Showing papers in "Journal of The Mechanics and Physics of Solids in 2001"

Effective properties of the octet-truss lattice material

Abstract: The effective mechanical properties of the octet-truss lattice structured material have been investigated both experimentally and theoretically. Analytical and FE calculations of the elastic properties and plastic yielding collapse surfaces are reported. The intervention of elastic buckling of the struts is also analysed in an approximate manner. Good agreement is found between the predictions of the strength and experimental observations from tests on the octet-truss material made from a casting aluminium alloy. Moreover, the strength and stiffness of the octet-truss material are stretching-dominated and compare favourably with the corresponding properties of metallic foams. Thus, the octet-truss lattice material can be considered as a promising alternative to metallic foams in lightweight structures.

A reformulation of strain gradient plasticity

Abstract: A class of phenomenological strain gradient plasticity theories is formulated to accommodate more than one material length parameter. The objective is a generalization of the classical J2 3ow theory of plasticity to account for strain gradient e4ects that emerge in deformation phenomena at the micron scale. A special case involves a single length parameter and is of similar form to that proposed by Aifantis and co-workers. Distinct computational advantages are associated with this class of theories that make them attractive for applications requiring the generation of numerical solutions. The higher-order nature of the theories is emphasized, involving both higher-order stresses and additional boundary conditions. Competing members in the class of theories will be examined in light of experimental data on wire torsion, sheet bending, indentation and other micron scale plasticity phenomena. The data strongly suggest that at least two distinct material length parameters must be introduced in any phenomenological gradient plasticity theory, one parameter characterizing problems for which stretch gradients are dominant and the other relevant to problems when rotation gradients (or shearing gradients) are controlling. Flow and deformation theory versions of the theory are highlighted that can accommodate multiple length parameters. Examination of several basic problems reveals that the new formulations predict quantitatively similar plastic behavior to the theory proposed earlier by the present authors. The new formulations improve on the earlier theory in the manner in which elastic and plastic strains are decomposed and in the representation of behavior in the elastic range. ? 2001 Elsevier Science Ltd. All rights reserved.

Rate and state dependent friction and the stability of sliding between elastically deformable solids

Abstract: We study the stability of steady sliding between elastically deformable continua using rate and state dependent friction laws That is done for both elastically identical and elastically dissimilar solids The focus is on linearized response to perturbations of steady-state sliding, and on studying how the positive direct effect (instantaneous increase or decrease of shear strength in response to a respective instantaneous increase or decrease of slip rate) of those laws allows the existence of a quasi-static range of response to perturbations at sufficiently low slip rate We discuss the physical basis of rate and state laws, including the likely basis for the direct effect in thermally activated processes allowing creep slippage at asperity contacts, and estimate activation parameters for quartzite and granite Also, a class of rate and state laws suitable for variable normal stress is presented As part of the work, we show that compromises from the rate and state framework for describing velocity-weakening friction lead to paradoxical results, like supersonic propagation of slip perturbations, or to ill-posedness, when applied to sliding between elastically deformable solids The case of sliding between elastically dissimilar solids has the inherently destabilizing feature that spatially inhomogeneous slip leads to an alteration of normal stress, hence of frictional resistance We show that the rate and state friction laws nevertheless lead to stability of response to sufficiently short wavelength perturbations, at very slow slip rates Further, for slow sliding between dissimilar solids, we show that there is a critical amplitude of velocity-strengthening above which there is stability to perturbations of all wavelengths

An analysis of the quasicontinuum method

Abstract: The aim of this paper is to present a streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al. (Philos. Mag. A 73 (1996) 1529; Langmuir 12 (1996) 4529) and to analyze its accuracy and convergence characteristics. Specifically, we assess the effect of the summation rules on accuracy; we determine the rate of convergence of the method in the presence of strong singularities, such as point loads; and we assess the effect of the refinement tolerance, which controls the rate at which new nodes are inserted in the model, on the development of dislocation microstructures.

Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium

Abstract: An elastic double-shell model is presented for infinitesimal buckling of a double-walled carbon nanotube embedded in an elastic matrix under axial compression. The analysis is based on a Winkler model for the surrounding elastic medium and a simplified model for the van der Waals interaction between the inner and outer nanotubes. An explicit formula is derived for the critical axial strain, which indicates the effects of the surrounding elastic matrix combined with the intertube van der Waals forces. In particular, the present model predicts that the critical axial strain of the embedded double-walled nanotube is lower than that of an embedded single-walled nanotube under otherwise identical conditions. This implies that inserting an inner tube lowers the critical axial strain of an embedded single-walled carbon nanotube, although the total critical compressive force could be increased due to the increase in the cross-sectional area of the nanotube. The reduced critical axial strain is attributed to the intertube slips between the inner and outer tubes. This result indicates that embedded multi-walled carbon nanotubes could be even more susceptible to infinitesimal axial buckling than embedded single-walled carbon nanotubes.

A model of crystal plasticity based on the theory of continuously distributed dislocations

Abstract: This work represents an attempt at developing a continuum theory of the elastic–plastic response of single crystals with structural dimensions of ∼100 μm or less, based on ideas rooted in the theory of continuously distributed dislocations. The constitutive inputs of the theory relate explicitly to dislocation velocity, dislocation generation and crystal elasticity. Constitutive nonlocality is a natural consequence of the physical considerations of the model. The theory reduces to the nonlinear elastic theory of continuously distributed dislocations in the case of a nonevolving dislocation distribution in the material and the nonlinear theory of elasticity in the absence of dislocations. A geometrically linear version of the theory is also developed. The work presented in this paper is intended to be of use in the prediction of time-dependent mechanical response of bodies containing a single, a few, or a distribution of dislocations. A few examples are solved to illustrate the recovery of conventional results and physically expected ones within the theory. Based on the theory of exterior differential equations, a nonsingular solution for stress/strain fields of a screw dislocation in an infinite, isotropic, linear elastic solid is derived. A solution for an infinite, neo-Hookean nonlinear elastic continuum is also derived. Both solutions match with existing results outside the core region. Bounded solutions are predicted within the core in both cases. The edge dislocation in the isotropic, linear theory is also discussed in the context of this work. Assuming a constant dislocation velocity for simplifying the analysis, an evolutionary solution resulting in a slip-step on the boundary of a stress-free crystal produced due to the passage and exit of an edge dislocation is also described.

Dynamic ruptures in recent models of earthquake faults

Abstract: We discuss several problems of dynamic rupture relevant to mechanics of earthquake faults, material sciences, and physics of spatially extended dissipative systems. The problems include dynamic rupture along an interface separating different elastic solids, dynamic rupture on a planar surface governed by strongly velocity-weakening friction, and elastodynamic calculations of long deformation history on a smooth fault in an elastic continuum. These separate problems share a number of methodological and conceptual issues that form recurring themes in the paper. An important methodological issue for computational schemes is dependency of numerical results on the used grid size. This arises inevitably in computer simulations when the assumed constitutive laws do not include a length scale (e.g., of shear or extensional displacement) over which material properties evolve. Such simulations do not have a stable underlying solution, to which they may converge with sufficient grid refinement. However, they may provide rough approximations—lacking at present a rigorous foundation—to the behavior of systems containing elements of discreteness (associated with abrupt fluctuations) at scales relevant to observations of interest. Related important conceptual issues are connections between, or when appropriate separation of, small scale phenomena (e.g., nucleation of rupture, processes at rupture front) and large scale features of the response (e.g., overall space–time dimensions of rupture, statistics of many events). Additional recurring conceptual topics are crack vs. pulse modes of dynamic rupture, the stress under which earthquake faults slip, and the origin of spatio-temporal complexities of earthquakes. These seemingly different issues probably have one or more common origins. Dynamic rupture on an interface between different solids, strongly velocity-weakening friction on a homogeneous fault, and strong fault zone heterogeneities can all produce narrow self-healing slip pulses with low dynamic stress (and low associated frictional heat) during the active part of slip. Strong fault heterogeneities probably play the dominant role in producing the observed earthquake complexities. Improved understanding of the discussed problems will require establishing connections between discrete and continuum descriptions of mechanical failure processes, generalization of current models to realistic three-dimensional dynamic models, and high-resolution laboratory and in-situ observations over broad scales of space and time. These challenging problems provide by their subject matter and involved great difficulties important targets for multi-disciplinary research by engineers, earth scientists, and physicists.

