Incremental analysis of large deflections of shells of revolution

Yaghmai, S.; Popov, Egor P.

doi:10.1016/0020-7683(71)90052-7

Cited by 35 publications

(6 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Eulerian formulation which is based on a mesh representing the current state of deformation has been used by Yaghmai and Popov [5]. In their presentations they derive equations from a current configuration version of the variational principle used in [4] and solve an elastic and an elastic-plastic problem.…”

mentioning

confidence: 99%

“…In their presentations they derive equations from a current configuration version of the variational principle used in [4] and solve an elastic and an elastic-plastic problem. Sharifi and Popov [6] extended the method of [5] to elastic-plastic analysis of infinitesimal strains but finite rotations, although they do not seem to consider the possibility that plastic deformation moduli may be of a size comparable to current stress levels. Another Eulerian formulation is due to Gunasekera and Alexander [7], who base their equations for a Prandtl-Reuss material on the principle of virtual work.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Finite-element formulations for problems of large elastic-plastic deformation

McMeeking

Rice

1975

International Journal of Solids and Structures

689

208

View full text Add to dashboard Cite

Abstract-An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is ideally suited to isotropically hardening Prandtl-Reuss materials. Further, the formulation is given in a manner which allows any conventions finite element program, for "small strain" elastic-plastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension.Tire paper closes with a unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures. Further, a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain, and the inadequacies of some of these are commented upon.

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Finite-element formulations for problems of large elastic-plastic deformation

McMeeking

Rice

1975

International Journal of Solids and Structures

689

208

View full text Add to dashboard Cite

show abstract

“…Incremental analysis of structures has long been used in the numerical analysis of "pathdependent" problems such as soil mechanics, plasticity, large (geometric) deformations, etc. [20][21][22][23][24][25]. In such frameworks, three configurations are considered in the deformation history, namely, reference configuration which is the original state at the beginning of the analysis, the current deformed configuration at time t + Δt, and the intermediate configuration at time t just before the deformed configuration.…”

Section: Introductionmentioning

confidence: 99%

ANN-aided incremental multiscale-remodelling-based finite strain poroelasticity

Dehghani

Zilian

2021

Comput Mech

View full text Add to dashboard Cite

Mechanical modelling of poroelastic media under finite strain is usually carried out via phenomenological models neglecting complex micro-macro scales interdependency. One reason is that the mathematical two-scale analysis is only straightforward assuming infinitesimal strain theory. Exploiting the potential of ANNs for fast and reliable upscaling and localisation procedures, we propose an incremental numerical approach that considers rearrangement of the cell properties based on its current deformation, which leads to the remodelling of the macroscopic model after each time increment. This computational framework is valid for finite strain and large deformation problems while it ensures infinitesimal strain increments within time steps. The full effects of the interdependency between the properties and response of macro and micro scales are considered for the first time providing more accurate predictive analysis of fluid-saturated porous media which is studied via a numerical consolidation example. Furthermore, the (nonlinear) deviation from Darcy’s law is captured in fluid filtration numerical analyses. Finally, the brain tissue mechanical response under uniaxial cyclic test is simulated and studied.

show abstract

“…Incremental analysis of structures has long been used in the numerical analysis of "path-dependent" problems such as soil mechanics, plasticity, large (geometric) deformations, etc. [20,21,22,23,24,25]. In such frameworks, three configurations are considered in the deformation history, namely, reference configuration which is the original state at the beginning of the analysis, the current deformed configuration at time t + ∆t, and the intermediate configuration at time t just before the deformed configuration.…”

Section: Introductionmentioning

confidence: 99%

ANN-aided incremental multiscale-remodelling-based finite strain poroelasticity

Dehghani,

Zilian

2021

Preprint

View full text Add to dashboard Cite

Mechanical modelling of poroelastic media under finite strain is usually carried out via phenomenological models neglecting complex micromacro scales interdependency. One reason is that the mathematical twoscale analysis is only straightforward assuming infinitesimal strain theory. Exploiting the potential of ANNs for fast and reliable upscaling and localisation procedures, we propose an incremental numerical approach that considers rearrangement of the cell properties based on its current deformation, which leads to the remodelling of the macroscopic model after each time increment. This computational framework is valid for finite strain and large deformation problems while it ensures infinitesimal strain increments within time steps. The full effects of the interdependency between the properties and response of macro and micro scales are considered for the first time providing more accurate predictive analysis of fluid-saturated porous media which is studied via a numerical consolidation example. Furthermore, the (nonlinear) deviation from Darcy's law is captured in fluid filtration numerical analyses. Finally, the brain tissue mechanical response under uniaxial cyclic test is simulated and studied.

show abstract

Incremental analysis of large deflections of shells of revolution

Cited by 35 publications

References 8 publications

Finite-element formulations for problems of large elastic-plastic deformation

Finite-element formulations for problems of large elastic-plastic deformation

ANN-aided incremental multiscale-remodelling-based finite strain poroelasticity

ANN-aided incremental multiscale-remodelling-based finite strain poroelasticity

Contact Info

Product

Resources

About