Elastic, defined loading

Loads will generally fall into one of two categories, direcdy applied loads and strain-induced loads (Chapter 2. Isolator). Direcdy applied loads are usually easy to understand. They are defined loads that are applied to defined areas of the product, whether they are concentrated at a point, line, or boundary or distributed over an area. The magnitude and direction of these loads are known or can easily be determined. An example of a strain-induced load is when it is required that a product be deflected. The load developed is direcdy related to the strain that occurs. Unlike direcdy applied loads, strain-induced loads are dependent on the modulus of elasticity when comparing TPs with TSs, the TPs will generally decrease quicker in magnitude over time. Many assembly and thermal stresses could be the result of these strain-induced loads. 

When a fiber is stressed, the instantaneous elongation that occurs is defined as instantaneous elastic deformation. The subsequent delayed additional elongation that occurs with increasing time is creep deformation. Upon stress removal, the instantaneous recovery that occurs is called instantaneous elastic recovery and is approximately equal to the instantaneous elastic deformation. If the subsequent creep recovery is 100%, ie, equal to the creep deformation, the specimen exhibits primary creep only and is thus completely elastic. In such a case, the specimen has probably not been extended beyond its yield point. If after loading and load removal, the specimen fails to recover to its original length, the portion of creep deformation that is recoverable is still called primary creep the portion that is nonrecoverable is called secondary creep. This nonrecoverable elongation is typically called permanent set. 

Elastic Behavior. Elastic deformation is defined as the reversible deformation that occurs when a load is appHed. Most ceramics deform in a linear elastic fashion, ie, the amount of reversible deformation is a linear function of the appHed stress up to a certain stress level. If the appHed stress is increased any further the ceramic fractures catastrophically. This is in contrast to most metals which initially deform elastically and then begin to deform plastically. Plastic deformation allows stresses to be dissipated rather than building to the point where bonds break irreversibly. 

Fig. 2.5. The idealized elastic/perfectly plastic behavior results in a well defined, two-step wave form propagating in response to a loading within the elastic-plastic regime. Such behavior is seldom, if ever, observed.

For purposes of this specification, stresses in the individual members of a latticed or trussed structure resulting from elastic deformation and rigidity of joints are defined as secondary stresses. These secondary stresses may be taken to be the difference between stresses from an analysis assuming fully rigid joints, with loads applied only at the joints, and stresses from a similar analysis with pinned joints. Stresses arising from eccentric joint connections, or from transverse loading of members between joints, or from applied moments, must be considered primary stresses. 

Although hardness is a somewhat nebulous term, it can be defined in terms of the tensile modulus of elasticity. From a more practical side, it is usually characterized by a combination of three measurable parameters (1) scratch resistance (2) abrasion or mar resistance and (3) indentation under load. To measure scratch resistance or hardness, an approach is where a specimen is moved laterally under a loaded diamond point. The hardness value is expressed as the load divided by the width of the scratch. In other tests, especially in the paint industry, the surface is scratched with lead pencils of different hardnesses. The hardness of the surface is defined by the pencil hardness that first causes a visible scratch. Other tests include a sand-blast spray evaluation. 

The two mechanical properties measured most frequently using indentation techniques are the hardness, H, and the elastic modulus, E. A t5pical load-displacement curve of an elastic-plastic sample during and after indentation is presented in Fig. 30, which also serves to define some of the experimental quantities involved in the measurement. 

Tensile stress-strain tests give another elastic constant, called Poisson s ratio, v. Poisson s ratio is defined for very small elongations as the decrease in width of the specimen per unit initial width divided by the increase in. length per unit initial length on the application of a tensile load ... 

Since all practical methods of measuring the hardness of mbber involve measuring the resistance to indentation, hardness may be defined simply as resistance to indentation . Hardness is an expression of the elastic modulus of the mbber. More specifically, the load required to press a ball of given diameter to a given depth into the mbber is proportional to its elastic modulus. See Hardness Testing, Pusey and Jones Plastometer, Microhardness Testing. 

