Strain memory

While shape (strain) memory has been traditionally used as a parameter to characterize shape memory capabilities of shape memory polymers, stress memory is more important for some... 

These functions are independent of the strain-memory function, and only kfc and Gfc can be determined from dynamic data of the viscoelastic moduli. As an example. 

The strain-memory function is derived from the first and second invariants of the Finger strain tensor. For simple shear flow, the strain-memory function is given as... 

In an inelastic, time-independent (Stokesian) fluid the extra stre.ss is considered to be a function of the in.stantaneous rate of defomiation (rate of strain). Therefore in this case the fluid does not retain any memory of the history of the deformation which it has experienced at previous stages of the flow. 

In Equation (1.28) function M(t - r ) is the time-dependent memory function of linear viscoelasticity, non-dimensional scalars 4>i and 4>2 and are the functions of the first invariant of Q(t - f ) and F, t t ), which are, respectively, the right Cauchy Green tensor and its inverse (called the Finger strain tensor) (Mitsoulis, 1990). The memory function is usually expressed as... 

This class of smart materials is the mechanical equivalent of electrostrictive and magnetostrictive materials. Elastorestrictive materials exhibit high hysteresis between strain and stress (14,15). This hysteresis can be caused by motion of ferroelastic domain walls. This behavior is more compHcated and complex near a martensitic phase transformation. At this transformation, both crystal stmctural changes iaduced by mechanical stress and by domain wall motion occur. Martensitic shape memory alloys have broad, diffuse phase transformations and coexisting high and low temperature phases. The domain wall movements disappear with fully transformation to the high temperature austentic (paraelastic) phase. 

Fig. 2. The shape-memory process, where Tis temperature, (a) The cycle where the parent phase undergoes a self-accommodating martensite transformation on cooling to the 24 variants of martensite. No macroscopic shape change occurs. The variants coalesce under stress to a single martensite variant, resulting in deformation. Then, upon heating, they revert back to the original austenite crystallographic orientation, and reverse transformation, undergoing complete recovery to complete the cycle, (b) Shape deformation. Strain recovery is typically ca 7%.

The design of smart materials and adaptive stmctures has required the development of constitutive equations that describe the temperature, stress, strain, and percentage of martensite volume transformation of a shape-memory alloy. These equations can be integrated with similar constitutive equations for composite materials to make possible the quantitative design of stmctures having embedded sensors and actuators for vibration control. The constitutive equations for one-dimensional systems as well as a three-dimensional representation have been developed (7). 

Here t has no memory of the rate of deformation in getting to the final plastic strain y. This differs from a path-dependent law, in which the strength (for example) depends in detail on the path followed in getting to the current macroscale state. 

Actually, some fluids and solids have both elastic (solid) properties and viscous (fluid) properties. These are said to be viscoelastic and are most notably materials composed of high polymers. The complete description of the rheological properties of these materials may involve a function relating the stress and strain as well as derivatives or integrals of these with respect to time. Because the elastic properties of these materials (both fluids and solids) impart memory to the material (as described previously), which results in a tendency to recover to a preferred state upon the removal of the force (stress), they are often termed memory materials and exhibit time-dependent properties. 

The effects of Pb on the mixed lymphocyte response (MLR) have been examined in prior studies. McCabe and colleagues [53] and Farrer and colleagues [54] demonstrated that Pb in vitro at very low concentrations (0.1 pM = 2 pg/dL) significantly enhanced the proliferation and expansion of murine alloreactive CD4+ T lymphocytes in the MLR. The expanded T cell population was found to have a high density of CD4 molecules on the cell surface making them phenotypically similar to memory/effector T lymphocytes. In a study using Lewis strain rats, Razani-Boroujerdi and coworkers [55] also found evidence for Pb-induced stimulation of the in vitro MLR. 

As the digging task relies upon external motivation, investigators should be careful not to misinterpret the results. For example, if different strains of mice spend different amounts of time digging in the CS+ during the test phase of the experiment, this should not be interpreted to mean that one strain has learned more than another strain (Schellinck et al. 2001). It is possible that the different strains are more sensitive to food restriction, however mild, or have different levels of activity. Both factors could lead to increased digging. With this caveat, the task is very useful for assessing acuity and long-term memory. 

Cyclic strain limit, of shape-memory alloys, 22 345... 

Cyclic stresses/strains, 13 481-483 Cyclic stress-strain curves, 13 491 Cyclic structures, nonaromatic, 15 5 Cyclic thermomechanical characterization, of shape-memory polymers, 22 358-362 Cyclic trimer ketone peroxides, 14 292 Cyclic trioxides, 18 448 Cyclic voltammetry, 9 580 Cyclitols, 4 710 Cyclization(s)... 

Strained silicon wafers, in scaling to deep submicron dimensions, 22 256 Strainers, in refrigeration systems, 27 539 Strain fixity rate (R ), in testing shape-memory polymers, 22 361... 

Strain hardening effect, 20 224 Straining efficiency, 77 340 Strain rate, 73 473 Strain recovery rate (Rr), in testing shape-memory polymers, 22 361 Strain sensors, 77 150, 151-152 Strain tensor, for noncentrosymmetry pont group crystals, 77 93-94 Strain versus time curve factors affecting, 73 473 material and microstructure effect on, 73 473-474... 

Finally it is worth noting an alternate form for the stress dependence of a series of strains. Some microstructural models utilise the memory function m t). This is the rate of change of the stress relaxation function ... 

The term y(t,t ) is the shear strain at time t relative to the strain at time t. The use of a memory function has been adopted in polymer modelling. For example this approach is used by Doi and Edwards11 to describe linear responses of solution polymers which they extended to non-linear viscoelastic responses in both shear and extension. 

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