Dynamical Problems In TheFree Hexagon Method

International Journal of Solids and Structures, 2006

It is now well established that for non-associated materials such as geomaterials, there exists a wide domain strictly within the plastic limit where different failure modes can coexist. In particular, material instability in the sense given by Hill, related to the vanishing of the second-order work, can potentially occur. In this paper we examine the occurrence of such instabilities from the simulation of drained triaxial paths, followed by the computation of two-dimensional, then fully three-dimensional Gudehus response-envelopes using the micro-directional model. This model can be seen in the continuity of HillÕs multi-slip theory, because it accounts for the association of a large number of elementary elasto-plastic bodies. Each body is linked to a contact direction in physical space and therefore takes into account the behavior of the contacts oriented along that direction. Simulations confirmed that some loading directions led to the vanishing of the second-order work. In line with the research initiated by Mandel, a micro-mechanical analysis of the origin of these potential instabilities revealed that this macro-scale phenomenon could be directly related to the constitutive nature of the local contact model between neighboring particles. Finally, this investigation provides a clear physical understanding of HillÕs material stability condition for frictional materials.

Doklady Earth Sciences

Journal of Engineering Mechanics, 2004

A novel mesoscale granular continuum model is derived by homogenizing the mechanical behavior of six particles in contact forming an octahedron structure. The elastic behavior at the particle contacts is simulated in accordance with Hertz theory and the frictional behavior is taken into account by means of an evolution law for the contact shear stiffness. The mesoscale continuum model is calibrated on discrete element simulations of a cuboidal volume filled with identical spheres and loaded under axisymmetric compression. By imposing a set of radial deviatoric stress paths, the failure contour is computed in the deviatoric plane of the principal stress space.

The material structure at the microscale reveals the particulate nature of solids. By exploiting the discrete aspect of materials, the so-called particle methods developed and applied to the simulation of solids and liquids have attracted the attention of several researchers in the field of computational mechanics. In the present paper, a particle method based on a suitable force potential is proposed to describe the nature and intensity of the forces existing between particles of either the same solid or different colliding solids. The formulation applies to problems involving both granular materials and solids interacting with granular materials. The above approach is applied to simulate different problems dealing with the 3D dynamic fracture and failure of solids.

Key Engineering Materials

The prediction of the spacing and opening of cracks in asphalt or concrete pavements, and particularly in airports (runway, taxiway and apron) is important for the durability assessment. A basic problem is the spacing of parallel planar cracks from a half space surface, approached and solved by numerous authors by means of macro-scale computational models. The calculated values of crack spacing are in relatively good agreement with the values reported in observations on asphalt concrete pavements. The constituents of granular solids are, fundamentally, made of grain in contact and, these materials are highly discontinuous and non-homogeneous with two or three phases (solid, voids with air or water), and finally binding among solid parts. The aim of this paper is to suggest a micromechanical approach in granular material solids, focusing the attention on a simple RVE (representative volume element) based on two rigid particles linked through an adhesive material (bitumen). Our final aim is to propose a micro-damageability parameter (interface loss) supposing the adhesion decreasing under the action of prescribed tangential and normal relative displacement. The reduction is attributed by progressive damage and comes with energy dissipation and moreover we assume unilateral contact conditions for normal displacement and Coulomb friction for the tangential displacement.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999

We examine the network of forces to be expected in a static assembly of hard, frictionless spherical beads of random sizes, such as a colloidal glass. Such an assembly is minimally connected: the ratio of constraint equations to contact forces approaches unity for a large assembly. However, the bead positions in a finite subregion of the assembly are underdetermined. Thus to maintain equilibrium, half of the exterior contact forces are determined by the other half. We argue that the transmission of force may be regarded as unidirectional, in contrast to the transmission of force in an elastic material. Specializing to sequentially deposited beads, we show that forces on a given buried bead can be uniquely specified in terms of forces involving more recently added beads. We derive equations for the transmission of stress averaged over scales much larger than a single bead. This derivation requires the ansatz that statistical fluctuations of the forces are independent of fluctuations ...

The incremental behaviour of a 3D discrete element model composed of spherical elements is investigated with respect to the sign of the second order work. The numerical experiments consist of stress probes in the axisymmetric plane of stress increments. Initial stress states, from which stress probes are performed, are obtained by axisymmetric triaxial compressions. From stresses and strains numerically determined at boundaries of the numerical specimen, the second order work (d²W) is computed for each initial stress state and each stress probe direction. Thus, for stress states approaching Mohr-Coulomb limit condition, cones of unstable stress directions are found and a potential failure/bifurcation domain strictly inside the plastic limit condition is exhibited. Then comparisons between the second order work (obtained from a macroscopic description) and the sum c c contacts dF dl ⋅ ∑ are carried out. Equality of the two expressions is observed for elastic strains.

For static compressions of spheres, a new stress analysis for isotropic elastic spheres compressed between two¯at rigid platens is proposed by incorporating the Hertz contact stress. The predictions of the failure load for various sizes and strengths of spheres agree very well with our static experiments on a brittle plaster material. For dynamic compressions of spheres, a simple crushing analysis illustrates that the size of the contact zone can be estimated quite accurately in terms of the size of the sphere, the dynamic hardness, and the impact energy. Although the maximum contact force at failure is larger in the static case than that in the dynamic case, the energy required for fragmentation of the solid spheres is larger under dynamic test than under static test. Comparisons of the static and dynamic tests show that the impact energy required for fragmentation of a sphere can be approximated as 1.5 times of that for the static test. As expected, the impact energy for fragmentation increases monotonically with the size and strength of the spheres. The contact time at failure, however, does not exhibit a clear trend with the changes in size and strength of the spheres. Ó

For static compressions of spheres, a new stress analysis for isotropic elastic spheres compressed between two¯at rigid platens is proposed by incorporating the Hertz contact stress. The predictions of the failure load for various sizes and strengths of spheres agree very well with our static experiments on a brittle plaster material. For dynamic compressions of spheres, a simple crushing analysis illustrates that the size of the contact zone can be estimated quite accurately in terms of the size of the sphere, the dynamic hardness, and the impact energy. Although the maximum contact force at failure is larger in the static case than that in the dynamic case, the energy required for fragmentation of the solid spheres is larger under dynamic test than under static test. Comparisons of the static and dynamic tests show that the impact energy required for fragmentation of a sphere can be approximated as 1.5 times of that for the static test. As expected, the impact energy for fragmentation increases monotonically with the size and strength of the spheres. The contact time at failure, however, does not exhibit a clear trend with the changes in size and strength of the spheres. Ó