Stability and Nonlinear Solid Mechanics

By Q. Nguyen. 2000

242 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/fdaf96aee6c8e869bd731c11bf275c1405a0810b

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Citations in the corpus

On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers (2007, background): “Non-linear standard materials based on these two scalar functions cover a broad spectrum of constitutive models in finite elasticity, viscoelasticity, plasticity or damage mechanics, see for example, Biot [37], Ziegler [38], Germain [39], Halphen and Nguyen [40] and Nguyen [41].”
A discrete geometric approach for simulating the dynamics of thin viscous threads (2012, unknown): “The discretization of bending in elastic rods is routinely done using flexural springs at hinges [49], and the extension to viscous bending is straightforward.”
Strain‐driven homogenization of inelastic microstructures and composites based on an incremental variational formulation (2002, background): “Finite Element formulations in the large-strain context have recently been considered for example in References [18–20].”
The Variational Approach to Fracture (2008, background): “[87] – and we merely extend them to the setting of fracture.”
When and how do cracks propagate? (2009, background): “As far as brittle fracture is concerned, it can be arguably found in [18], although Nguyen was probably first and foremost in acknowledging and formally importing meta-stability into solid mechanics; see [24] for a review of his prior work.”
From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models (2013, background): “Such energetic formulations— first introduced by Nguyen (1987, 2000) and then justified by Marigo (1989, 2000) (see also DeSimone et al. (2001)) by thermodynamical arguments for a large class of rate independent behaviors— constitute a very promising way to treat in a unified framework the…”
The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models (2011, methodology): “Indeed, whatever the method used, as well that based on the loss of ellipticity (Hill, 1958) as that based on the loss of stability (Nguyen, 2000; Marigo, 2000), the conclusion is the same: the homogeneous response is not observable.”