A strong discontinuity approach to crystal plasticity theory

Fohrmeister, Volker; Díaz, G.; Mosler, Jörn

doi:10.1002/pamm.201800295

Cited by 1 publication

(2 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, the key point is how to treat each

{\overset{ˇ}{\overset{ϕ}{true}}}^{β} th

optimally. For this, the classic Karush‐Kuhn‐Tucker (KKT) conditions are rewritten using the Fisher‐Burmeister (FB) equations 73,74 :

normalΔ {\overset{ˇ}{λ}}^{β} \geq 0; {\overset{ˇ}{\overset{ϕ}{true}}}_{n + 1}^{\overset{ˇ}{β}} goodbreak= \sqrt{{\overset{\overset{true¯}{ϕ}}{true}}^{β^{2}}_{n + 1} + normalΔ {\overset{ˇ}{λ}}_{n + 1}^{β^{2}}} goodbreak+ {\overset{ˇ}{\overset{ϕ}{true}}}_{n + 1}^{β} goodbreak- normalΔ {\overset{ˇ}{λ}}_{n + 1}^{β};

R_{{\overset{\overset{true¯}{ϕ}}{true}}^{\overset{ˇ}{β}}} ((),, normalΔ {\overset{ˇ}{λ}}^{1}, normalΔ {\overset{ˇ}{λ}}^{2} \dots normalΔ {\overset{ˇ}{λ}}^{n_{act}}) goodbreak= ([], \begin{array}{l} {\overset{ˇ}{\overset{ϕ}{true}}}^{\overset{ˇ}{1}} \\ {\overset{ˇ}{\overset{ϕ}{true}}}^{\overset{ˇ}{1}} \\ ⋮ {\overset{ˇ}{\overset{ϕ}{true}}}^{{\overset{n}{true}}_{act}} \end{array}) goodbreak= bold0

both loading and unloading conditions (either the classic KKT or FB) are equivalent. However, since the FB equation depends solely on

{\overset{ˇ}{\overset{ϕ}{true}}}^{\overset{ˇ}{β}}

, it ends up being more computationally efficient.…”

Section: Composite Model Integrationmentioning

confidence: 99%

See 1 more Smart Citation

Multi‐scale composite finite element modeling of three‐dimensional prestressed reinforced concrete structural members: Part I—A comprehensive framework

Díaz¹

2022

Civil Engineering Design

Self Cite

View full text Add to dashboard Cite

The goal of this work is to develop a complete theoretical framework for the numerical modeling of three‐dimensional prestressed reinforced concrete structural members, soil mixture, and their interactions. This numerical formulation is based on the construction of a new composite finite element, in order to tackle the multi‐scale problem. For this purpose, the mechanical behavior of each microstructure component material will be modeled as follows: (a) for the plain concrete (PC) and the soil mixture, an anisotropic‐damage‐elastoplastic model equipped with the strong discontinuity approach will be taken into account; (b) a polycrystal plasticity model, for the steel rebars and prestrssed tendons will be captured through a new strategy solution of discontinuous bifurcation problem, with the main objective to represent the multi‐cracking phenomenon; (c) regarding the mechanical behavior of the aggregates and rocks (skeleton—hydro mechanic problem) in the PC and soil mixture, respectively, an anisotropic‐damage‐double‐poro‐polycrystal plasticity model equipped with softening material will be considered. An advanced failure algorithm based on the marching tetrahedron and the pseudo‐termic problem will be developed. Finally, the zone that characterizes the interaction between the structural member and the soil mixture will be encrusted inside the composite finite element.

show abstract

“…Therefore, the key point is how to treat each

{\overset{ˇ}{\overset{ϕ}{true}}}^{β} th

optimally. For this, the classic Karush‐Kuhn‐Tucker (KKT) conditions are rewritten using the Fisher‐Burmeister (FB) equations 73,74 :

normalΔ {\overset{ˇ}{λ}}^{β} \geq 0; {\overset{ˇ}{\overset{ϕ}{true}}}_{n + 1}^{\overset{ˇ}{β}} goodbreak= \sqrt{{\overset{\overset{true¯}{ϕ}}{true}}^{β^{2}}_{n + 1} + normalΔ {\overset{ˇ}{λ}}_{n + 1}^{β^{2}}} goodbreak+ {\overset{ˇ}{\overset{ϕ}{true}}}_{n + 1}^{β} goodbreak- normalΔ {\overset{ˇ}{λ}}_{n + 1}^{β};

R_{{\overset{\overset{true¯}{ϕ}}{true}}^{\overset{ˇ}{β}}} ((),, normalΔ {\overset{ˇ}{λ}}^{1}, normalΔ {\overset{ˇ}{λ}}^{2} \dots normalΔ {\overset{ˇ}{λ}}^{n_{act}}) goodbreak= ([], \begin{array}{l} {\overset{ˇ}{\overset{ϕ}{true}}}^{\overset{ˇ}{1}} \\ {\overset{ˇ}{\overset{ϕ}{true}}}^{\overset{ˇ}{1}} \\ ⋮ {\overset{ˇ}{\overset{ϕ}{true}}}^{{\overset{n}{true}}_{act}} \end{array}) goodbreak= bold0

both loading and unloading conditions (either the classic KKT or FB) are equivalent. However, since the FB equation depends solely on

{\overset{ˇ}{\overset{ϕ}{true}}}^{\overset{ˇ}{β}}

, it ends up being more computationally efficient.…”

Section: Composite Model Integrationmentioning

confidence: 99%

“…Therefore, the key point is how to treat each ϕ β th optimally. For this, the classic Karush-Kuhn-Tucker (KKT) conditions are rewritten using the Fisher-Burmeister (FB) equations 73,74 :…”

Section: General Multisurface Crystal Plasticity Theorymentioning

confidence: 99%

Multi‐scale composite finite element modeling of three‐dimensional prestressed reinforced concrete structural members: Part I—A comprehensive framework

Díaz¹

2022

Civil Engineering Design

Self Cite

View full text Add to dashboard Cite

show abstract

A strong discontinuity approach to crystal plasticity theory

Cited by 1 publication

References 8 publications

Multi‐scale composite finite element modeling of three‐dimensional prestressed reinforced concrete structural members: Part I—A comprehensive framework

Multi‐scale composite finite element modeling of three‐dimensional prestressed reinforced concrete structural members: Part I—A comprehensive framework

Contact Info

Product

Resources

About