Non‐Linear Finite Element Analysis of Solids and Structures

Borst, René de; Crisfield, M. A.; Remmers, Jjc Joris; Verhoosel, Clemens V.

doi:10.1002/9781118375938

Cited by 518 publications

(549 citation statements)

References 0 publications

Supporting

Mentioning

512

Contrasting

Unclassified

Order By: Relevance

“…Originally applied predominantly to geometrically non-linear behaviour of slender structures, it is nowadays applied in any situation where severe non-linearities play a role, including plasticity and damage, and concomitant strain localisation phenomena. The latter type of non-linearities are very demanding on the non-linear solver, and constraint equations originally used in arc-length methods proved not sufficiently robust [5,6,17].…”

Section: Discussionmentioning

confidence: 99%

A new arc-length control method based on the rates of the internal and the dissipated energy

May

Vignollet

Borst

2016

Engineering Computations

Self Cite

View full text Add to dashboard Cite

A new arc-length control method based on the rates of the internal and the dissipated energy AbstractPurpose:The purpose of this paper is to introduce a new arc-length control method for physically non-linear problems based on the rates of the internal and the dissipated energy. Design/methodology/approach: In this paper, the authors derive from the second law of thermodynamics the arc-length method based on the rate of the dissipated energy and from the time derivative of the energy density the arc-length method based on the rate of the internal energy. Findings:The method requires only two parameters and can automatically trace equilibrium paths which display multiple snap-back phenomena. Originality/value: A fully energy-based control procedure is developed, which facilitates switching between dissipative and non-dissipative arc-length control equations in a natural way.The method is applied to a plate with an eccentric hole using the phase field model for brittle fracture and to a perforated beam using interface elements with decohesion.

show abstract

Section: Discussionmentioning

confidence: 99%

A new arc-length control method based on the rates of the internal and the dissipated energy

May

Vignollet

Borst

2016

Engineering Computations

Self Cite

View full text Add to dashboard Cite

show abstract

“…The XFEM features used for this investigation are provided below in some detail. For a didactic overview of XFEM the interested reader is referred to [42,43]. The enrichment is basically an interpolation based on additional degrees of freedom to account for special features as crack discontinuity [44], see Equation 4, where x is a point within a FEM model and there is a discontinuity which is in a domain discretised into n number of finite elements.…”

Section: Extended Finite Element Methods Featuresmentioning

confidence: 99%

What triggers a microcrack in printed engineering parts produced by selective laser sintering on the first place?

et al. 2015

View full text Add to dashboard Cite

The proximity of un-melted particles within Selective Laser Sintered (SLS) printed engineering parts made of nylon-12 is found as a major triggering effect for cracking and ultimately failure. The numerical investigation, by means of the eXtended Finite Element Method (XFEM), was performed over samples with different arrangements of un-melted particles obtained experimentally . The onset and propagation of microcracks was simulated. This included inherently how the degree of particle melt (DPM) in SLS parts affects and controls both crack initiation and propagation. The results evidenced that a microcrack started invariably between the two closest un-melted particles in all numerical tests performed considering different arrangements of un-melted particles.

show abstract

“…The arrays a and d contain the discrete variables of the displacement and the phase field. In order to capture possible snapback behaviour, the finite element formulation can be augmented by an arc-length solver [39]. The resulting set of coupled, nonlinear equations is linearised and solved using a Newton-Raphson iterative scheme.…”

Section: Discrete Format Of Phase-field Models For Brittle Fracturementioning

confidence: 99%

Gradient damage vs phase-field approaches for fracture: Similarities and differences

Borst

Verhoosel

2016

Computer Methods in Applied Mechanics and Engineering

Self Cite

258

122

View full text Add to dashboard Cite

Non‐Linear Finite Element Analysis of Solids and Structures

Cited by 518 publications

References 0 publications

A new arc-length control method based on the rates of the internal and the dissipated energy

A new arc-length control method based on the rates of the internal and the dissipated energy

What triggers a microcrack in printed engineering parts produced by selective laser sintering on the first place?

Gradient damage vs phase-field approaches for fracture: Similarities and differences

Contact Info

Product

Resources

About