On the characterization of geometrically necessary dislocations in finite plasticity

Abstract: We develop a general theory of geometrically necessary dislocations based on the decomposition F=FeFp. The incompatibility of Fe and that of Fp are characterized by a single tensor G giving the Burgers vector, measured and reckoned per unit area in the microstructural (intermediate) configuration. We show that G may be expressed in terms of Fp and the referential curl of Fp, or equivalently in terms of Fe−1 and the spatial curl of Fe−1. We derive explicit relations for G in terms of Euler angles for a rigid-plastic material and — without neglecting elastic strains — for strict plane strain and strict anti-plane shear. We discuss the relationship between G and the distortion of microstructural planes. We show that kinematics alone yields a balance law for the transport of geometrically necessary dislocations.

Multi-axial electrical switching of a ferroelectric: theory versus experiment

Abstract: Samples of the polycrystalline ferroelectric ceramic PZT-5H were poled by applying an electric field at room temperature. Subsequently, an electric field was applied to the samples at a range of angles to the poling direction. The measured non-linear responses in electric displacement are used to construct “yield surfaces” in electric field space corresponding to the onset of ferroelectric switching. The results are compared with predictions from three models: (i) a previous self-consistent polycrystal calculation with rate-independent, non-hardening crystal plasticity; (ii) a simplified crystal plasticity model with viscoplastic (rate-dependent) behaviour and a sufficient number of transformation systems to reproduce the polycrystalline behaviour; (iii) a phenomenological model based on rate-independent flow theory, using kinematic hardening and a quadratic yield surface in electric field and stress space. The experiments suggest that the self-consistent crystal plasticity formulation is most able to reproduce the multi-axial electrical response and yield surface of the polycrystal. The phenomenological model is able to reproduce the uniaxial response accurately, but gives relatively poor performance for multi-axial loading paths, in its present form. A tolerable compromise in multi-axial modelling is the simplified crystal plasticity approach. This is able to reproduce multi-axial constitutive behaviour with reasonable accuracy, whilst offering computational simplicity and speed similar to that of the phenomenological model.

Polycrystalline shape-memory materials: effect of crystallographic texture

Abstract: A crystal-mechanics-based constitutive model for polycrystalline shape-memory materials has been developed. The model has been implemented in a finite-element program. In our finite-element model of a polycrystal, each element represents one crystal, and a set of crystal orientations which approximate the initial crystallographic texture of the shape-memory alloy are assigned to the elements. The macroscopic stress–strain responses are calculated as volume averages over the entire aggregate. Pseudoelasticity experiments in tension, compression, and shear have been performed on an initially textured polycrystalline Ti–Ni alloy. In order to determine the material parameters for Ti–Ni, the stress–strain results from a finite-element calculation of a polycrystalline aggregate subjected to simple tension have been fit to corresponding results obtained from the physical experiment. Using the material parameters so determined, the predicted pseudoelastic stress–strain curves for simple compression and thin-walled tubular torsion of the initially textured Ti–Ni are shown to be in good accord with the corresponding experiments. Our calculations also show that the crystallographic texture is the main cause for the observed tension–compression asymmetry in the pseudoelastic response of Ti–Ni. The predictive capability of the model for the variation of the pseudoelastic behavior with temperature is shown by comparing the calculated stress–strain response from the model against results from experiments of Shaw and Kyriakides (J. Mech. Phys. Solids 43 (1995) 1243) on Ti–Ni wires at a few different temperatures. By performing numerical experiments, we show that our model is able to qualitatively capture the shape-memory effect by transformation. We have also evaluated the applicability of a simple Taylor-type model for shape-memory materials. Our calculations show that the Taylor model predicts the macroscopic pseudoelastic stress–strain curves in simple tension, simple compression and tubular torsion fairly well. Therefore, it may be used as a relatively inexpensive computational tool for the design of components made from shape-memory materials.

