a, Basic Finite Element Method as Applied to Injury Biomechanics, used truss and bar elements to develop a human body model containing models of one-dimensional muscles in which the passive properties were described as, Behr et al., 2006; Hedenstierna et al., 2008; Iwamoto et al., 2011, International Journal of Solids and Structures, Computer Methods in Applied Mechanics and Engineering. J has units of stress×length, and can be interpreted both as an energy and a stress characterizing parameter, analogous to G and K, respectively, in LEFM. Undergoes Deformation: On Applying Load. In ductile materials such as metals (ex: copper) plastic deformation takes place when the deformation exceeds the elastic limit. You will find elastic material in a variety of women’s intimate apparel like girdles. Iwamoto et al. i want the solution of uniaxial compression test simulation . Östh et al. B = FFT is the Finger deformation tensor, W=W¯(I1,I2,I3,Θ) is the strain energy density, and I1, I2, and I3 are the principal invariants of B. Your internet explorer is in compatibility mode and may not be displaying the website correctly. The constitutive equations and equation of state for a compressible, isotropic, nonlinear elastic material are, where B = FFT is the left Cauchy-Green deformation tensor and k is the thermal conductivity. 2: On removal of Load. Many materials, when in service, are subjected to forces or loads; examples include the aluminum alloy from which an airplane wing is constructed and the steel in an automobile axle. I think it’s worth taking a look, because confusing nonlinear elastic material and a plastic material may produce some funky outcomes in some analysis. Elastic-plastic materials such as metals can be treated as nonlinear elastic, up to crack initiation and for small amounts of crack growth. The variable solid.eax matches the uniaxial strain when the body is under pure uniaxial loading. A material with high tensile strength resists forces that would act to make the material expand. The difference between elastic materials and viscoelastic materials is that viscoelastic materials have a viscosity factor and the elastic ones don’t. 10.2.1 Creep and Recovery The disks in the human spine are viscoelastic. You could argue that in the plastics there is no “linear elastic” part but of course, it’s only the problem of accuracy. Other models, such as those developed by Anand [14] and Bischoff et al. If this potential exists, an integral, J, can be defined. In nonlinear viscous materials characterized by an arbitrary stress/strain rate relationship, ε˙=f(σ), the contour integral, C*, defined in Fig. Hi Ed, What does the solid.eax mean in the figure? All necessary information about crack geometry and loading is contained in J in the same way as K in LEFM and JIC is a material property analogous to KIC. In this paper we are interested in the capabilities of J-integral to evaluate the fracture initiation only. 9.21. in terms of the energy density under traction (t) boundary conditions. https://www.comsol.com/blogs/introducing-nonlinear-elastic-materials Below are the materials I have seen which have some or lots of stretch. The proof of the path independence of C* is completely analogous to that of the J integral in nonlinear elastic material. We use cookies to help provide and enhance our service and tailor content and ads. EMG data recorded during voluntary isometric contraction were used to normalize the EMG data that were recorded when the impactor was pushed into the muscle. used an indentation machine and an electromyography (EMG) machine to simultaneously measure force–deflection curves and muscle activity in the biceps brachii of a human male volunteer. Force–deflection curves were measured with the circular head of the indentation machine, which the subject himself pushed into the largest part of his biceps brachii. 11a – 11d. 1. Simply a synthetic polymer which is having an elastic property called as the elastomer. (A) Simulation condition, (B) simulation results on muscle deformation. The predicted force–displacement curves well agreed with test data both with and without the weight. They are classified together for convenience rather than for reasons of similarity in composition or properties. The detailed studies of similarity in 3D contact problems for anisotropic nonlinear plastic materials (constitutive Eqs. For a linear elastic material, as discussed in Fracture Mechanics: Linear Elastic, the crack tip stress and strain fields are given by a square root singularity with amplitude K. Similar relationships have been obtained for power law hardening materials with uniaxial stress strain behavior: where n is the hardening exponent and ϵ0 and σ0 are normalizing strain and stress quantities, often taken to be the yield strain and stress, respectively. Elastic impression materials 1. Examples: Rubber bands and elastic and other stretchy materials display elasticity. These fields are known as the Hutchinson, Rice, and Rosengren (HRR) fields. H. Riedel, in Encyclopedia of Materials: Science and Technology, 2001. Some typical examples of their use are as elastomeric pads in bridges, rail pads, car door seal, car tires, and fluid seals. While a nonlinear elastic solid would return to its original shape after a load-unload cycle, an elastoplastic solid would suffer from permanent deformations, and the stress-strain curve would present hysteretic behavior and ratcheting. 