A. Piccolroaz

An elastoplastic framework for granular materials becoming cohesive through mechanical densification. Part I – small strain formulation

Mechanical densification of granular bodies is a process in which a loose material becomes increasingly cohesive as the applied pressure increases. A constitutive description of this process faces the formidable problem that granular and dense materials have completely different mechanical behaviours (nonlinear elastic properties, yield limit, plastic flow and hardening laws), which must both be, in a sense, included in the formulation. A treatment of this problem is provided here, so that a new phenomenological, elastoplastic constitutive model is formulated, calibrated by experimental data, implemented and tested, that is capable of describing the transition between granular and fully dense states of a given material. The formulation involves a novel use of elastoplastic coupling to describe the dependence of cohesion and elastic properties on the plastic strain. The treatment falls within small strain theory, which is thought to be appropriate in several situations; however, a generalization of the model to large strain is provided in Part II of this paper.

Symmetric and skew-symmetric weight functions in 2D perturbation models for semi-infinite interfacial cracks

Abstract In 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.

Evaluation of the Lazarus-Leblond constants in the asymptotic model of the interfacial wavy crack

Piccolroaz, A; Mishuris, G; Movchan, AB. Evaluation of the Lazarus-Leblond constants in the asymptotic model of the interfacial wavy crack. Journal of the mechanics and Physics of Solids. 2007, 55(8), 1575-1600

Steady-state propagation of a mode II crack in couple stress elasticity

The present work deals with the problem of a semi-infinite crack steadily propagating in an elastic body subject to plane-strain shear loading. It is assumed that the mechanical response of the body is governed by the theory of couple-stress elasticity including also micro-rotational inertial effects. This theory introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying microstructure and has proved to be very effective for modeling complex microstructured materials. It is assumed that the crack propagates at a constant sub-Rayleigh speed. An exact full field solution is then obtained based on integral transforms and the Wiener–Hopf technique. Numerical results are presented illustrating the dependence of the stress intensity factor and the energy release rate upon the propagation velocity and the characteristic material lengths in couple-stress elasticity. The present analysis confirms and extends previous results within the context of couple-stress elasticity concerning stationary cracks by including inertial and micro-inertial effects.

An elastoplastic framework for granular materials becoming cohesive through mechanical densification. Part II – the formulation of elastoplastic coupling at large strain

The two key phenomena occurring in the process of ceramic powder compaction are the progressive gain in cohesion and the increase of elastic stiffness, both related to the development of plastic deformation. The latter effect is an example of ‘elastoplastic coupling’, in which the plastic flow affects the elastic properties of the material, and has been so far considered only within the framework of small strain assumption (mainly to describe elastic degradation in rock-like materials), so that it remains completely unexplored for large strain. Therefore, a new finite strain generalization of elastoplastic coupling theory is given to describe the mechanical behaviour of materials evolving from a granular to a dense state. The correct account of elastoplastic coupling and of the specific characteristics of materials evolving from a loose to a dense state (for instance, nonlinear – or linear – dependence of the elastic part of the deformation on the forming pressure in the granular – or dense – state) makes the use of existing large strain formulations awkward, if even possible. Therefore, first, we have resorted to a very general setting allowing general transformations between work-conjugate stress and strain measures; second, we have introduced the multiplicative decomposition of the deformation gradient and, third, employing isotropy and hyperelasticity of elastic response, we have obtained a relation between the Biot stress and its ‘total’ and ‘plastic’ work-conjugate strain measure. This is a key result, since it allows an immediate achievement of the rate elastoplastic constitutive equations. Knowing the general form of these equations, all the specific laws governing the behaviour of ceramic powders are finally introduced as generalizations of the small strain counterparts given in Part I of this paper.  2005 Elsevier SAS. All rights reserved.