An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution

Abstract: For estimating the effective properties (elasticity, conductivity, piezoelectricity, etc.) of composites of the matrix-inclusion type, we develop a new micromechanical model, the effective self-consistent scheme (ESCS), based on the three-phase model. As a simplified and explicit version of the ESCS estimate, the interaction direct derivative (IDD) estimate is further proposed. The IDD estimate has an explicit and almost the simplest structure in comparison with other existing micromechanical estimates, with clear physical significance for all the involved components. It is universally applicable for various multiphase composites of the matrix-inclusion type, for any material symmetries of matrix, inclusions and effective medium, and distribution, shapes, orientations, and concentration of inclusions. Applications to effective elastic properties of composites with spherical inclusions and materials damaged due to voids of various shapes and microcracks (up to any high microcrack density) are presented, in comparison with a number of refined or accurate numerical simulation results. The IDD estimate seems to provide the best predictions in most of our examined cases. A further exploration of the proposed two estimates is given by Du and Zheng (Acta Mech. (2001), in press).

Effects of cell irregularity on the elastic properties of 2D Voronoi honeycombs

Abstract: Foams are more and more widely used in different areas. Most available mechanical models are usually based on idealised unit cell structures, and are not able to account for the natural variations in microstructure which are typical for most foam structures. The objective of this work has been to investigate how the cell irregularity affects the elastic properties of 2D random foams. We have constructed periodical random structures with different degrees of irregularity, and applied finite element analysis (FEA) to determine their effective elastic properties. The results indicate that, the more irregular the 2D random foams, the larger will be their effective Young's modulus and shear modulus, and the smaller will be their bulk modulus at a constant overall relative density. However, for varying degrees of irregularity, the foams remain isotropic and the Poisson's ratios are very close to 1. Both Young's modulus and Poisson's ratio of random Voronoi honeycombs having different degrees of regularity ?, decrease gradually with increasing relative density ?.

Slip dynamics at an interface between dissimilar materials

Abstract: It has been shown recently that steady frictional sliding along an interface between dissimilar elastic solids with Coulomb friction acting at the interface is ill-posed for a wide range of material parameters and friction coefficients. The ill-posedness is manifest in the unstable growth of interfacial disturbances of all wavelengths, with growth rate inversely proportional to the wavelength. We first establish the connection between the ill-posedness and the existence of a certain interfacial wave in frictionless contact, called the generalized Rayleigh wave. Precisely, it is shown that for material combinations where the generalized Rayleigh wave exists, steady sliding with Coulomb friction is ill-posed for arbitrarily small values of friction. In addition, intersonic unstable modes and supersonic steady-state modes exist for sufficiently large values of the friction coefficient. Secondly, regularization of the problem by an experimentally motivated friction law is studied. We show that a friction law with no instantaneous dependence on normal stress but a simple fading memory of prior history of normal stress makes the problem well-posed.

Indentation of a soft metal film on a hard substrate: Strain gradient hardening effects

Abstract: A new type of nanoindentation experiment showing the effect of a strain gradient on the flow strength of a crystalline material is conducted and analyzed. We show that by indenting a soft metal film (Al) on a hard substrate (glass) with a sharp diamond indenter a strong gradient of plastic strain is created. The true hardness of the film is observed to increase with increasing depth of indentation when the indenter tip approaches the hard substrate, in sharp contrast to the falling hardness with increasing depth in bulk materials. We associate this rise in hardness with the strong gradient of plastic strain created between the indenter and the hard substrate. We use the mechanism-based strain gradient (MSG) plasticity theory to model the observed indentation behavior. The modeling shows that the MSG plasticity theory is capable of describing not only the decreasing hardness with increasing depth of indentation at shallow indentations, as observed in bulk materials, but also the rise in hardness that occurs when the indenter tip approaches the film/substrate interface.

