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Elastic, perfectly plastic hollow sphere problem: a finite strain solution and energetic analysis

Zambelli S., Hild F., Trumel H., Roy G., Pellegrini Y. -P.

Foundations of Civil and Environmental Engineering

2010

No. 13

117--127

The growth of a void in a sphere of an elastic perfectly plastic material subjected to an external hydrostatic loading is modeled in the framework of irrotational finite strains. It is shown that, for small initial void volume fractions, the infinitesimal plastic strain hypothesis leads to a gross overestimation of the void growth kinetics. This assumption is relaxed in the present work, and the analytical results compare exactly with numerical simulations carried out with the commercial finite element code ABAQUS. A thermodynamic analysis is then performed, and will be considered as a basis for investigating thermal softening and micro-inertia effects on the damage process.

Damage modelling framework for viscoelastic particulate composites via a scale transition approach

Nadot C., Dragon A., Trumel H., Fanget A.

Journal of Theoretical and Applied Mechanics

2006

Vol. 44 nr 3

553-583

The aim of this paper is to pursue, in the wake of the work by Nadot-Martin et al. (2003), a non-classical micromechanical study and scale transition for highly filled particulate composites with viscoelastic matrices. The present extension of a morphology-based approach due to Christoffersen (1983), carried forward to the viscoelastic small strain context by Nadot-Martin et al. (2003), consists here in introducing a supplementary mechanism, namely damage by grain/matrix debonding. Displacement discontinuities (microcracks) on grain/matrix interfaces are first incorporated in a compatible way within geometric and kinematic hypotheses regarding the grains-and-layers assembly of Christoffersen. Then, local field expressions as well as homogenized stresses are established and discussed for a given state of damage (i.e. for a given actual number of open and closed microcracks) and using the hypothesis of no sliding on closed crack lips. A comparison with the results obtained for the sound viscoelastic composite by Nadot-Martin et al. (2003) allows to quantify the damage influence on local and global levels. At last, the basic formulation of the model obtained by scale transition is completed by the second stage leading to a thermodynamically consistent formulation eliminating some superfluous damaged-induced strain-like variables related to open cracks. This second stage is presented here for a simplified system where delayed (viscoelastic) effects are (tentatively) neglected. It appears as a preliminary and crucial step for further generalization in viscoelasticity.

Celem tej publikacji jest sformułowanie wieloskalowego modelu mikromechanicznego dla granulowanych kompozytów o wysokim stopniu upakowania inkluzji w osnowie lepkosprężystej. Przedstawiony model, będący rozwinięciem morfologicznego podejścia Christoffersena (1983) i Nadot-Martin i in. (2003) w zakresie małych odkształceń lepkosprężystych, polega na wprowadzeniu do analizy dodatkowego mechanizmu uszkodzenia - mikropękania na granicy inkluzji i osnowy. Mikroszczeliny na granicy inkluzji i osnowy uwzględniono w hipotezie geometrycznej i kinematycznej metody Christoffersena. Następnie, wyznaczono lokalne oraz uśrednione pola naprężenia dla zadanego stanu uszkodzenia (tzn. dla zadanej liczby otwartych i zamkniętych mikroszczelin przy pominięciu poślizgów na powierzchniach mikroszczelin zamkniętych). Porównanie z wynikami uzyskanymi przez Nadot-Martin i in. (2003) dla nieuszkodzonego kompozytu lepkosprężystego pozwoliło na określenie wpływu uszkodzenia na poziomie lokalnym i globalnym. Na koniec, podstawowy model wieloskalowy uzupełniono o drugą część sformułowania, która pozwoliła usunąć pewne nadmiarowe odkształcenia związane z mikroszczelinami otwartymi, czyniąc cały model termodynamicznie spójnym. Ta druga część modelu wieloskalowego jest przeprowadzona przy założeniu upraszczającym, polegającym na (tymczasowym) pominięciu efektów lepkosprężystych.

Modelling adiabatic shear banding via damage mechanics approach

Longere P., Dragon A., Trumel H., Resseguier T. de, Deprince X., Petitpas E.

Archives of Mechanics

2003

Vol. 55, nr 1

3-38

During dynamic loading processes, large plastic deformation associated with high strain rates leads, for a broad class of ductile metals, to degradation and failure by adiabatic shear banding. The paper presents an attempt to model some salient features of this process viewed as an anisotropic damage mechanism coupled with thermo--elastic/viscoplastic deformation. The model is destined to be applied in the context of high velocity impact and penetration mechanism. The methodology employed within the framework of the internal state variable structure strives to keep a middle way between extensive description of complex viscoplastic flow and damage events and application-oriented accessibility requirements. Model capabilities are prelaminarily illustrated for shear loading process.