Integration algorithms of elastoplasticity for ceramic powder compaction

Inelastic deformation of ceramic powders (and of a broad class of rock-like and granular materials), can be described with the yield function proposed by Bigoni and Piccolroaz (2004. Yield criteria for quasibrittle and frictional materials. Int J Solids Struct, 41:2855–78). This yield function is not defined outside the yield locus, so that ‘gradient-based’ integration algorithms of elastoplasticity cannot be directly employed. Therefore, we propose two ad hoc algorithms: (i) an explicit integration scheme based on a forward Euler technique with a ‘centre-of-mass’ return correction and (ii) an implicit integration scheme based on a ‘cutoff-substepping’ return algorithm. Iso-error maps and comparisons of the results provided by the two algorithms with two exact solutions (the compaction of a ceramic powder against a rigid spherical cup and the expansion of a thick spherical shell made up of a green body), show that both the proposed algorithms perform correctly and accurately.

Elastoplastic coupling to model cold ceramic powder compaction

Abstract The simulation of industrial processes involving cold compaction of powders allows for the optimization of the production of both traditional and advanced ceramics. The capabilities of a constitutive model previously proposed by the authors are explored to simulate simple forming processes, both in the small and in the large strain formulation. The model is based on the concept of elastoplastic coupling – providing a relation between density changes and variation of elastic properties – and has been tailored to describe the transition between a granular ceramic powder and a dense green body. Finite element simulations have been compared with experiments on an alumina ready-to-press powder and an aluminum silicate spray-dried granulate. The simulations show that it is possible to take into account friction at the die wall and to predict the state of residual stress, density distribution and elastic properties in the green body at the end of the forming process.

A dynamical interpretation of flutter instability in a continuous medium

Flutter instability in an infinite medium is a form of material instability corresponding to the occurrence of complex conjugate squares of the acceleration wave velocities. Although its occurrence is known to be possible in elastoplastic materials with nonassociative flow law and to correspond to some dynamically growing disturbance, its mechanical meaning has to date still eluded a precise interpretation. This is provided here by constructing the infinite-body, time-harmonic Greens function for the loading branch of an elastoplastic material in flutter conditions. Used as a perturbation, it reveals that flutter corresponds to a spatially blowing-up disturbance, exhibiting well-defined directional properties, determined by the wave directions for which the eigenvalues become complex conjugate. Flutter is shown to be connected to the formation of localized deformations, a dynamical phenomenon sharing geometrical similarities with the well-known mechanism of shear banding occurring under quasi-static loading. Flutter may occur much earlier than shear banding in a process of continued plastic deformation.

A simple and robust elastoplastic constitutive model for concrete

An elasto-plastic model for concrete, based on a recently-proposed yield surface and simple hardening laws, is formulated, implemented, numerically tested and validated against available test results. The yield surface is smooth and particularly suited to represent the behaviour of rock-like materials, such as concrete, mortar, ceramic and rock. A new class of isotropic hardening laws is proposed, which can be given both an incremental and the corresponding finite form. These laws describe a smooth transition from linear elastic to plastic behaviour, incorporating linear and nonlinear hardening, and may approach the perfectly plastic limit in the latter case. The reliability of the model is demonstrated by its capability of correctly describing the results yielded by a number of well documented triaxial tests on concrete subjected to various confinement levels. Thanks to its simplicity, the model turns out to be very robust and well suited to be used in complex design situations, as those involving dynamic loads.

Energy release rate in hydraulic fracture: Can we neglect an impact of the hydraulically induced shear stress?

Abstract A novel hydraulic fracture (HF) formulation is introduced which accounts for the hydraulically induced shear stress at the crack faces. It utilizes a general form of the elasticity operator alongside a revised fracture propagation condition based on the critical value of the energy release rate. It is shown that the revised formulation describes the underlying physics of HF in a more accurate way and is in agreement with the asymptotic behaviour of the linear elastic fracture mechanics. A number of numerical simulations by means of the universal HF algorithm previously developed in [Wrobel M., Mishuris G. (2015) Hydraulic fracture revisited: Particle velocity based simulation. International Journal of Engineering Science , 94: 23–58] are performed in order to: (i) compare the modified HF formulation with its classic counterpart and (ii) investigate the peculiarities of the former. Computational advantages of the revised HF model are demonstrated. Asymptotic estimations of the main solution elements are provided for the cases of small and large toughness. The modified formulation opens new ways to analyse the physical phenomenon of HF and also improves the reliability and efficiency of its numerical simulations.