Incompatibility and a simple gradient theory of plasticity

Abstract: In the continuum theory, at finite strains the crystal lattice is assumed to distort only elastically during plastic flow, while generally the elastic distortion itself is not compatible with a single-valued displacement field. Lattice incompatibility is characterized by a certain skew-symmetry property of the gradient of the elastic deformation field, and this measure can play a natural role in nonlocal theories of plasticity. A simple constitutive proposal is discussed where incompatibility only enters the instantaneous hardening relations. As a result, the incremental boundary value problem for rate-independent and rate-dependent behaviors has a classical structure and rather straightforward modifications of standard finite element programs can be utilized. Two examples are presented in this paper: one for size-scale effects in the torsion of thin wires in the setting of an isotropic J2 flow theory and the other for hardening of microstructures containing small particles embedded in a single crystal matrix.

Boundary layers in constrained plastic flow: comparison of nonlocal and discrete dislocation plasticity

Abstract: Simple shear of a constrained strip is analyzed using discrete dislocation plasticity and strain gradient crystal plasticity theory. Both single slip and symmetric double slip are considered. The loading is such that for a local continuum description of plastic flow the deformation state is one of homogeneous shear. In the discrete dislocation formulation the dislocations are all of edge character and are modeled as line singularities in an elastic material. Dislocation nucleation, the lattice resistance to dislocation motion and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. A complementary solution that enforces the boundary conditions is obtained via the finite element method. The discrete dislocation solutions give rise to boundary layers in the deformation field and in the dislocation distributions. The back-extrapolated flow strength for symmetric double slip increases with decreasing strip thickness, so that a size effect is observed. The strain gradient plasticity theory used here is also found to predict a boundary layer and a size effect. Nonlocal material parameters can be chosen to fit some, but not all, of the features of the discrete dislocation results. Additional physical insight into the slip distribution across the strip is provided by simple models for an array of mode II cracks.

On the magneto-elastic properties of elastomer–ferromagnet composites

Abstract: We study the macroscopic magneto-mechanical behavior of composite materials consisting of a random, statistically homogeneous distribution of ferromagnetic, rigid inclusions embedded firmly in a non-magnetic elastic matrix. Specifically, for given applied elastic and magnetic fields, we calculate the overall deformation and stress–strain relation for such a composite, correct to second order in the particle volume fraction. Our solution accounts for the fully coupled magneto-elastic interactions; the distribution of magnetization in the composite is calculated from the basic minimum energy principle of magneto-elasticity.

Thermomechanical response of AL-6XN stainless steel over a wide range of strain rates and temperatures

Abstract: To understand and model the thermomechanical response of AL-6XN stainless steel, uniaxial compression tests are performed on cylindrical samples, using an Instron servohydraulic testing machine and UCSD's enhanced Hopkinson technique. True strains exceeding 40% are achieved in these tests, over the range of strain rates from 0.001/s to about 8000/s, and at initial temperatures from 77 to 1000 K. In an effort to understand the underlying deformation mechanisms, some interrupted tests involving temperature and low- and high-strain rates, are also performed. The microstructure of the undeformed and deformed samples is observed by optical microscopy. The experimental results show: (1) AL-6XN stainless steel displays good ductility (strain >40%) at low temperatures and high-strain rates, with its ductility increasing with temperature; (2) at high-strain rates and 77 K initial temperature, adiabatic shearbands develop at strains exceeding about 40%, and the sample breaks, while at low-strain rates and 77 K, axial microcracks develop at strains close to 50% or greater; (3) dynamic strain aging occurs at temperatures between 500 and 1000 K and at a strain rate of 0.001/s, with the peak value of the stress occurring at about 800 K, and becoming more pronounced with increasing strain and less pronounced with increasing strain rate; and (4) the microstructure of this material evolves with temperature, but is not very sensitive to the changes in the strain rate. Finally, based on the mechanism of dislocation motion, paralleled with a systematic experimental investigation, a physically based model is developed for the deformation behavior of this material, including the effect of viscous drag on the motion of dislocations, but excluding the dynamic strain aging effects. The model predictions are compared with the results of the experiments. Good agreement between the theoretical predictions and experimental results is obtained. In order to verify the model independently of the experiments used in the modeling, additional compression tests at a strain rate of 8000/s and various initial temperatures, are performed, and the results are compared with the model predictions. Good correlation is observed.

