Bifurcation of equilibrium solutions and defects nucleation

Stolz, Claude

doi:10.1007/s10704-007-9147-5

Cited by 12 publications

(3 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The conditions of stability and no-bifurcation can also be used to determine criterion of initiation of defect as pointed out in Refs. [22,23].…”

Section: Discussionmentioning

confidence: 99%

Stability and Bifurcation in Nonlinear Mechanics

Stolz

2023

Bifurcation Theory and Applications [Working Title]

Self Cite

View full text Add to dashboard Cite

Analysis of stability and bifurcation is studied in nonlinear mechanics with mechanisms of dissipation: plasticity, damage, fracture. With introduction of a set of internal variables, this framework allows a systematic description of the material behavior via two potentials: the free energy and the potential of dissipation. For standard generalized materials, internal state evolution is governed by a variational inequality depending on the mechanism of dissipation. This inequality is obtained through energetic considerations in an unified description based upon energy and driving forces associated with internal variable evolution. This formulation provides criterion for existence and uniqueness of the system evolution. Examples are presented for plasticity, fracture and damaged materials.

show abstract

“…The conditions of stability and no-bifurcation can also be used to determine criterion of initiation of defect as pointed out in Refs. [22,23].…”

Section: Discussionmentioning

confidence: 99%

Stability and Bifurcation in Nonlinear Mechanics

Stolz

2023

Bifurcation Theory and Applications [Working Title]

Self Cite

View full text Add to dashboard Cite

show abstract

“…Unless initiation of defects can be analysed as an equilibrium bifurcation based on evolution of infinitesimal defect and imperfection analysis [13], this approach does not unify initiation and propagation of defects using the same constitutive behaviour. In presence of a surface energy density β the analysis implies that the critical loading for initiation of defect becomes infinite in the case of spherical infinitesimal defect.…”

Section: Introductionmentioning

confidence: 99%

From Damage to Fracture, a Modelization Based on Moving Discontinuities and Layers

Stolz

2015

AMM

Self Cite

View full text Add to dashboard Cite

A damage modelization is proposed based on a continuous transition from undamaged to damaged material. The evolution of damage is associated with a moving layer of finite thickness $l_c$, then initiation and propagation of damage can be unified in the same constitutive law. The driving force associated to the layer motion is a generalized release rate of energy. Using a normality rule based on this force the solution of the rate boundary value problem of propagation and displacement satisfies a variational inequation. Applications of the model are proposed.

show abstract

“…Criteria of uniqueness and of stability of the propagation have been also established. In this approach, nucleation of defects can be considered as a bifurcation of equilibrium solution (Stolz 2007).…”

Section: Introductionmentioning

confidence: 99%

A new model of damage: a moving thick layer approach

Stolz

Moës

2012

Int J Fract

Self Cite

View full text Add to dashboard Cite

International audienceA new formulation of a damage law is proposed based on a continuous transition between a sound material and a totally or partially broken material. The evolution of damage is then associated with a moving layer. This point of view permits the description of initiation and propagation of defects in an unified framework. The motion of the thick layer is defined in the frame of the moving surface I" (o) separating the sound material and the damaged material. When the damage parameters are continuous functions of the distance to I" (o) , they satisfy the conditions of transport. For particular geometries and loadings the evolution of the system is discussed. Comparison with description of damage with discontinuities and sharp interface is also presented

show abstract

Bifurcation of equilibrium solutions and defects nucleation

Cited by 12 publications

References 4 publications

Stability and Bifurcation in Nonlinear Mechanics

Stability and Bifurcation in Nonlinear Mechanics

From Damage to Fracture, a Modelization Based on Moving Discontinuities and Layers

A new model of damage: a moving thick layer approach

Contact Info

Product

Resources

About