Porous plasticity: Predictive second moment homogenization models coupled with Gurson's single cavity stress-strain solution

Ghezal, Marieme Imene El; Doghri, Issam

doi:10.1016/j.ijplas.2018.05.006

Cited by 21 publications

(9 citation statements)

References 53 publications

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“…We use the plane-strain-adapted averaging kernel 𝛼 plane strain ∞ given by Equations ( 9) and (11). Since only the upper half of the tube's cross-section is modelled, the presence of the symmetry plane is accounted for using Equation (39). Here we benefit from the property that different types of spatial symmetries can be combined (cf.…”

Section: Damage Of a Thick-walled Tubementioning

confidence: 99%

Integral‐based averaging with spatial symmetries for non‐local damage modelling

Shutov

Klyuchantsev

2022

Z Angew Math Mech

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Simulations utilizing local constitutive equations for strain‐softening materials are known to be pathologically mesh‐dependent. The rational solution to this problem is to use nonlocal material models. In this paper, we discuss the application of the integral‐based approach to the simulation of non‐local damage accumulation and fracture. Various combinations of non‐localities with common spatial symmetries are analysed analytically and numerically. The symmetries include the plane strain and the axisymmetric cases, as well as the presence of symmetry planes and cyclic symmetries. Although not a symmetry, the practically important case of thin plates is also analysed. We show that the delocalization procedure should be executed using symmetry‐adapted averaging kernels. For the considered spatial symmetries, analytical closed‐form expressions are obtained. Moreover, a new easy‐to‐use averaging kernel is suggested, the same for 3D, plane strain and plane stress applications. To showcase the delocalization procedures, we consider a ductile damage model, based on the multiplicative decomposition of the deformation gradient, as well as hyperelastic relations between stresses and strains. FEM solutions for a series of problems are presented, including graduate damage accumulation, crack initiation and fracture.

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Section: Damage Of a Thick-walled Tubementioning

confidence: 99%

Integral‐based averaging with spatial symmetries for non‐local damage modelling

Shutov

Klyuchantsev

2022

Z Angew Math Mech

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“…11(c). For a discussion and a recent proposal for spherical cavities embedded in a rigid-plastic matrix, we refer to [42].…”

Section: Porous Materialsmentioning

confidence: 99%

A finite strain incremental-secant homogenization model for elasto-plastic composites

Ghezal

Noels

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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This paper presents a finite strain extension of the incremental-secant mean-field homogenization (MFH) formulation for two-phase elasto-plastic composites. The formulation of the local finite strain elasto-plastic constitutive equations of each phase is based on a multiplicative decomposition of the deformation gradient as suggested by Simo in (Computer Methods in Applied Mechanics and Engineering, 99(1):61-112, 1992.). The latter has proposed algorithms which preserve the classical return mapping schemes of the infinitesimal theory by using principal Kirchhoff stresses and logarithmic eigenvalues of the left elastic Cauchy-Green strain. Relying on this property, we show that, by considering a quadratic logarithmic free energy and J2-flow theory at the local level, infinitesimal strain incremental-secant MFH is readily extended to finite strains. The proposed formulation and corresponding numerical algorithms are then presented. Finally, the predictions are illustrated with several numerical simulations which are verified against full-field finite element simulations of composite cells, demonstrating that the micro-mechanically based approach is able to predict the influence of the micro-structure and of its evolution on the macroscopic properties in a very cost-effective manner.

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“…The constitutive behavior of the porous materials should be described by a suitable yield function for the shakedown analysis. Several authors proposed yield functions for this type of material [8,9,12,14,24,28,30].…”

Section: Introductionmentioning

confidence: 99%

Shakedown analysis of porous materials via mixed meshless methods

Ruiz

Silveira

2020

J Braz. Soc. Mech. Sci. Eng.

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In this paper, the elastic shakedown analysis of porous materials is performed by means of meshless methods using mixed approximations. Based on a mixed variational principle for shakedown analysis and using a yield function for porous materials, two meshless methods are adapted to perform mixed approximations of the stress and velocity fields for the solution of the discrete shakedown problem. These two new methods are named mixed moving least squares method and mixed Shepard's method and are used to solve some numerical examples. The numerical results obtained showed a good agreement with available analytical solutions and published results by the finite element method. The proposed mixed methods can be applied in the analysis of structural and machine parts made of porous materials and subjected to variable loads.

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Porous plasticity: Predictive second moment homogenization models coupled with Gurson's single cavity stress-strain solution

Cited by 21 publications

References 53 publications

Integral‐based averaging with spatial symmetries for non‐local damage modelling

Integral‐based averaging with spatial symmetries for non‐local damage modelling

A finite strain incremental-secant homogenization model for elasto-plastic composites

Shakedown analysis of porous materials via mixed meshless methods

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