The past 20 years have seen substantial work on the modeling of ductile damage and fracture. Several factors explain this interest. (i) There is a growing demand to provide tools which allow to increase the efficiency of structures (reduce weight, increase service temperature or load, etc.) while keeping or increasing safety. This goal is indeed first achieved by using better materials but also by improving design tools. Better tools have been provided which consist (ii) of material constitutive equations integrating a physically-based description of damage processes and (iii) of better numerical tools which allow to use the improved constitutive equations in structural computations which become more and more realistic. This article reviews the material constitutive equations and computational tools, which have been recently developed to simulate ductile rupture.

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Continuum Models of Ductile Fracture: A Review

The past 20 years have seen substantial work on the modeling ofductile damage and fracture Several factors explain this interest (i) There is agrowing demand to provide tools which allow to increase the efficiency of structures(reduce weight, increase service temperature or load, etc) while keeping or increasingsafety This goal is indeed first achieved by using better materials but also byimproving design tools Better tools have been provided which consist (ii) of materialconstitutive equations integrating a physically-based description of damage processesand (iii) of better numerical tools which allow to use the improved constitutiveequations in structural computations which become more and more realistic Thisarticle reviews the material constitutive equations and computational tools, whichhave been recently developed to simulate ductile ruptureKEY WORDS: ductile rupture, models, numerical simulation INTRODUCTION P REDICTIVE NUMERICAL SIMULATIONS of ductile fracture may be ofgreat interest in industrial situations for which full-scale experimentalapproaches are either too costly or even impracticable This is the case ofductile tearing of gas pipelines over several hundred meters, of crackpropagation in large nuclear vessels or of ductile tearing of aircraft fuselageFor such applications, simulations should predict crack paths, stability,stress states, etc Several techniques may be used to achieve these objectivesThe approach based on Rice (1968) J-integral is widely used for industrialapplications but suffers from various limitations: (i) It can only deal withpreexisting cracks and cannot be applied to model crack initiation and pro-pagation from a notch (ii) It is not a material intrinsic property asit stronglydepends on specimen geometry as experimentally shown in Sumpter and

Thermo-Fluid Dynamics of Two-Phase Flow

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Validation of a two-fluid model on unsteady liquid–vapor water flows

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Pascal Galon

Papers

Numerical experiments using a HLLC-type scheme with ALE formulation for compressible two-phase flows five-equation models with phase transition

Numerical investigations of water-hammer with column-separation induced by vaporous cavitation using a one-dimensional Finite-Volume approach

Validation of a two-fluid model on unsteady liquid–vapor water flows

HLLC-type Riemann solver with approximated two-phase contact for the computation of the Baer-Nunziato two-fluid model

On the computation of the Baer-Nunziato model using ALE formulation with HLL- and HLLC-type solvers towards fluid-structure interactions