A new yield/damage function is proposed for modelling the inelastic behaviour of a broad class of pressure-sensitive, frictional, ductile and brittle-cohesive materials. The yield function allows the possibility of describing a transition between the shape of a yield surface typical of a class of materials to that typical of another class of materials. This is a fundamental key to model the behaviour of materials which become cohesive during hardening (so that the shape of the yield surface evolves from that typical of a granular material to that typical of a dense material), or which decrease cohesion due to damage accumulation. The proposed yield function is shown to agree with a variety of experimental data relative to soil, concrete, rock, metallic and composite powders, metallic foams, porous metals, and polymers. The yield function represents a single, convex and smooth surface in stress space approaching as limit situations well-known criteria and the extreme limits of convexity in the deviatoric plane. The yield function is therefore a generalization of several criteria, including von Mises, Drucker-Prager, Tresca, modified Tresca, Coulomb-Mohr, modified Cam-clay, and--concerning the deviatoric section--Rankine and Ottosen. Convexity of the function is proved by developing two general propositions relating convexity of the yield surface to convexity of the corresponding function. These propositions are general and therefore may be employed to generate other convex yield functions.

Piccolroaz, A; Mishuris, G; Movchan AB. Symmetric and skew-symmetric weight functions in 2D perturbation models for semi-infinite interfacial cracks. Journal of the Mechanics and Physics of Solids. 2009, 57(9), 1657-1682In this paper we address the vector problem of a 2D half-plane interfacial crack loaded by a general asymmetric distribution of forces acting on its faces. It is shown that the general integral formula for the evaluation of stress intensity factors, as well as high-order terms, requires both symmetric and skew-symmetric weight function matrices. The symmetric weight function matrix is obtained via the solution of a Wiener-Hopf functional equation, whereas the derivation of the skew-symmetric weight function matrix requires the construction of the corresponding full field singular solution. The weight function matrices are then used in the perturbation analysis of a crack advancing quasi-statically along the interface between two dissimilar media. A general and rigorous asymptotic procedure is developed to compute the perturbations of stress intensity factors as well as high-order terms.Peer reviewe

This paper is concerned with the problem of a semi-infinite crack steadily propagating in an elastic solidwith microstructures subject to antiplane loading applied on the crack surfaces. The loading is movingwith the same constant velocity as that of the crack tip. We assume subsonic regime, that is the crackvelocity is smaller than the shear wave velocity. The material behaviour is described by the indeterminatetheory of couple stress elasticity developed by Koiter. This constitutive model includes the characteristiclengths in bending and torsion and thus it is able to account for the underlying microstructure of thematerial as well as for the strong size effects arising at small scales and observed when the representativescale of the deformation field becomes comparable with the length scale of the microstructure, such asthe grain size in a polycrystalline or granular aggregate.The present analysis confirms and extends earlier results on the static case by including the effectsof crack velocity and rotational inertia. By adopting the criterion of maximum total shear stress, wediscuss the effects of microstructural parameters on the stability of crack propagation

a b s t r a c tConvexity of a yield function (or phase-transformation function) and its relations to convexity of the corresponding yield surface (or phase-transformation surface) is essential to the invention, definition and comparison with experiments of new yield (or phase-transformation) criteria. This issue was previously addressed only under the hypothesis of smoothness of the surface, but yield surfaces with corners (for instance, the Hill, Tresca or Coulomb-Mohr yield criteria) are known to be of fundamental importance in plasticity theory. The generalization of a proposition relating convexity of the function and the corresponding surface to nonsmooth yield and phase-transformation surfaces is provided in this paper, together with the (necessary to the proof) extension of a theorem on nonsmooth elastic potential functions. While the former of these generalizations is crucial for yield and phase-transformation functions, the latter may find applications for potential energy functions describing phase-transforming materials, or materials with discontinuous locking in tension, or contact of a body with a discrete elastic/frictional support.

A model of a shear band as a zero-thickness non-linear interface is proposed and tested using finite element simulations. An imperfection approach is used in this model where a shear band that is assumed to lie in a ductile matrix material (obeying von Mises plasticity with linear hardening), is present from the beginning of loading and is considered to be a zone in which yielding occurs before the rest of the matrix. This approach is contrasted with a perturbative approach, developed for a J 2 -deformation theory material, in which the shear band is modeled to emerge at a certain stage of a uniform deformation. Both approaches concur in showing that the shear bands (differently from cracks) propagate rectilinearly under shear loading and that a strong stress concentration should be expected to be present at the tip of the shear band, two key features in the understanding of failure mechanisms of ductile materials.