Plastic response

The fact that shock waves continue to steepen until dissipative mechanisms take over means that entropy is generated by the conversion of mechanical energy to heat, so the process is irreversible. By contrast, in a fluid, rarefactions do not usually involve significant energy dissipation, so they can be regarded as reversible, or isentropic, processes. There are circumstances, however, such as in materials with elastic-plastic response, in which plastic deformation during the release process dissipates energy in an irreversible fashion, and the expansion wave is therefore not isentropic. 

For a given amplitude of the quasi-elastic release wave, the more the release wave approaches the ideal elastic-plastic response the greater the strength at pressure of the material. The lack of an ideally elastic-plastic release wave in copper appears to suggest a limited reversal component, however, this is much less than in the silicon bronze. Collectively, the differences in wave profiles between these two materials are consistent with a micro-structurally controlled Bauschinger component as supported by the shock-recovery results. Further study is required to quantify these findings and... 

D.E. Mikkola and R.N. Wright, Dislocation Generation and its Relation to the Dynamic Plastic Response of Shock Loaded Metals, in Shock Waves in Condensed Matter—1983 (edited by J.R. Asay, R.A. Graham, and G.K. Straub), Elsevier Science, New York, 1984, 415 pp. 

We imagine a finite-duration shock pulse arriving at some point in the material. The strain as a function of time is shown as the upper diagram in Fig. 7.11 for elastic-perfectly-plastic response (solid line) and quasi-elastic response generally observed (dash-dot line). The maximum volume strain = 1 - PoIp is designated... 

Figure 7.11. Quasi-elastic release (dash-dot line) from shock-compressed state. Solid line represents elastic-perfectly-plastic response.

According to the theory proposed by Maugis and Pollock, hereafter referred to as the MP model, if the adhesion induced stresses cause at least one of the contacting materials to yield and undergo a totally plastic response, the contact region formed will increase in size until the force causing the yielding is balanced... 

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. 

J. J. Gilman, The Plastic Response of Solids, in Dislocation Dynamics, Edited by A. R. Rosenfield, G. T. Hahn, A. L. Bement, and R. I. Jaffee, McGraw-Hill Book Company, New York, USA, p. 16 (1968). 

Biggs (Ref. 21) discusses responses of simple dynamic systems in great detail, including the important intermediate case of elastic, perfectly-plastic systems. He also presents dimensionless response curves for various levels of elastic-plastic response, and for several different regular pulse shapes. 

The primary failure mechanisms encountered in reinforced concrete buildings arc flexure, diagonal tension, and direct shear. Of these three mechanisms,. flexure is preferred under blast loading because an extended plastic response is provider prior to failure. To assure a ductile response, sections are designed so that the flexural capacity is less than the capacity of non-ductile mechanisms. 

Shear reinforcing is not commonly used in wall and roof elements even though reinforced elements can undergo an extended plastic response. Shear reinforcing increases the diagonal shear capacity of the member, but more importantly, it... 

Hajicek, J.D. The Automotive Challenge and Plastics Response, Conference Proceedings (1987) Detroit, November 2—4, 1987, The Society of Plastics Engineers, Brookfield Center CT, p. 120-122... 

Possible Roles of insoluble Carbohydrates in Texture Development. Based on data obtained frcm soy isolate-soy hull blend texturization experiments, insoluble carbohydrates and crude fiber play an important role in modulating the morphology of final texturized products (Figures 11-14). Insoluble carbohydrates, because of their plastic response to deformation, control the type of alveolation developed during processing. 

Evans, A.G. etal. (1978), Impact damage in brittle materials in the elastic-plastic response regime , Proc. R. Soc. London, Ser. A, 361, 343-65. 

In addition to the properties discussed above, there are several others whose determination would be of great use within a mesoscopic modeling framework. Among these are the melt curve TmeirTmeU(p), the temperature and pressure dependent specific heat, initial efforts towards understanding plastic response, and studies of solid-solid phase transitions. 

During neonatal development, the brain possesses the striking ability to transfer initially lost functions to new, unaffected cortical areas when irreversible lesions prohibit function of the original representation fields - an ability that is still to a lesser degree present in mature brain. This type of plastic response has been studied in rats with a well defined lesion of the somatosensory cortex that was induced 1 day after birth. Six months later functional MRI (fMRI) was performed with a forepaw stimulation paradigm when the animals showed no neurological... 

Fig. 5a,b Schematic representation of a the tip-sample contact upon high loading b the according compliance curve. In the case of perfectly plastic response the unloading curve is identical to the vertical line intersecting with the abscissa at hmax. In general, some viscoelastic recovery occurs and the residual impression depth hy is smaller than hmax. The difference hc—hy represents the extent of viscoelastic recovery. Ap and Ae denote the dissipated and the recovered work, respectively. Ap=0 for perfect elastic behaviour, whereas Ae=0 for perfect plastic behaviour. The viscoelastic-plastic properties of the material may be described by the parameter Ap(Ap+Ae) l. The contact strain increases with the attack angle 6. Adapted from [138]... 

For VVVr<10 no modification is obtained. For VJV,=25, Vneg is approximately equal to Vpos. For higher modulation amplitudes Vpos is very much larger than Vneg. The elasto-plastic response of the sample can be described by means of the parameter... 

Since the force-displacement curve contains information about the whole indentation process, the elastic deformation of the sample can be measured and used to calculate the stiffness S=dFldh at h=hmax, where F is the force and h is the indentation. As already explained in Sect. 3.1.1., in order to relate the stiffness to the Young s modulus, it is necessary to make assumptions about the contact area. The depth of the permanent indentation (plastic deformation), i.e. the depth DFdi shown in Fig. 26b, and the maximum indentation (sum of the plastic and of the elastic deformation) can be used to calculate a parameter that describes the relative weight of the elastic and of the plastic response. 

Nicotiana Plastic Responses Induced By Herbivore Attack.208... 

Baker, W.E., The Elastic Plastic Response to Thin Spherical... 

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