Modeling of finite strain viscoplasticity based on the logarithmic corotational description

Abstract

It has been proven that the deformation rate is identical to the logarithmic corotational rate of the spatial logarithmic strain. Based on the logarithmic corotational description we present an extension of a Chaboche's infinitesimal viscoplastic law for finite strain cases. An additive decomposition of the logarithmic corotational rate of the logarithmic strain, implicitly included in an internal dissipation inequality, is applied for the extension. Functionally, this additive decomposition corresponds to the additive decomposition of the material derivative of the logarithmic strain used in infinitesimal inelastic problems. Using the additive decomposition and replacing the material time derivatives of all second-order tensors in the infinitesimal viscoplastic law with the corresponding logarithmic corotational rates we arrive at a new finite viscoplastic law with nonlinear isotropic and kinematic hardening. The numerical algorithms suitable for the finite element implementation of this law are formulated and several numerical examples are presented. These numerical examples prove that the finite viscoplastic law and the algorithms are effective and reliable.

Frame indifferent elastoplasticity of frictional materials at finite strain

“…Large transformations of elasto-plastic materials has been the subject of an extensive research work to describe the behaviour of metals (Lin, 2002;Lin and Brocks, 2004;Lin et al, 2006b), polymers (Nedjar, 2001a,b;Wu et al, 2005), rubber-like materials (Reese and Wriggers, 1997), frictional materials (Betten, 1982;Callari et al, 1998;Meschke and Liu, 1999;Borja, 2004;Rouainia and Wood, 2006), etc. Most of these formulations are based on the pioneering numerical developments of Simo and Pister (1984), Simo and Ortiz (1985), Simo and Taylor (1985), Simo (1985Simo ( , 1988Simo ( , 1992, Amero and Simo (1993), etc.…”

Numerical Investigation into the Influence of Grain Orientation Distribution on the Local and Global Elastic-Plastic Behaviour of Polycrystalline Nickel-Based Superalloy INC-738 LC

“…The elastic constants for IN-738 LC [16] were linearly interpolated between the given temperatures of 800 • C and 898 • C to calculate the elastic constants at 850 • C, as given in Table 2. In order to model the plastic behaviour, IN-738 LC experimental tensile test data (for an assumed random orientation distribution) at 850 • C [24] were fitted and optimized against a model with sufficient amounts of grains for a strain rate of 0.001 s −1 . Figure 1 shows the experimental stress-strain data as well as the corresponding fitted elastic plastic material model.…”

Creep Mechanics

“…A lot of results have been published by PHILLIPS and WU (1973), CHABOCHE (1977), EISENBERG and YEN (1981), BODNER and PARTOM (1975), LIU and KREMPL (1979), KREMPL (1987), CRISTESCU andSULI-CIU (1982), SOBOTKA (1984), SKRZYPEK (1993), SHIN (1990), BETTEN and SHIN (1991;, HAUPT (2000), LIN, BETTEN and BROCKS (2006), to name just a few. A lot of results have been published by PHILLIPS and WU (1973), CHABOCHE (1977), EISENBERG and YEN (1981), BODNER and PARTOM (1975), LIU and KREMPL (1979), KREMPL (1987), CRISTESCU andSULI-CIU (1982), SOBOTKA (1984), SKRZYPEK (1993), SHIN (1990), BETTEN and SHIN (1991;, HAUPT (2000), LIN, BETTEN and BROCKS (2006), to name just a few.…”