Constitutive Equations for Elastic-Viscoplastic Strain-Hardening Materials

Abstract

A set of constitutive equations has been formulated to represent elastic-viscoplastic strain-hardening material behavior for large deformations and arbitrary loading histories. An essential feature of the formulation is that the total deformation rate is considered to be separable into elastic and inelastic components which are functions of state variables at all stages of loading and unloading. The theory, therefore, is independent of a yield criterion or loading and unloading conditions. The deformation rate components are determinable from the current state which permits an incremental formulation of problems. Strain hardening is considered in the equations by introducing plastic work as the representative state variable. The problem of tensile straining has been examined for a number of histories that included straining at various rates, rapid changes of strain rate, unloading and reloading, and stress relaxation. The calculations were based on material constants chosen to represent commercially pure titanium. The results are in good agreement with corresponding experiments on titanium specimens.

A Coupled Creep Plasticity Model for Residual Stress Relaxation of a Shot Peened Nickel-Base Superalloy

“…A number of modeling approaches have been developed to account for the combined contributions of plasticity and creep [18][19][20][25][26][27][28][29]. The trend has been to incorporate plasticity and creep into a single unified inelastic model.…”

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

“…Most of them were initially used for metals and then extended to polymers. In this category, the Perzyna viscoplasticity theory (Perzyna, 1971) can be used to model the rate-dependent behavior of polymers as demonstrated by Van Der Sluis et al (2001); Kim and Muliana (2010); Abu Al-Rub et al (2015); the viscoplastic theory based on the overstress (VBO) concept (Krempl et al, 1986) can be considered for polymers as shown by Colak (2005); the Bodner and Partom viscoplastic model (Bodner and Partom, 1975) can be applied to polymers as also shown by Frank and Brockman (2001); Zaïri et al (2008). The complex behavior of polymers can thus be captured using a viscoelastic-viscoplastic constitutive model with a robust integration algorithm to be implemented in finite element codes (Miled et al, 2011) by combining a viscoelastic constitutive model with a phenomenological-based viscoplastic one.…”

Analysis of shear bands in dynamic axisymmetric compression of a thermoviscoplastic cylinder

“…Batra [lo] proposed and used equation (4)* to study the steady-state axisymmetric deformations of a thermoviscoplastic target being penetrated by a fast moving rigid cylindrical rod, and it has been referred to as the Litonski-Batra flow rule. Batra and Jayachandran (111 have shown that the Litonski-Batra flow rule and those proposed by Bodner and Partom [12] and Brown et al [13], when calibrated against a hypothetical compression test and subsequently used to study the axisymmetric steady-state penetration problem, predict essentially identical patterns of target deformations. We note that Bell [14], Lin and Wagoner 1151, and Lindholm and Johnson [16] concluded from their test results that the flow stress decreases linearly with the temperature rise for the materials they tested.…”