Concret does not have well defined elastic and plastic regions due to its brittle nature. A maximum compressive stress value is reached at relatively low strains and is maintained for small deformations until crushing occurs. The stress-strain relationship for concrete is a nonlinear curve. Thus, the elastic modulus varies continuously with strain. The secant modulus at service load is normally used to define a single value for the modulus of elasticity. This procedure is given in most concrete texts. Masonry lias a stress-strain diagram similar to concrete but is typically of lower compressive strength and modulus of elasticity. 

Stress-strain relationships for soil are difficult to model due to their complexity. In normal practice, response of soil consists of analyzing compression and shear stresses produced by the structure, applied as static loads. Change in soil strength with deformation is usually disregarded. Clay soils will exhibit some elastic response and are capable of absorbing blast-energy however, there may be insufficient test data to define this response quantitatively. Soil has a very low tensile capacity thus the stress-strain relationship is radically different in the tension region than in compression. 

Fig. 14. One-dimensional cross section of an elliptic weighting filter. The characteristic length is defined as the section length when the relative weight has dropped to 2/a. The filter shape corresponds to the deformation profile of an elastic material under distributed load in a circle of radius Z./2.

Load Sharing of Filler Particles. Comparison of ultimate strength of a propellant and its unfilled binder matrix almost always shows that the propellant has up to several times the tensile strength of the matrix. This filler reinforcement is presently thought to stem from additional crosslinks formed between filler particles and the network chains of the binder matrix (5, 8, 9, 34). Effective network chains are defined as the chain segments between crosslinks. From the classical theory of elasticity, the strength and/or modulus of an elastomer is proportional to the number of effective network chains per unit volume, N, or... 

An elastic field, although complex, remains well defined up to critical loading, at which point a cone-shaped crack suddenly develops in the sample. Cracking always starts just beyond the contact edge where surface defects occur and where the stress is highest. 

Although in practice the formation of inner cracks requires a certain threshold loading, for most brittle ceramic materials this threshold is negligibly small (usually less than 1 newton, seen clearly in hardness tests). It is thought that cracks make well defined spheres entirely beneath the contact zone, and that they grow downwards as the load is applied. Such a system presents a complicated elastic-plastic problem. 

The storage modulus is proportional to the amount of energy which is stored in the material elastically, whereas the loss modulus corresponds to the energy that is dissipated during one load cycle. Both quantities are combined in the damping factor tan 8 which is defined as... 

With the second category of hardness tests the measurement is carried out after the load is removed. This is the case with Rockwell R, S, V. L, M and P under a small prestress the position of the sphere is measured, so the permanent penetration depth, h (mm). The sphere diameter isy or j inch, the load is 60, 100 or 150 kg force, dependent on which of the six types of test is chosen. The hardness is defined as HR = 130 - hi0.002. This hardness value has no relation at all to the modulus of elasticity the permanent deformation after recovery is being measured (such a type of test would result in a very high value for rubbers ). 

Figure 7.2. Definitions of stress, strain, and modulus. Stress is defined as force per unit area, and strain is the change in length divided by the original length. When stress is plotted versus strain, then the slope is the modulus (A). When the load is removed, any strain remaining is called permanent or plastic deformation (B). When elastic materials are loaded, they are characterized by a constant strain as a function of time, whereas viscoelastic materials have strains that increase with time (C).

Extracellular matrices (ECM) are the primary structural materials found in connective tissue in vertebrates that serve to maintain tissue shape (skin), aid in locomotion (bone), transmit and absorb mechanical loads (tendon and ligament), prevent premature mechanical failure (tendon, ligament, skin, and blood vessel wall), partition cells and tissues into functional units (fascia), act as scaffolds that define tissue and organ architecture (organ parenchyma), act as storage devices for elastic energy (tendon and blood vessel wall), and as the substrate for cell adhesion, growth, and differentiation of a variety of cell types. 

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