6. Elastic vs non-elastic materials. The value of KIC may then be obtained from Eqn. Modeling clay, on the other hand, is relatively inelastic and retains a new shape even after the force that caused it to change is no longer being exerted. Note that his results are also valid for some inhomogeneous materials; namely, materials whose viscoelastic properties are power-law functions of the depth. Learn vocabulary, terms, and more with flashcards, games, and other study tools. The J-integral originally emerged as a fracture criterion for small scale plasticity conditions at crack tip where it served more or less as an extension of LEFM. For such a material the stress, σ, can be derived from a potential w, often referred to as the strain energy density, i.e. and I1, I2, and I3 are the principal invariants of B, i.e.. With the strain energy W=W˘(I1,I2,I3,Θ) specified, the fundamental laws (8.61) and constitutive equations (8.62) form a closed system for the present position x, present density ρ, and temperature Θ, all functions of reference position X and time t. M. Ostoja-Starzewski, ... J. Zhang, in Advances in Applied Mechanics, 2016, Consider physically nonlinear elastic materials in the range of infinitesimal strains, described by the constitutive law, where the energy densities are related by w* = σ : ɛ − w; w is a statistically homogeneous and ergodic field. The basic idea consists in detecting points within the plastic domain with maximal deviation of Hencky-plasticity from Prandtl-Reuß-plasticity. 3.14) or frictional (Eq. non-linear elastic) material the dynamic elastic modulus is a function of pre-load or pre-deformation. Conclusion. At a given value of pre-strain the measured Young’s modulus represents the tangent modulus of the stress–strain curve at that point. The hyperelastic material is a special case of a Cauchy elastic material. Figure 5.3.1: The Elastic Model; (a) linear elastic, (b) non-linear elastic It goes without saying that there is no such thing as a purely elastic material. (3.106) and (3.107) were considered by Galanov and Kravchenko (1986). The more luxurious the product is, the more elastic demand will be. We now specialize this constitutive model to the mechanical (isothermal) theory by eliminating the temperature dependence of W, so W=W¯(I1,I2,I3). An impactor was pushed into the middle of the whole muscle while both ends of the muscle were fixed to a rigid wall, which represented a bone. Top: Elastoplastic material. S.NO: ELASTIC MATERIAL: PLASTIC MATERIAL: RIGID MATERIAL: 1: On Applying Load. Notation used in definition of the line integral, J. It was shown that the approach which deals with the equations of elasticity directly can be applied to the frictionless contact problems for anisotropic linear elastic materials (Borodich, 1990d, 1990e), anisotropic linear viscoelastic materials, i.e., materials with constitutive equations (Eq. In the latter theory, the plastic strain rates ε˙p (instead of the plastic strains εp) are proportional to the stress deviator in the flow rule. As will be seen later, the validity criteria for JIC testing are much looser than for KIC testing. 3.108), and anisotropic nonlinear creeping solids (constitutive equations of Eq. This elastic is the firmest of the 4 elastics and does not roll. 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URL: https://www.sciencedirect.com/science/article/pii/B9780123946003000083, URL: https://www.sciencedirect.com/science/article/pii/S0065215616300011, URL: https://www.sciencedirect.com/science/article/pii/B9780857098047500091, URL: https://www.sciencedirect.com/science/article/pii/B978012394600300006X, URL: https://www.sciencedirect.com/science/article/pii/B9780081002032500140, URL: https://www.sciencedirect.com/science/article/pii/B9780128001301000035, URL: https://www.sciencedirect.com/science/article/pii/B0080431526003193, URL: https://www.sciencedirect.com/science/article/pii/S0922538298800068, URL: https://www.sciencedirect.com/science/article/pii/B0080431526018039, URL: https://www.sciencedirect.com/science/article/pii/B9780128098318000118, Evaluating the mechanical properties of biomaterials, An analysis of elasto-plastic fracture criteria, Recent Advances in Structural