Idealizing Material Response

Physically, constitutive equations represent various forms of idealized material response which serve as model of the behavior of actual substances. The predictive value of models, as assessed experimentally over particular ranges of physical conditions, affords justification for the special continuum mentioned above. 

Fig. 16. Response (strain) of different idealized materials to an instantaneous appHcation of a stress at time t = tg ( ) elastic, (b) viscous, and (c)...

It is instructive to describe elastic-plastic responses in terms of idealized behaviors. Generally, elastic-deformation models describe the solid as either linearly or nonlinearly elastic. The plastic deformation material models describe rate-independent behaviors in terms of either ideal plasticity, strainhardening plasticity, strain-softening plasticity, or as stress-history dependent, e.g. the Bauschinger effect [64J01, 91S01]. Rate-dependent descriptions are more physically realistic and are the basis for viscoplastic models. The degree of flexibility afforded elastic-plastic model development has typically led to descriptions of materials response that contain more adjustable parameters than can be independently verified. 

For an idealized material with a single absorption frequency, the connection between absorption spectrum and imaginary-frequency response looks like Fig. LI. 8. 

Several criteria define the ideal material for a cell transplantation matrix, (i) The material should be biocompatible, in the sense that it does not provoke a connective tissue response which will impair the function of the new tissue (ii) it should be resorbable, to leave a completely natural tissue replacement (this is important, because it could avoid some of the problems that occur in long-lasting polymers such as those used in breast implants) (iii) it should be processable into a variety of shapes and structures which retain their shape once implanted and (iv) the surface should interact with transplanted cells in a way which allows retention of differentiated cell function and which promotes cell growth if such growth is desired. 

A recently developed industrial-scale application is a textbook example of the main advantages of supercritical carbon dioxide in extractions from natural products. The Diamond process, jointly developed by the Centre d Energie Atomique and the French company Sabate, [2] extracts the contaminant trichloroanisol (TCA) from cork stoppers for wine bottles. This contaminant is produced by fungi and is responsible for the infamous cork taint taste of wines, which has brought serious financial losses to the wine industry and damaged the image of cork as the ideal material for bottle stoppers. 

The ideal elastie response is typified by the stress-strain behavior of a spring. A spring has a constant modulus that is independent of the strain rate or the speed of testing stress is a funetion of strain only. For the pure Hookean spring the inertial effects are neglected. For the ideal elastic material, the mechanical response is deseribed by Hooke s law ... 

PVDF is generally an ideal material for transducers operating at frequencies above 0.5 MHz in hydrophones and pulse echo probes for medical and nonmedical testing. A 64-element linear array transducer has been produced that, operating at 5 MHz, offers a wide-bandwidth pulse response, sharp ultrasonic field distribution, and a high energy conversion efficiency. 

We call the fields (3.114)-(3.116) fulfilling the balances of mass (3.63), (3.65), momentum (3.76), moment of momentum (3.93), and energy (3.107) a thermodynamic process, because only these are of practical interest. Then we denote the fields (3.114) as the thermokinetic process and the fields (3.115) as the responses (we limit to the models with symmetric T (3.93) in more general models we must introduce also the torque M into responses (3.115), cf. Rems. 17, 32). The fields (3.116) are controlled from the outside (at least in principle). Just constitutive equations, which express the difference among materials, represent the missing equations and are relations between (3.114) and (3.115) [6, 7, 9, 10, 23, 34, 38, 40, 41, 44, 45], Referring to Sect. 2.1 we briefiy recall that constitutive equations are definitions of ideal materials which approximate real materials in the circumstances studied (i.e at chosen time and space scales). Constitutive equations may be proposed in rational thermodynamics using the constitutive principles of determinism, local action, memory, equipresence, objectivity, symmetry, and admissibility. 

Creep rupture tests are used to measure the long-term response of a material to a continuously applied stress at a given temperature. The ideal material should be able to support significant stresses for extended periods of time without accumulated permanent strain or breakage. The SiOC-Nextel 312 BN 2-D composites were tested in limited stress... 

Although assumptions of ideal material properties such as linear elasticity and isotropy were considered during simulations of the 3D reconstructed microstructures, the isotropy of the actual microstructures remained questioned. One of the factors responsible for the fact that the microstructures of the films could not possibly be ideally isotropic was that the films experienced constrained sintering which induced greater lateral shrinkage/densification across the direction normal to the surface than that in the other two directions which might result in non-identical... 

An additional point of interest in cyclic straining was the MuUins effect. It was helpful to have a quantitative measure of how close the materials come to exhibiting an ideal Mullins response, as defined for example by Ogden et al (1999) [175, 296]. To this end we defined a Mullins factor M, such that an ideal Mullins response was characterized by M = 1 [175] ... 

The materials and structures associated with primary sensors contain dissipative, storage and inertial elements. These translate into the time derivatives appearing in the differential equation that models the sensor system. Hence another major defect is represented by the time (or frequency) response. The means to neutralise this imperfection involves filtering, which may be thought of in terms of pole-zero cancelation. If the device has a frequency response H s) then a cascaded filter of response G s) = 1/H s) will compensate for the non-ideal time response. The realisation of such a filter in analogue form presents a major obstacle that is greatly diminished in the digital case. 

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