Return Mapping Algorithms (RMAs) for Two-Yield Surface Thermoviscoplastic Models Using the Consistent Tangent Operator

The return mapping algorithms (RMAs) presented here are designed for use with pressure-dependent thermoviscoplastic constitutive models involving irreversible effects associated with solid–solid phase transformations. During the volume solid–solid phase transformations occurring under mechanical loads, an “anomalous” plasticity, the so-called “TRansformation Induced Plasticity” (TRIP), is generated at much lower stress levels than those related to the yield stress of the material in the context of the classical plasticity. TRIP mechanisms are superimposed on the classical plasticity which is liable to occur in the case of metallic materials. Based on a non-standard generalized material framework, two different models are presented in which an “associative” plastic flow is introduced in the context of classical plasticity and a “non-associative” flow rule in the context of TRIP-like plasticity. In this paper, a complete algorithmic treatment of these two rate-dependent constitutive models is therefore proposed with the associated consistent tangent operator for dealing the quasi-surface irreversible solid–solid transformations which can appear in metal alloys during specific thermomechanical solicitations. The predictive abilities of the presented numerical procedure for modelling this kind of the irreversible solid–solid transformations involving two plasticity processes are tested and assessed by performing a two-dimensional finite-element analysis on some numerical examples.

An efficiency comparison of numerical implementation approaches of hyperelastic constitutive model in ABAQUS/Standard

The main goal of the article is to compare a computational efficiency of different implementation of a hyperelastic material model in the ABAQUS/Standard v. 6.14 [1]. The software offers basically two ways to proceed, namely UMAT and UHYPER user subroutines [2]. The procedures are employed to implement an isotropic, compressible neo-Hookean material model [3]. Corresponding stored-energy function, constitutive equations and the consistent tangent operator are presented. These are essential to program the subroutines. Some theoretical and numerical aspects of different implementation approaches are discussed. As examples, a tube under axial compression and a contact problem of disc are considered. On the basis of obtained results, selected aspects of computational efficiency and quality of solutions are compared.

Numerical Algorithms for J2 Viscoplastic Models

An algorithmic scheme is illustrated for the numerical integration of evolutive problems in viscoplasticity. The analysis is restricted for brevity to J2 models in viscoplasticity by presenting a unified treatment of different elasto/viscoplastic constitutive models. An appropriate consistent tangent operator is applied which is suitable to be adopted for general numerical schemes. The treatment can be applied to different constitutive models by simply specializing the flow function. Computational results and examples are also illustrated in order to show the effectiveness of the presented algorithmic procedure.

Computational Aspects in the Elasto/Viscoplastic Material Behavior of Solids

In the present paper a computational algorithmic procedure is presented for modeling the elasto/viscoplastic behavior of solid materials. The effects of different loading programs on the inelastic behavior of rate-sensitive materials are analyzed with specific numerical examples. An appropriate solution scheme and a consistent tangent operator are applied which are capable to be adopted for general computational procedures. Numerical computations and results are reported which illustrate the rate-dependence of the constitutive model in use.