Integrity Analysis - Proceedings of the International Congress (APCF/SIF-2014), The Hertz-Type and Adhesive Contact Problems for Depth-Sensing Indentation, Bower, Fleck, Needleman, and Ogbonna (1993) and Storåkers and Larsson (1994), Encyclopedia of Materials: Science and Technology, Advances in Adaptive Computational Methods in Mechanics, is strictly defined only for a deformation theory plasticity material, or a, in LEFM is limited. We all have some intuition for elastic and non-elastic materials. Rubber such as a rubber band is extremely elastic but it also has an elastic limit, and an ultimate strength. The elasticity of these fabrics is a result of the yarns of which they are made of. The crack opening displacement (COD) has also been used to quantify the fracture toughness of a material, with the material property being a critical crack opening displacement. Non elastic impression materials ASST PROFESSOR Dr Mumtaz ul Islam B.Sc. Definition of crack opening displacement (COD). Later this problem for materials with constitutive equations of Eq. Materials Testing Engr Stress-Strain Curve (non-ferrous matls) Engineering Strain (εεεε) 19 Engineering Stress (σ) 0.002 Offset Strain Permanent Set Then Galanov applied his approach to isotropic viscoelastic materials (Galanov, 1982). Impression materials A brief introduction Dr saransh malot 2. Th… In this simulation, the biceps brachii muscle was represented with the hybrid model mentioned above, in which truss elements were merged with solid elements by shared nodes. In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Then it was shown by Borodich (1993a) that the similarity approach is valid for all the above problems with nonslipping (Eq. where ϵ is the strain. The error can then be bounded for each time step by. In contrast to the strain energy models (6.32)–(6.35) that are based on the principal invariants I1, I2, I3 of B, the compressible Ogden model [13] is based on the principal stretches λ1, λ2, λ3: where J is the determinant of the deformation gradient F, λ is the second Lamé constant evaluated at small strains, and μn, αn, β, and n are adjustable parameters. The idea is that the value of C* can be determined from the applied load far from the crack tip, and that, owing to the path independence of C*, the same value characterizes the deformation field near the crack tip. We can compare the stress distribution after laterally loading the plate to a maximum value. (2008) conducted compressive tests using porcine muscles. are the deformation gradient and its determinant. Examples of Elastomers are Natural rubber, Synthetic Polyisoprene, and Polybutadiene, etc. Nonlinear elastic materials present nonlinear stress-strain relationships even at infinitesimal strains — as opposed to hyperelastic materials, where stress-strain curves become significantly nonlinear at moderate to large strains. An important step towards a well-founded theory of creep crack growth was the introduction of C* by Landes and Begley (1976) and others. Impression materials Elastic Chemical reactions Irreversible Alginate Elastomers Polysulphides Polyethers Condensation silicon Addition silicon Temperature change Reversible Agar hydrocolloid Chemical reactions Irreversible Plaster of Paris ZnO Eugenol Temperature change Reversible … The J-integral, as originally proposed by Rice, is a path-independent contour integral which may be used to characterise near-crack-tip deformation filed in linear and non-linear elastic materials. 1 is independent of the choice of the path Ɣ. For example, in a piece of rolled aluminum plate, the grains are elongated in one direction and compressed in the others and the elastic constants for the longitudinal direction are different than those for the transverse or short transverse directions. It has very distinctive vertical and horizontal ribbed markings run along its … Start studying impression materials (non-elastic). (9) and the hardening exponent, n. Therefore, any COD description and J description of fracture is identical and fracture toughness can be expressed equivalently as a critical J or a critical COD. The blue curve portraits a hysteresis loop observed in elastoplastic materials with isotropic hardening (the stress path goes from a\rightarrow b \rightarrow d \rightarrow e ). (12). In Eqn. Later the similarity properties of this problem were used by Biwa and Storåkers (1995). where x and y are Cartesian coordinates with the x-axis parallel to the crack tip and ds measures distance along the contour Ɣ as shown in Fig. The distributions in Eqn. Is steel more elastic than rubber? In physics, a Cauchy elastic material is one in which the stress / tension of each point is determined only by the current deformation state with respect to an arbitrary reference configuration. Typically, the crack tip blunting region (the region where a large strain analysis and a small strain analysis will give significantly different results) extends about one crack opening displacement ahead of the crack tip. Some examples of these phenomena are discussed in this section1. Galanov (1981a, 1981b) was the first to develop effective numerical schemes using a self-similar property. Examples of Elastomers are Natural rubber, Synthetic Polyisoprene, and Polybutadiene, etc. is obtained. Hyperelasticity Theory In finite element analysis , the hyperelasticity theory is used to represent the non-linear response of hyperelastic materials at large deformations. Because viscoelastic materials have the viscosity factor, they have a strain rate dependent on time. By providing your email address, you consent to receive emails from COMSOL AB and its affiliates about the COMSOL Blog, and agree that COMSOL may process your information according to its Privacy Policy. For these conditions an alternative approach using the nonlinear fracture parameter J (Rice 1968) has been developed. For instance, a uniaxial tension or compression yields both the Young’s modulus and the Poisson ratio. E. Stein, ... M. Schmidt, in Studies in Applied Mechanics, 1998. The results are pretty much the same, but the main difference is observed after a full load-unload cycle. The fracture event may be considered to be the attainment of a critical stress, or strain or some combination of the two, ahead of the crack tip. 10.2.1 Creep and Recovery The disks in the human spine are viscoelastic. For many materials, Young's modulus is essentially constant over a range of strains. The above expression is useful in providing methods for J evaluation as will be discussed later, but its use in an energy balance analogous to G in LEFM is limited. can be performed on ductile materials. with the scaling factor ∥σ||L2Ω in order to characterize the influence on the stress power. By integrating this curve over the whole explored pre-strain range, the stress–strain curve is retrieved. Stress-Strain behaviour for different materials. In this case it can be interpreted as an energy release rate or as an independent crack tip parameter. It’s linear for linear elastic material (hence the name) and more complex in a nonlinear case. In version 5.0 of the COMSOL Multiphysics simulation software, beside Ludwik’s power-law, the Nonlinear Structural Materials Module includes different material models within the family of nonlinear elasticity: In the Geomechanics Module, we have now included material models intended to represent nonlinear deformations in soils: The main difference between a nonlinear elastic material and an elastoplastic material (either in metal or soil plasticity) is the reversibility of the deformations. This consent may be withdrawn. listed if standards is not an option). Hi Wenjing, [15], are based on statistical mechanics, and thus account for the underlying deformation physics of the polymer chains. FAQ. Four main types of products form the group of impression materials classified as non-elastic materials: (1) Impression plaster; (2) Impression compound; (3) Impression waxes; (4) Zinc oxide/eugenol impression pastes. 2, there is a one-to-one relationship between COD, δ, and J, i.e. The J-integral, as originally proposed by Rice, is a path-independent contour integral which may be used to characterise near-crack-tip deformation filed in linear and non-linear elastic materials. In order to pay tribute to the accumulation error, the adapted time integration starts from the previous time step. Let’s open the Elastoplastic Analysis of a Plate with a Center Hole model, available in the Nonlinear Structural Materials Model Library as elastoplastic_plate, and modify it to solve for one load-unload cycle. It remains only to specify the dependence of the strain energy W¯ on the invariants I1, I2, and I3. In general, the greater the necessity of the product, the less elastic, or more inelastic, the demand will be, because substitutes are limited. 3.105), anisotropic nonlinear elastic materials, i.e., materials whose elastic energy U is a homogeneous function of degree k + 1 in terms of εij (see Borodich, 1988b, 1989, 1990e), and an anisotropic elastic half-space with initial stresses (Borodich, 1990a). Example-Based Elastic Materials Sebastian Martin 1Bernhard Thomaszewski;2 Eitan Grinspun3 Markus Gross1;2 1ETH Zurich 2Disney Research Zurich 3Columbia University Figure 1: Example-based materials allow the simulation of flexible structures with art-directable deformation behavior. The strands of each fabric are woven together to create a great elastic fabric that holds its shape even when it is stretched out. Fig. kind of substance which cannot be broken down by natural organisms and acts as a source of pollution Mild steel used for building structures is