An alternative approach to finite deformation

In elastoplasticity formulation constitutive relations are usually given in rate form, i.e. they represent relations between stress rate and strain rate. The adopted constitutive laws have to stay independent in relation to the change of frame of reference, i.e. to stay objective. While the objectivity requirement in a material description is automatically satisfied, in an Eulerian description, especially in the case of large deformations, the objectivity requirement can be violated even for objective quantities. Thus, instead of a material time derivative in the Eulerian description objective time derivatives have to be implemented. In this work the importance of the objective rate implementation in the constitutive relations of finite elastoplasticity is clarified. Likewise, it shows the overview of the most frequently used objective rates nowadays, their advantages and shortcomings, as well as the distinctive features of the recently introduced logarithmic rate.

A generalised algorithm for anelastic processes in elastoplasticity and biomechanics

A computational algorithm for solving anelastic problems in finite deformations is introduced. The presented procedure, termed the Generalised Plasticity Algorithm (GPA) hereafter, takes inspiration from the Return Mapping Algorithm (RMA), which is typically employed to solve the Karush–Kuhn–Tucker (KKT) system arising in finite elastoplasticity, but aims to modify and extend the RMA to the case of more general flow rules and strain energy density functions as well as to non-classical formulations of elastoplasticity, in which the plastic variables are not treated as internal variables. To assess its reliability, the GPA is tested in two different contexts. First, it is used for solving two classical problems (a shear-compression test and the necking of a circular bar). In both cases, the GPA is compared with the RMA in terms of structural set-up, computational effort and flexibility, and its convergence is evaluated by solving several benchmarks. Some restrictions of the classical form of the RMA are pointed out, and it is shown how these can be overcome by adopting the proposed algorithm. Second, the GPA is applied to characterise the mechanical response of a biological tissue that undergoes large deformations and remodelling of its internal structure.

Modeling Tension-Compression Asymmetry of Shape Memory Alloys Based on Finite Elastoplasticity Model

A combined hardening J2-flow elastoplasticity model is proposed to model tension-compression asymmetry of shape memory alloys in a direct sense. Results show excellent accord with test data for realistic pseudo-elastic behavior.