Viscoplastic-elastic model

Cao, B. and Campbell, G.A. (1990) Viscoplastic-elastic modeling of tubular blown film processing. AIChE J., 36, 420 30. 

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. 

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. 

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. 

Petrie and Ito (84) used numerical methods to analyze the dynamic deformation of axisymmetric cylindrical HDPE parisons and estimate final thickness. One of the early and important contributions to parison inflation simulation came from DeLorenzi et al. (85-89), who studied thermoforming and isothermal and nonisothermal parison inflation with both two- and three-dimensional formulation, using FEM with a hyperelastic, solidlike constitutive model. Hyperelastic constitutive models (i.e., models that account for the strains that go beyond the linear elastic into the nonlinear elastic region) were also used, among others, by Charrier (90) and by Marckmann et al. (91), who developed a three-dimensional dynamic FEM procedure using a nonlinear hyperelastic Mooney-Rivlin membrane, and who also used a viscoelastic model (92). However, as was pointed out by Laroche et al. (93), hyperelastic constitutive equations do not allow for time dependence and strain-rate dependence. Thus, their assumption of quasi-static equilibrium during parison inflation, and overpredicts stresses because they cannot account for stress relaxation furthermore, the solutions are prone to numerical instabilities. Hyperelastic models like viscoplastic models do allow for strain hardening, however, which is a very important element of the actual inflation process. 

The key point in the rheological classification of substances is the question as to whether the substance has a preferred shape or a natural state or not [19]. If the answer is yes, then this substance is said to be solid-shaped otherwise it is referred to as fluid-shaped [508]. The simplest model of a viscoelastic solid-shaped substance is the Kelvin body [396] or the Voigt body [508], which consists of a Hooke and a Newton body connected in parallel. This model describes deformations with time-lag and elastic aftereffects. A classical model of viscoplastic fluid-shaped substance is the Maxwell body [396], which consists of a Hooke and a Newton body connected in series and describes stress relaxation. 

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. 

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... 

The flow behavior of a vtscoplaslir fluid is identified by the. appearance of a yield Stress, i.e., the fluid flows in a viscous manner only after a threshold ha.s been exceeded. Below this threshold, or yield stress, the behavior of the fluid is similar to an elastic solid and should obey Eq. [4) when subjected to a strain or stress sweep. The simplest type of viscoplastic fluid is the so-called Bingham plastic, and its behavior can be expressed by means of the following mathematical model ... 

Hyperelastic models are often used to represent the behavior of crosslinked elastomers, where the viscoelastic response can sometimes be neglected compared with the nonlinear elastic response. Because UHMWPE behaves differently than do elastomers, there are only a few specific cases when a hyperelastic representation is appropriate for UHMWPE simulations. One such case is when the loading is purely monotonic and at one single loading rate. Under these conditions it is not possible to distinguish between nonlinear elastic and viscoplastic behavior, and a hyperelastic representation might be considered. Note that if a hyperelastic model is used in an attempt to capture the... 

The HM is a constitutive model aimed at predicting the large strain time-dependent behavior of both crosslinked and uncrosslinked UHMWPE. The kinematic framework used in the HM is based on a decomposition of the applied deformation gradient into elastic and viscoplastic components F = P... 

Results of the mechanical tests can be understood in terms of a physical model in which the stress is separated objectively into two distinct contributions an elastic-viscoplastic stress cr rising from bond-stretching in the hard phase, and a hyperelastic stress a. This separation has been carried out in the case of the EG-PEA... 

Belbachir, S., Zairi, F., Ayoub, G., Mascbke, U., Nait-Abdelaziz, M., Gloaguen, J.M., et al., 2010. Modelling of photodegradation effect on elastic-viscoplastic behavior of amorphous polylactic acid films. J. Mech. Phys. Solids 58, 241—255. 

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. 

Component B in Figure 35.16A was added to the model to incorporate time-dependent viscoplasticity in the back-stress network. The decomposition of the deformation gradient associated with this component, F, into elastic and viscoelastic deformation gradients (F =FdFd) allows... 

A key step in this procedure is prescribing the material or constitutive model, that is, the relationship between the stress the material experiences and the resulting deformation it undergoes. Conventional macro-scale finite element simulations assume that the material can be described by measurable macroscopic material properties. Typical examples for solids include materials that are modeled as elastic, viscoelastic, plastic, and viscoplastic. The presentation in this chapter will be confined to linear elastic materials. 

As law of mechanical behavior we use the viscoplastic model with internal variables of Chaboche [Chaboche, 1977 Lemaitre and Chaboche, 1988]. The strain is partitioned into an elastic and plastic part ... 

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