Some micromechanical aspects of failure in granular materials based on second-order work

This paper discusses the notion of failure in a granular assembly by examining the key microstructural mechanisms which are most likely to trigger the nucleation and propagation of instabilities within a granular material. For this purpose, the key variable to predict the occurrence of failure, known as second-order work, is expressed from variables on the grain scale. The local behaviour incidents (where contacts may open or slide), compared to the global response of the assembly, are analysed by two approaches. First, numerical computations made by a discrete element model confirm the microscopic definition of the second-order work. Secondly, a micromechanical model, based on a homogenization procedure, relating the macroscopic behaviour to microscopic ingredients, namely contact planes, points to a close link between the occurrence of failure on the macroscopic scale as well as on the contact planes.     

Delamination in sandwich panels due to local water slamming loads

We study delamination in a sandwich panel due to transient finite plane strain elastic deformations caused by local water slamming loads and use the boundary element method to analyze motion of water and the finite element method to determine deformations of the panel. The cohesive zone model is used to study delamination initiation and propagation. The fluid is assumed to be incompressible and inviscid, and undergo irrotational motion. A layer-wise third order shear and normal deformable plate/shell theory is employed to simulate deformations of the panel by considering all geometric nonlinearities (i.e., all non-linear terms in strain–displacement relations) and taking the panel material to be St. Venant–Kirchhoff (i.e., the second Piola–Kirchhoff stress tensor is a linear function of the Green–St. Venant strain tensor). The Rayleigh damping is introduced to account for structural damping that reduces oscillations in the pressure acting on the panel/water interface. Results have been computed for water entry of (i) straight and circular sandwich panels made of Hookean materials with and without consideration of delamination failure, and (ii) flat sandwich panels made of the St. Venant–Kirchhoff materials. The face sheets and the core of sandwich panels are made, respectively, of fiber reinforced composites and soft materials. It is found that for the same entry speed (i) the peak pressure for a curved panel is less than that for a straight panel, (ii) the consideration of geometric nonlinearities significantly increases the peak hydrodynamic pressure, (iii) delamination occurs in mode-II, and (iv) the delamination reduces the hydroelastic pressure acting on the panel surface and hence alters deformations of the panel.     

Study on the generalized prandtl-reuss constitutive equation and the corotational rates of stress tensor

I.IntroductionTilepl'ogl'ess11as.toifcertainextent,beenmadeintheelastic-plasticconstitutivetheoryatII[litedefbrlllations.Coil'paredwitllotherconstitutiverelations,thegeneralizedPrandtlReuss(P-R)equatiollsareextensivelystudiedandwidelyapplied.IndevelopingthegeneralizedP-Requation.itisusuallyassumedthatthedeformationrate(thesymmetricpartorvelocitygradiellt)isdecolllposedintotheelasticpartandplasticpart.TheplasticLIcf\'l.llliltlollrittcobeystilenormalfi(,xvrilleasillthecaseofinfinitcsilllnld…     

Universal Deformations for a Class of Compressible Isotropic Hyperelastic Materials

Differential conditions are derived for a smooth deformation to be universal for a class of isotropic hyperelastic materials that we regard as a compressible variant (a notion we make precise) of Mooney–Rivlin’s class, and that includes the materials studied originally by Tolotti in 1943 and later, independently, by Blatz. The collection of all universal deformations for an incompressible material class is shown to contain, modulo a uniform dilation, all the universal deformations for its compressible variants. As an application of this result, by searching the known families of universal deformations for all incompressible isotropic materials, a nontrivial universal deformation for Tolotti materials is found. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dynamic analysis of an offshore pipe laying operation using the reel method

A system designed for a rigid and flexible pipe laying purposes is presented in the paper.Mathematical and numerical models are developed by using the rigid finite element method(RFEM).The RFEM is an efficient solution in the time domain.Static and dynamic problems related to pipe installation are solved by taking the advantage of simple interpretation and implementation of the method.Large deformations of the pipe during spooling and when it is reeled out at sea are considered.A material model implemented is used to take into consideration nonlinear material properties.In particular,the full elasto-plastic material characteristics with hardening and Bauschinger effect are included.Dynamic analyses are performed and the results attached in this work demonstrates how the sea conditions influence the machinery and pipeline,assuming a passive reel drive system. The influence of several other operational parameters on dynamic loads is verified.An active system,implemented as a part of the mathematical model,improves the system performance.Some results are presented as well.     

Constitutive modeling of temperature and strain rate dependent elastoplastic hardening materials using a corotational rate associated with the plastic deformation

In this paper, a constitutive model with a temperature and strain rate dependent flow stress (Bergstrom hardening rule) and modified Armstrong-Frederick kinematic evolution equation for elastoplastic hardening materials is introduced. Based on the multiplicative decomposition of the deformation gradient,new kinematic relations for the elastic and plastic left stretch tensors as well as the plastic deformation-dependent spin tensor are proposed. Also, a closed-form solution has been obtained for the elastic and plastic left stretch tensors for the simple shear problem.To evaluate model validity, results are compared with known experimental data for SUS 304 stainless steel, which shows a good agreement with the results of the proposed theoretical model.Finally, the stress-deformation curve, as predicted by the model, is plotted for the simple shear problem at room and elevated temperatures using the same material properties for AA5754-O aluminium alloy.     

A comparative study of kinematic hardening rules at finite deformations

Kinematic hardening models describe a specific kind of plastic anisotropy which evolves with the deformation process. It is well known that the extension of constitutive relations from small to finite deformations is not unique. This applies also to well-established kinematic hardening rules like that of Armstrong-Frederick or Chaboche. However, the second law of thermodynamics offers some possibilities for generalizing constitutive equations so that this ambiguity may, in some extent, be moderated. The present paper is concerned with three possible extensions, from small to finite deformations, of the Armstrong-Frederick rule, which are derived as sufficient conditions for the validity of the second law. All three models rely upon the multiplicative decomposition of the deformation gradient tensor into elastic and plastic parts and make use of a yield function expressed in terms of the so-called Mandel stress tensor. In conformity with this approach, the back-stress tensor is defined to be of Mandel stress type as well. In order to compare the properties of the three models, predicted responses for processes with homogeneous and inhomogeneous deformations are discussed. To this end, the models are implemented in a finite element code (ABAQUS).     

Large deformations of homogeneous and fiber-reinforced cylinders under the action of centrifugal forces

The problem on large deformations of round cylinders made of homogeneous and fiber-reinforced elastomeric materials under the action of inertia forces caused by rotatory motion is solved. The solution is given in a plane axisymmetric statement, where the deformation parameters of the cylinders depend only on the radial coordinate. Based on the mathematical model presented, the deformation of revolving cylinders made of homogeneous elastomeric materials and reinforced with fibers in the axial, circumferential, and radial directions is investigated. The ultimate rotational speeds for cylinders with different reinforcement schemes and tight and loose fits are found at which their limiting configurations are reached. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 347-366, May-June, 2009.