Viscoplastic component

If we further denote the deformation gradient acting on the elastic-viscoplastic component by and the deformation gradient acting on the network orientation spring by F , the following constitutive relations are established [61] ... 

The nonequilibrium stress response acting on the elastic-viscoplastic component can be determined through the elastic contribution Fg. 

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... 

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. 

It is assumed that for each dynamic loading increment, the strain rate can be expressed as the sum of the elastic and viscoplastic components ... 

Where the subscripts e and vp denote the elastic and viscoplastic components,... 

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... 

Several constitutive forms were proposed to describe the viscoplastic term of Eq. 23.113 by various researchers. Among these, Sokolovsky (1948) used the assumption that the viscoplastic component is a function of the over-stress above the yield point. On the basis of... 

In this constitutive framework, the total deformation gradient F is decomposed into viscoplastic and viscoelastic components F = F F. The viscoelastic deformation gradient acts on both the equilibrium network A, and on the time-dependent network F = F = F. The Cauchy stress acting on network A is given by the eight-chain representa-... 

In addition, a time-dependent viscoelastic component described by the so-called Voigt-Kelvin configuration, i.e. the combination of spring E and damper Yf comes into action. Further, a viscoplastic flow component may exist, modelled by the damper of viscosity... 

The time-dependence of deformation renders the parameters measured in simple tensile tests (see section 3.2) much less important than they are in metals, for instance. Although they do describe the behaviour at short-termed loads, time-dependent parameters obtained, for example, from isochrones -have to be used to design polymer components. Viscoelastic and viscoplastic effects can be neglected only if strains and loading times both are small. 

Zhang, Qian, Dasgupta, Abhijit, and Haswell, Peter, Viscoplastic Constitutive Properties and Energy-Partitioning Model of Lead-Free Sn3.9AgO.6Cu Solder Alloy, Electronic Components and Technology Conference, 2003, pp. 1862-1868. 

The components of the viscoplastic strain rate are calculated using the above-mentioned plastic flow rule for rate-sensitive material ... 

The first component of the backstress network, A, controls the equihbrium behavior of the viscoplastic response and is dependent on F. The stress, T, acting on this component can be calculated by ... 

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... 

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