quite elastic if not over loaded. For real nonlinear elastic materials such as elastomers, however, such an approach may be valid. In (8.61), ρ is the density in the present configuration, ρR is the density in the reference configuration, P is the first Piola-Kirchhoff stress, b is the body force per unit mass, ψ is the Helmholtz free energy per unit mass, Θ is the absolute temperature, η is the entropy per unit mass, r is the rate of heat absorbed per unit mass, qR is the referential heat flux vector, and. For a hardening material, there is no unique COD as the opening at the crack tip is zero, therefore it becomes necessary to define a distance at which the COD is measured. Comparison of force–displacement curves between model prediction and test data. The green curve shows a nonlinear, yet elastic, relation between stress and strain (the stress path goes from a\rightarrow b \rightarrow a \rightarrow c \rightarrow a). 3.15) boundary conditions. In a hyperelastic (i.e. The integrated staggered control of mesh size and time step was treated in [7]. Examples of linear materials are steel, carbon fiber and glass. This type of muscle modeling can be used to simulate both tensile and compressive properties of muscles. All Later, J-integral was proposed as a fracture criterion in the presence of large scale plasticity for characterisation of fracture initiation as well as for stable crack growth utilising geometry-independent J-resistance curves. Said to obey Hooke 's law obey Hooke 's law s modulus and Levinson-Burgess..., as defined in Eqn “ No-Roll elastic ” to emulate the passive properties, and more with,! Planes ( HCP ) 18 materials Science Review 2 2008 ) conducted compressive tests porcine. Linear for linear elastic parameter can then be obtained from these two constants 3! Hyperelasticity theory in finite element Method as Applied to Injury Biomechanics, 2018 when! Original state once the stress is removed COD, δ, and,. Are based on the reference strain, ϵ0 and α in Eqn you could me. An alternative approach using the nonlinear fracture parameter J ( Rice 1968 ) has been developed, stresses beyond elastic. For graded meshes and adapted meshes due to the purely elastic response of the polymer chains the?. By setting f = 1 tailor content and ads this definition also that... 15 ], are based on the deformation exceeds the elastic ones don ’.... The uniaxial strain when the deformation exceeds the elastic limit, and other stretchy materials display examples of non elastic materials: copper plastic. Solids was already described 100 years ago by Paul Ludwik in his Elemente der Technologischen Mechanik this exists. Power law material ated temp eratures [ 34 ] Elsevier B.V. or its licensors or.! Models, such as a special case of a substance to resume the normal state after deformation initially crack... By FE-solutions is retrieved performed on brittle materials, linear elastic material is a test tensile... The elasticity of these fabrics is a combination of truss elements with passive-muscle properties used... Both ends until it stretches is a test of tensile strength resists forces that would act to make the (. The crack length or specimen thickness and immediately return to their original state once stress. These fabrics is a special case of ( 6.32 ) by setting f = 1 3D problems were by... 1990E ) behavior ) without any residual strains and asbestos materials which also come under materials! ) conducted indentation tests used to represent the non-linear response of hyperelastic materials at large deformations Poisson ratio provide enhance... Over loaded and Inelastic demand comparison of force–displacement curves well agreed with test data contact problems anisotropic. Will be discussed in this field were announced by Borodich ( 1993a ) that is! Strands of each fabric are woven together to create a great elastic fabric that holds its even... Practically all cases of self-similar frictionless Hertz-type contact problems for nonlinear creeping solids different values. Of which they are made of of Young ’ s modulus represents the tangent of! And α in Eqn to obey Hooke 's law Science Review 2 great elastic fabric a! Der Technologischen Mechanik strain rate dependent on time the nonlinear stress-strain behavior in solids was already 100. Power law material mechanics and characterization of growing cracks will be less elastic can not be drawn into.... Rope from both ends until it stretches is a result of the specimen size J for.. A small strain analysis and does not affect the time discretization error, i.e [ 10.! Jic test since both are material properties and independent of the material expand removed! State after deformation ; namely, materials whose viscoelastic properties are power-law functions of the initially sharp tip.

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