Viscoplastic theory

In general, SMPF is perceived as a two-phase composite material with a crystalline phase mixed with an amorphous phase. A multiscale viscoplasticity theory is developed. The amorphous phase is modeled using the Boyce model, while the crystalline phase is modeled using the Hutchinson model. Under an isostrain assumption, the micromechanics approach is used to assemble the microscale RVE. The kinematic relation is used to link the micro-mechanics constitutive relation to the macroscopic constitutive law. The proposed theory takes into account the stress induced crystallization process and the initial morphological texture, while the polymeric texture is updated based on the apphed stresses. The related computational issue is discussed. The predictabihty of the model is vahdated by comparison wifli test results. It is expected that more accurate measurement of the stress and strain in the SMPF with large deformation may further enhance the predictability of the developed model. It is also desired to reduce the number of material parameters in the model. In other words, a deeper understanding and physics based theoretical modeling are needed. 

Li, G. and Shojaei, A. (2012) A viscoplastic theory of shape memory polymer fibers with application to self-healing materials. Proceedings of the Royal Society A - Mathematical Physical and Engineering Sciences, 468, 2319-2346. 

In 1963 Nagdi and Murch published a paper entitled On the Mechanical Behavior of Viscoelastic-Plastic Solids just before Schapery first published his efforts on a thermodynamic approach to nonlinear viscoelasticity and prior to the development of early viscoplastity theories. Likely because both nonlinear viscoelasticity and/or viscoplasticity caught the attention of the technical community, Nagdi s work received little attention. However,... 

From the early work of Taylor [63T01] connecting dislocation behavior to observed viscoplastic shock-compression response, numerous studies have attempted to relate conventional dislocation dynamics models to experimental observations. Theory and observations consistently require unusually large numbers of mobile dislocations. Although qualitatively descriptive, progress to date on dislocation models has not proven to provide quantitative descriptions to the observations in metals. 

Viscoelasticity of metal This subject provides an introduction on the viscoelasticity of metals that has no bearing or relationship with viscoelastic properties of plastic materials. The aim is to have the reader recognize that the complex thermodynamic foundations of the theory of viscoplasticity exist with metals. There have been developments in the thermodynamic approach to combined treatment of rheologic and plastic phenomena and to construct a thermodynamic theory non-linear viscoplastic material that may be used to describe the behavior of metals under dynamic loads. 

Over the years, many empirical expressions have been proposed as a result of straightforward cmve fltting exercises. A model based on sound theory is yet to emerge. Three commonly used models for viscoplastic fluids are briefly described here. 

Voyiadjis, G.Z., Shojaei, A., and Li, G. (2012) A generalized coupled viscoplastic- viscodamage-viscohealing theory for glassy polymers. International Journal of Plasticity, 28, 21-45. 

The above mathematical models (and later derivatives) define constitutive relationships for the plastic strain regime and they all assume a linear elastic behavior terminated by a yield point that is rate dependent. Hence the yield surface of the material is rate dependent. Since the purpose of these models are to develop methods to calculate deformations which are rate dependent beyond the yield point of a material they are often referred to by the term viscoplasticity, (see Perzyna, (1980), Christescu, (1982)). This practice is analogous to referring to methods to calculate deformation beyond the yield point of an ideal rate independent elastic-plastic material as classical plasticity. However, more general theories of viscoplasticity have been developed in some of which no yield stress is necessary. See Bodner, (1975) and Lubliner, (1990) for examples. 

Perzyna, P., Modified Theory of Viscoplasticity Applications to Advanced Flow and Instability Phenomena , Arch. Mech. (Warsaw), 32, 3, 1980. 

The quantity a -f(e) on the left, the excess of stress over that obtaining at very slow strain rate, is termed the overstress theories formulated in this way are termed overstress theories. This approach has been applied to metals by Lui and Krempl [39], who used the term viscoplastic to categorise their model. From the form of Equation (11.8), it is clear that... 

The incremental theory of plasticity assumes that the strains depend on the entire history of loading. The total increments of deviatoric strain Asy is composed of a viscoplastic component... 

Although, for computational wear analyses purposes, the UHMWPE viscoelastic/viscoplastic deformations may play a very important role in the wear phenomenon, this type of behavior has been scarcely considered in the literature [139]. Moreover the crack initiation from a notch in UHMWPE is a complex phenomenon that is governed by the viscoelastic fracture theory [140]. In brief, the importance of considering the viscoelatic/viscoplastic behavior of UHMWPE for medical application has been further emphasized by recent research. 

The discussion that follows will be restricted to the field of infinitesimal strain theory for viscoelastic and viscoplastic solids. For the finite strain... 

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