A total Lagrangian framework for simulation of powder compaction process based on a smooth three‐surface Cap model and a mesh‐free method

a b s t r a c tThis paper describes a constitutive law modeling isotropic polymeric foam materials. Focus has been placed on modeling the relative density dependency effect on polymeric foams subjected to large deformations using uniaxial and hydrostatic compressive hardening laws. The constitutive model is written in terms of the rotated Kirchhoff stress and of its conjugate logarithmic, or Hencky, strain measure. A numerical scheme for solving the constitutive model is described and implemented using both the finite element and the element-free Galerkin methods, in a Total Lagrangian finite strain framework. The imposition of the unilateral contact with friction and the essential boundary conditions are obtained by applying the Augmented Lagrangian method. Numerical examples are presented in order to attest the performance of the proposed constitutive model.

show abstract

“…For more details regarding the linearizations of Eqs. (29) and (30) one can refers to Rossi et al [23]. Moreover, the linearization of Eq.…”

Section: Frictionmentioning

confidence: 97%

“…Moreover, the linearization of Eq. (28) leads to the derivation of the so-called global material tangent modulus [23] which requires the derivation of the consistent tangent operator associated with the constitutive model proposed in Section 3.…”

Section: Frictionmentioning

confidence: 99%

Numerical modeling of large strain behavior of polymeric crushable foams

Machado

Alves

Rossi

et al. 2011

Applied Mathematical Modelling

View full text Add to dashboard Cite

show abstract

“…. A more detailed explanation about the derivation of each term described in this section, the discretization of the weak forms and an outline of the algorithm applied to impose the essential boundary and the contact with friction conditions can be seen in Rossi et al (2008).…”

Section: 24mentioning

confidence: 99%

An element‐free Galerkin method for metal forming simulations

Rossi

Alves²,

Al-Qureshi³

2009

Engineering Computations

Self Cite

View full text Add to dashboard Cite

Purpose -The purpose of this paper is to investigate the application of the element-free Galerkin (EFG) method to the simulation of metal forming processes and to propose a strategy to deal with volumetric locking problem in this context. Design/methodology/approach -The J 2 elastoplastic material model, employed in the work, assumes a multiplicative decomposition of the deformation gradient into an elastic and a plastic part and incorporates a non-linear isotropic hardening response. The constitutive model is written in terms of the rotated Kirchhoff stress and the logarithmic strain measure. A Total Lagrangian formulation of the problem is considered in order to improve the computational performance of the proposed algorithm. The imposition of the essential boundary conditions and also of the unilateral contact with friction condition are made by the application of the Augmented Lagrangian method. Here, aspects related to the volumetric locking are investigated and an F-bar approach is applied. Findings -The results show that the proposed approach presents no volumetric locking phenomenon when using the mean dilation approach. Moreover, differently from finite element approximations, no hour-glass instabilities in the deformation pattern are observed, avoiding in this way the need to devise additional stabilization procedures in the proposed procedure. Originality/value -This paper demonstrates the implementation and validation of the mean dilation approach, in the scope of the EFG, which was successful in coping with the volumetric locking phenomena and presented no hour-glass instabilities in the problem cases considered in this work.

show abstract