International audienceThis paper presents a synthesis of the works performed by various teams from France, Italy and Canada around the question of second-order work criterion. Because of the non-associative character of geomaterials plastic strains, it is now recognized that a whole bifurcation domain exists in the stress space with various possible modes of failure. In a first part these failure modes are observed in lab experimental tests and in discrete element modelling. Then a theoretical study of second-order work allows to establish a link with the kinetic energy, giving a basis to explain the transition from a prefailure (quasi)static regime to a postfailure dynamic regime. Eventually the main features of geomaterials failure are obtained by applying second-order work criterion to five different constitutive rate-independent models-three being phenomenological and two micromechanical. As a whole this paper tries to gather together all the elements for a proper understanding and use of second-order work criterion in geomechanics

International audienceThis paper is concerned with diffuse and other ensuing failure modes in geomaterials when tested under homogeneous states of shearing in various loading programs and drainage conditions. Material instability is indeed the basic property that accounts for the instability of an initially homogeneous deformation field leading to diffuse failure and strain localization in geomaterials. The former is normally characterized by a runaway type of failure accompanied with a sudden and violent collapse of the material in the absence of any localization phenomena. Against this backdrop, we present a brief overview of material instability in elastoplastic solids where one finds a rich source of theoretical concepts including bifurcation, strain localization, diffuse failure and second-order work, as well as a considerable body of experiments. Some compelling laboratory experimental studies of material instability with focus to diffuse failure are then presented and interpreted based on the second-order work. Finally, various material instability analyses using an elastoplastic constitutive and a general finite element analysis of the above-mentioned laboratory experimental tests are presented as a boundary value problem. It is shown that instability can be captured from otherwise uniform stress, density and hydraulic states, whereas uniform deviatoric loads are being applied on the external boundaries of a specimen. Although the numerical simulations reproduce well the laboratory experimental results, they also highlight the hierarchy of failure modes where localization phenomena emerge in the post-bifurcation regime as a result of a degradation of homogeneity starting from a diffuse mode signalled by a zero second-order work

SUMMARY This paper is concerned with a fundamental assumption in the theory of plasticity: the direction of plastic strain increments is independent of the loading (stress) increment direction. This assumption, also known as plastic flow rule postulate, works quite well for metal‐like materials. However, geomaterials such as sand present deformational mechanisms that are distinctive from those of metals when they are loaded. As such, we hereby examine the validity of this postulate for granular media accounting for their discrete nature. This is accomplished by analysing the mechanical behaviour of a cubic assembly of polydispersed spherical articles using a particle flow code. An extension to Gudehus' response envelope to three‐dimensional conditions is used to study the incremental character and influence of loading direction on the behaviour of these materials. It is found that plastic flow in granular media is governed by both current state variables and incremental loading direction and magnitude, especially under non‐axisymmetric stress conditions. The flow rule postulate of plasticity remains valid only in axisymmetric and biaxial conditions. We also verified that the plastic response might be significantly influenced by the stress path (or history) taken prior to loading. These findings raise the question of whether or not classic elastoplastic models based on the above postulate will have serious shortcomings, especially in true‐triaxial conditions. Copyright © 2013 John Wiley & Sons, Ltd.

SUMMARYIn this paper, we study material instabilities in geomaterials through an elastoplastic constitutive model endowed with appropriate attributes, such as stress, density and fabric dependencies. The analyses reveal the possibility of having diffuse instability, bifurcation and loss of uniqueness within the plastic limit surface. The resulting domain of bifurcation encompasses the intrinsic effects of stress-strain history, direction of loading, type of loading and fabric. The computations start at a material point level and are later on extended to an initial boundary value setting where diffuse failure of a three-dimensional sand specimen with a random distribution of void ratio is examined. We restrict our simulations to the study of a q-constant laboratory experimental test under different sets of control parameters. Diffuse failure is also revealed in a slope analysis under water infiltration following similar loading paths as in the q-constant test. The analysis shows common material instability features observed in the above test.

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