On the use of large time steps with an energy momentum conserving algorithm for non-linear hypoelastic constitutive models

A symmetric constitutive matrix for the non‐linear analysis of hypoelastic solids based on a formulation leading to a non‐symmetric stiffness matrix

“…Here, it was assumed that there is not a strain energy function and, hence, a rate-independent hypoelastic corotated Kirchhoff stress with large strains and displacement model, was adopted. Interest of this formulation remains [1][2][3][4][5] because it offers a straightforward extension of the small-strain plasticity theory, it is not restricted to isotropic materials and meets the frame indifference principle [6]. In contrast, this kind of model leads to a somewhat awkward implementation due to the appearance of non-symmetric matrices and deformation-dependent constitutive tensors.…”

An energy momentum conserving algorithm using the variational formulation of visco‐plastic updates

“…Reference [35]). It was also studied in the framework of consistent time algorithms for hyper-elastic based elasto-plastic models by Meng and Laursen [10], and in the framework of consistent time algorithms for hypo-elastic based elasto-plastic models by Noels et al [12] . In this paper we compare previous results with Figure 6.…”

“…In Reference [12], nodes belonging to the face z = 0 have no initial velocity to be able to verify the balance of the energy. In fact, if these nodes have an initial velocity, the constraints correspond to a modification of the boundary conditions, and therefore the sum of the kinetic energy and the work of internal forces does not remain constant.…”

Numerical Modelling of Contact Elastic-Plastic Flows

“…"Integration algorithm in plasticity have been introduced by Wilkins in the form of radial return algorithm with reference to the Mises criterion, and successively extended by Krieg and Key to the case of isotropic and kinematic hardering" Alfano et al [1]. We refer also to the works by Auricchio [3], Balagansky et al [5], Papadopoulos and Lu [49], Christensen [17], Düster and Rank [20], Howell and Ball [29], Mahnken [41], Parshikov and Medin [50], Rubin and Bodner [55], Le van et al [35], Noels et al [48], Balokhonov et al [6], Cherepanov [15], Fellows and Barton [21], Luccioni et al [39], Wallin and Ristnmaa [64], Kiselev and Kiselev [34], Ponthot [52], Bessette et al [10] and others.…”