Theoretical and computational issues in modelling material failure in strong discontinuity scenarios

OLIVER, J

doi:10.1016/s0045-7825(04)00117-3

Cited by 25 publications

(37 citation statements)

References 5 publications

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“…Becker used the Gurson constitutive model in combination with a failure criterion based on material stability and bifurcation in a finite element model to predict fracture and fragmentation in a dynamic expanding ring experiment. Oliver and Huespe provided closed‐form solutions for the detection of the singularity of the acoustic tensor for a wide class of small deformation isotropic and anisotropic damage models. On the basis of the general Hadamard instability criterion, Xue and Belytschko derived a closed‐form expression to determine the onset of instability and the bifurcation directions for a particular damage plasticity model.…”

Section: Introductionmentioning

confidence: 99%

A Cartesian parametrization for the numerical analysis of material instability

Mota

Chen

Foulk

et al. 2016

Numerical Meth Engineering

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SUMMARYWe examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. The performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.

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Section: Introductionmentioning

confidence: 99%

A Cartesian parametrization for the numerical analysis of material instability

Mota

Chen

Foulk

et al. 2016

Numerical Meth Engineering

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“…-where the involved entities (strains, stresses, displacements) can be non-smooth or even unbounded [18]. For these non-smooth problems, two options emerge:…”

Section: Introductionmentioning

confidence: 99%

“…In both scales, a continuum (stress-strain) constitutive relationship is considered, instead of the most common discrete traction/separation-law, this contributing to provide a unified setting for smooth and non-smooth problems. This is achieved by resorting to the well-established Continuum Strong Discontinuity Approach (CSDA) to material failure [28,29,18]. 3.…”

Section: Introductionmentioning

confidence: 99%

Continuum approach to computational multiscale modeling of propagating fracture

Oliver

Caicedo

Roubin

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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A new approach to two-scale modeling of propagating fracture, based on computational homogenization (FE2), is presented. The specific features of the approach are: a) a continuum setting for representation of the fracture at both scales based on the Continuum Strong Discontinuity Approach (CSDA), and b) the use, for the considered non-smooth (discontinuous) problem, of the same computational homogenization framework than for classical smooth cases. As a key issue, the approach retrieves a characteristic length computed at the lower scale, which is exported to the upper one and used therein as a regularization parameter for a propagating strong discontinuity kinematics. This guarantees the correct transfer of fracture energy between scales and the proper dissipation at the upper scale. Representative simulations show that the resulting formulation provides consistent results, which are objective with respect to, both, size and bias of the upper-scale mesh, and with respect to the size of the lower-scale RVE/failure cell, as well as the capability to model propagating cracks at the upper scale, in combination with crack-path-field and strain injection techniques. The continuum character of the approach confers to the formulation a minimal invasive character, with respect to standard procedures for multi-scale computational homogenization.Peer ReviewedPostprint (published version

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“…For the latter phase, it is possible to establish a strain equivalence with a strong discontinuity [11]; another method consists in computing a displacement jump by isolating the inelastic part if any of the strain tensor concurring to open the crack, so ignoring the elastic part released upon unloading [26]. In order to obtain the crack path, a method has recently been developed in [10], inspired by the Global Tracking Method used in [33,32]; the crack path is an isoline of a scalar field obtained from a secondary gradient problem. However, this method is, so far, limited to radial loading and mode I failure, since it is based on the assumption that, at the time the crack path is computed, the principal direction of the largest principal strain is perpendicular to the crack.…”

Section: Introductionmentioning

confidence: 99%