Material models viscoplastic materials

Analytical viscoplastic solutions More accurate than elastic or viscoelastic for simple geometries. No standard solutions available. Requires some numerical analysis given complexity of material model. Some material testing may be required. 

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. 

Tanaka et al. (1971) have used a two-element mechanical model (Figure 8-32) to represent fats as viscoplastic materials. The model consists of a dashpot representing the viscous element in parallel with a friction element that represents the yield value. 

Figure 8-32 Mechanical Model for Foods as Viscoplastic Materials. Source From M. Tanaka, et al., Measurement of Textural Properties of Foods with a Constant Speed Cone Penetrometer, J. Texture Studies, Vol. 2, pp. 301-315, 1971.

A natural extension of linear elasticity is h rperelasticity.l l H rperelasticity is a collective term for a family of models that all have a strain energy density that only depends on the applied deformation state. This class of material models is characterized by a nonlinear elastic response, and does not capture yielding, viscoplasticity, or time-dependence. The strain energy density is the energy that is stored in the material as it is deformed, and is typically represented either in terms of invariants... 

Kletschkowski, T., Schomburg, U., and Bertram, A., Endochronic Viscoplastic Material Model for Filled VTTE, Mechanics of Materials, 34 795-808 (2002)... 

Kletschkowski T., U. Schomburg, and A. Bertram. 2002. Endochronic viscoplastic material models for filled PTFE. Mech Mater 34 795-808. 

Fig. 8.7. Mechanical models of viscoelastic and viscoplastic materials, built as systems containing spring and dashpot elements...

Ghoneim and Chen(33) developed a viscoelastic-viscoplastic law based on the assumption that the total strain rate tensor can be decomposed into a viscoelastic and a viscoplastic component. A linear viscoelasticity model is used in conjunction with a modified plasticity model in which hardening is assumed to be a function of viscoplastic strains as well as the total strain rate. The resulting finite-element algorithm is then used to analyze the strain rate and pressure effects on the mechanical behavior of a viscoelastic-viscoplastic material. 

Several models for viscoplastic materials are contained in the expression... 

For viscoplastic materials the rheograms (i.e. plots of shear stress x versus strain rate dU/dy) are very often approximated by the Bingham model, a straight line of the form... 

Perhaps the best picture of a viscoplastic fluid is that of a very viscous, even solidlike, material at low stresses. Over a narrow stress range, which can often be modeled as a single yield stress, its viscosity drops dramatically. This is shown clearly in Figure 2.5.5b, where viscosity drops over five decades as shear stress increases from 1 to 3 Pa. (The drop is even more dramatic in Figure 10.7.2.) Above this yield stress the fluid flows like a relatively low viscosity, even Newtonian, liquid. Because of the different behaviors exhibited by these fluids, the model (Bingham, Casson, etc.) and the range of shear rates used to calculate the parameters must be chosen carefully. In Section 10.7 we will discuss microstructural bases for r. It is also important to note that experimental problems like wall slip are particularly prevelant with viscoplastic materials. Aspects of slip are discussed in Section 5.3. 

Kletschkowski T, Schomburg U, Bertram A. Endochronic viscoplastic material models for filled FIFE. Mech Mater 2002 December 34(12) 795-808. 

For the simulation of isotropic thermoplastics elasto-viscoplastic material models are used. They are composed of an elastic part consisting of a constant Young s modulus and Poisson s ration and a plastic part being described by true stress/strain-curves depending on the true plastic strain-rate. As a failure criterion a maximal endurable hydrostatic stress, a critical equivalent plastic strain or a combination of these can be used. The strain criterion can also be set as a function of the strain-rate. 

Fiber-reinforced composite materials such as boron-epoxy and graphite-epoxy are usually treated as linear elastic materials because the essentially linear elastic fibers provide the majority of the strength and stiffness. Refinement of that approximation requires consideration of some form of plasticity, viscoelasticity, or both (viscoplasticity). Very little work has been done to implement those models or idealizations of composite material behavior in structural applications. 

We present a constitutive model for amorphous polymers in their glassy state (T < Tg) when no crazing takes place (like in shear or in compression). The formulation is supplemented with a simple description of the material response when the temperature gets higher than Tg, as found experimentally to occur at sufficiently high loading rates [2,3]. Therefore, two descriptions of the viscoplastic response of amorphous polymers are used, depending on the... 

Analytical models of pore collapse follow two approaches, termed hydrodynamic [162] or viscoplastic. In Mader s hydrodynamic model [162] (Fig. 17a), a steep planar shock front hits the upstream surface of an empty spherical pore of diameter d (for nanopores, gas inside the pore can be neglected [52,162]), it accelerating the free surface to velocity 2Up [5]. The pore s free surface undergoes hydrodynamic focusing [61,162]. A material spike strikes the downstream surface, causing impact heating. In molecular dynamics simulations, individual molecules from the upstream surface are observed to break off and strike the downstream surface [61,163]. The hydrodynamic time constant for pore collapse is approximately the material transit time across the pore. 

In the viscoplastic model of Carroll and Holt [49], later extended by Khasainov et al., [52] Butler et al., [158] and Frey [164] (Fig. 17b), pores in a viscous material collapse slowly behind the shock front via ID (radial) plastic deformation. Heating results from viscoplastic work. In the small Reynolds number limit (see below), the viscous time constant Xyis is independent of pore diameter [52] ... 

The DNF model incorporates the experimentally observed characteristics by using a micromechanism-inspired approach in which the material behavior is decomposed into a viscoplastic response, corresponding to irreversible molecular chain sliding due to the lack of chemical crosslinks in the material, and atime-dependent viscoelastic response. The viscoelastic response is further decomposed into the response of two molecular networks acting in parallel the first network (A) captures the equilibrium response and the second network (B) the time-dependent deviation from the viscoelastic equilibrium state. A onedimensional rheological representation of the model framework and a schematic illustrating the kinematics of deformation are shown in Fig. 11.6. 

This model allows for direct simulations of the viscoplastic flow and temperature behavior of the hose in the different loading scenarios. Material parameters for the DNF model were obtained from the literature and the tension tests described above. 

A comprehensive analytical model for predicting long term durability of resins and of fibre reinforced plastics (FRP) taking into account viscoelastic/viscoplastic creep, hygrothermal effects and the effects of physical and chemical aging on polymer response has been presented. An analytical tool consisting of a specialized test-bed finite element code, NOVA-3D, was used for the solution of complex stress analysis problems, including interactions between non-linear material constitutive behavior and environmental effects. 

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