Elastic strains

Elasticity is another manifestation of non-Newtonian behavior. Elastic Hquids resist stress and deform reversibly provided that the strain is not too large. The elastic modulus is the ratio of the stress to the strain. Elasticity can be characterized usiag transient measurements such as recoil when a spinning bob stops rotating, or by steady-state measurements such as normal stress ia rotating plates. 

In a tensile test, as the load increases, the specimen at first is strained elastically, that is reversibly. Above a limiting stress - the elastic limit - some of the strain is permanent this is plastic deformation. 

Important physical properties include the density, melt flow index, crystallinity, and average molecular weight. Mechanical properties of a polymer, such as modulus (the ratio of stress to strain), elasticity, and breaking strength, essentially follow from the physical properties. 

Tissue Maximum Strength (MPa) Maximum Strain (%) Elastic Modulus (MPa)... 

Mechanical Properties Stress-strain, Elasticity, DuctiUty Fatigue, Fracture, Creep Viscoelasticity, Elastomers Laminates Sutures, Bone, Teeth... 

In classical elasticity (small strains) W is a quadratic function of the coefficients of infinitesimal strain ey, whereas in large strain elasticity the relationship is not quadratic and W is then expressed as a polynomial in the strain coefficients or, as is usual in continuum mechanics, as a polynomial in the nine components of the deformation gra-... 

It is shown in works on large strain elasticity (Green and Adkins25) that when 0 is large there is a normal stress term proportional to 67. 

Our reason for stressing the concept of representative volume element is that it seems to provide a valuable dividing boundary between continuum theories and molecular or microscopic theories. For scales larger than the RVE we can use continuum mechanics (classical and large strain elasticity, linear and non-linear viscoelasticity) and derive from experiment useful and reproducible properties of the material as a whole and of the RVE in particular. Below the scale of the RVE we must consider the micromechanics if we can - which may still be analysable by continuum theories but which eventually must be studied by the consideration of the forces and displacements of polymer chains and their interactions. 

Since the stiffness of the bonds transfers to the stiffness of the whole filler network, the small strain elastic modulus of highly filled composites is expected to reflect the specific properties of the filler-filler bonds. In particular, the small strain modulus increases with decreasing gap size during heat treatment as observed in Fig. 32a. Furthermore, it exhibits the same temperature dependence as that of the bonds, i.e., the characteristic Arrhenius behavior typical for glassy polymers. Note however that the stiffness of the filler network is also strongly affected by its global structure on mesoscopic length scales. This will be considered in more detail in the next section. 

Accordingly, we expect a power law behavior G,0 (O/Op)3 5 of the small strain elastic modulus for 0>0. Thereby, the exponent (3+df [j)/(3—df)w3.5 reflects the characteristic structure of the fractal heterogeneity of the filler network, i.e., the CCA-clusters. The strong dependency of G 0 on the solid fraction Op of primary aggregates reflects the effect of structure on the storage modulus. 

Correlation function Elongational strain Strain rate Craze strain Elastic strain Shear strain Interfacial length Extension ratio... 

INTRODUCTION PRESSURE AND TEMPERATURE SPONTANEOUS STRAIN Experimental methods Fitting high-pressure lattice parameters Calculating strains ELASTICITY OTHER TECHNIQUES ACKNOWLEDGMENTS APPENDIX... 

If a crystal is subjected to small strain elastic deformation it is convenient to imagine the energetics of the strained solid in terms of the linear theory of elasticity. As we noted in chap. 2, the stored strain energy may be captured via the elastic strain energy density which in this context is a strictly local quantity of the form... 

The equilibrium small-strain elastic behavior of an "incompressible" rubbery network polymer can be specified by a single number—either the shear modulus or the Young s modulus (which for an incompressible elastomer is equal to 3. This modulus being known, the stress-strain behavior in uniaxial tension, biaxial tension, shear, or compression can be calculated in a simple manner. (If compressibility is taken into account, two moduli are required and the bulk modulus. ) The relation between elastic properties and molecular architecture becomes a simple relation between two numbers the shear modulus and the cross-link density (or the... 

Alternative compressive loading and load removal indicates nearly complete recovery from strain, as long as the original strain is below the yield strain elastic range. PTFE does not experience work hardening. ... 

R.HEOLOGY IS THE STUDY OF THE RESPONSE OF MATERIALS to an applied shear stress or strain (I). In other words, rheology is a science of deformation (a typical response of solids to an applied strain, elasticity) and flow (a typical response of a fluid to an applied shear, viscosity). Sometimes, the methods that impose a strain are classified as the plasticity approach, whereas the methods that apply shear rates or shear stresses are termed the rheological approach (2). In this review, we focus on the rheological approach, whereas the plasticity approach is dealt with only briefly. 

Figure 2. Three main stages of the ion explosion spike according to Fleischer et al. (1975). (a) The highly charged fission fragment ionizes lattice atoms along its trajectory, (b) Electrostatic repulsion causes displacement of lattice atoms along fragment path, (c) The matrix is strained elastically in proximity to defects and defect clusters. Some relaxation occurs in the lattice.

Specimen ID. Yield Strength (MPa) Yield Strain Offset (%) Yield Strength (MPa) Yield Strain Tensile Strength (MPa) Rupture Strain Elastic Modulus (MPa)... 

Yield Yield Tensile Rupture Strain Elastic... 

Conflicting data exist on the creep behavior of latex-modified mortar and concrete. The creep characteristics of SBR- and PAE-modified concretes reported by Ohamal l are represented in Fig. 4.40. Like ordinary cement concrete, the relationships between loading time (t) and creep strain (ec) or creep coefficient (< )) (i.e., creq) strain/elastic strain ratio) of the latex-modified concretes fit approximately the expression ... 

Some fracture mechanics jargon can be confusing, because similar expressions have different meanings elsewhere in mechanics. In Appendix C, plane strain elastic deformation means that the non-zero strains (in a pipe wall) occur in one plane. In plane strain fracture, the non-zero plastic strains in the yielded zone occur in thexy plane (Fig. 9.9a), that is perpendicular to the crack tip line. The strain e z = 0, so the sides of the specimen do not move inwards, and the fracture surface appears macroscopically flat. If a crack grows through a craze, a plane strain fracture will result. Voiding in the craze allows it to open, while the strain e z in the craze remains zero, and the surrounding material remains elastic. 

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