Abstract
In the present study, we investigate the strength properties of ductile porous materials reinforced by rigid particles. The microporous medium is constituted of a Drucker–Prager solid phase containing spherical voids; its behavior is described by means of an elliptic criterion (issued from a modified secant moduli approach) whose corresponding support function is determined. The latter is then implemented in a limit analysis approach in which a careful attention is paid for the contribution of the inclusion matrix-interface. This delivers parametric equations of the effective strength properties of the porous material reinforced by rigid particles. The predictions are compared to available results obtained by means of variational homogenization methods successively applied for micro-to-meso and then for meso-to-macro scales transitions. Moreover, additional static solutions are derived and compared to the kinematics limit analysis ones in order to prove the accuracy of the strength predictions under isotropic loading. Thereafter, the theoretical predictions (by the two methods) under shear loading are assessed by comparison with experimental data. The influences of mineralogical compositions and porosity are also discussed. Finally, we derive an approximate closed-form expression of the macroscopic strength which proves to be very accurate. Then, we examine in Appendix the particular case of a von Mises solid phase of the porous matrix for which our results are compared to the available estimates.
Highlights
Being hard clayey rocks, COx Argillite is a porous clay matrix in which quartz or silica inclusions are embedded
The result of the first homogenization step is the derivation of the strength properties of the porous clay matrix at the mesoscopic scale where it is described as a homogeneous material
On the basis of a limit analysis approach, we have proposed an extension of available models
Summary
COx Argillite is a porous clay matrix in which quartz or silica inclusions are embedded. The behaviour of the microporous clay is described by means of an elliptic criterion [2] whose corresponding support function is determined in this paper. By using this support function, we explore an alternative approach which can be viewed as an extension of the original Gurson model. The failure criterion of this ’rigid core sphere model’ is derived in the framework of the cinematic approach of limit analysis (LA). Notations: 1 and I are the second and fourth order identity tensors. J = (1/ 3)1 ⊗1, K = I−J are respectively the spherical and deviatoric projectors of isotropic fourth order symmetric tensor
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