Microstructure-sensitive design of a compliant beam

Abstract: We show that mechanical design can be conducted where consideration of polycrystalline microstructure as a continuous design variable is facilitated by use of a spectral representation space. Design of a compliant fixed-guided beam is used as a case study to illustrate the main tenets of the new approach, called microstructure-sensitive design (MSD). Selection of the mechanical framework for the design (e.g., mechanical constitutive model) dictates the dimensionality of the pertinent representation. Microstructure is considered to be comprised of basic elements that belong to the material set. For the compliant beam problem, these are uni-axial distribution functions. The universe of pertinent microstructures is found to be the convex hull of the material set, and is named the material hull. Design performance, in terms of specified design objectives and constraints, is represented by one or more surfaces (often hyperplanes) of finite dimension that intersect the material hull. Thus, the full range of microstructure, and concomitant design performance, can be exploited for any material class. Optimal placement of the salient iso-property surfaces within the material hull dictates the optimal set of microstructures for the problem. Extensions of MSD to highly constrained design problems of higher dimension is also described.

Physically based strain invariant set for materials exhibiting transversely isotropic behavior

Abstract: A novel set of 5 strain invariants for materials exhibiting transversely isotropic behavior with respect to a reference configuration is developed through analysis of physical attributes of deformation. Experimental advantage for hyperelastic materials is demonstrated by showing that common tests can directly determine terms in W , the strain energy per unit reference volume. An analysis of symmetry allows the general form of W to be refined a priori. Moreover, this kinematics framework is potentially useful for solving inverse problems since the 5 response terms in the Cauchy stress t are mostly orthogonal (9 of the 10 mutual inner products vanish). For small deformation they are fully orthogonal (all 10 inner products vanish). A response term in t consists of an invariant response function multiplied by its associated kinematic tensor.

Continuum and atomistic studies of intersonic crack propagation

Abstract: Mechanisms of intersonic crack propagation along a weak interface under shear dominated loading are studied by both molecular dynamics and continuum elastodynamics methods. Part of the objective is to test if continuum theory can accurately predict the critical time and length scales observed in molecular dynamics simulations. To facilitate the continuum-atomistic linkage, the problem is selected such that a block of linearly isotropic, plane-stress elastic solid consisting of a two-dimensional triangular atomic lattice with pair interatomic potential is loaded by constant shear velocities along the boundary. A pre-existing notch is introduced to represent an initial crack which starts to grow at a critical time after the loading process begins. We observe that the crack quickly accelerates to the Rayleigh wave speed and, after propagating at this speed for a short time period, nucleates an intersonic daughter crack which jumps to the longitudinal wave speed. The daughter crack emerges at a distance ahead of the mother crack. The challenge here is to test if a continuum elastodynamics analysis of the same problem can correctly predict the length and time scales observed in the molecular dynamics simulations. We make two assumptions in the continuum analysis. First, the crack initiation is assumed to be governed by the Griffith criterion. Second, the nucleation of the daughter crack is assumed to be governed by the Burridge–Andrew mechanism of a peak of shear stress ahead of the crack tip reaching the cohesive strength of the interface. Material properties such as elastic constants, fracture surface energy and cohesive strength are determined from the interatomic potential. Under these assumptions, it is shown that the predictions based on the continuum analysis agree remarkably well with the simulation results.

Closed-form expressions for the effective coefficients of fibre-reinforced composite with transversely isotropic constituents. I: Elastic and hexagonal symmetry

Abstract: The purpose of this paper is to determine the effective elastic, piezoelectric and dielectric properties of reinforced piezoelectric composite materials with unidirectional cylindrical fibres periodically distributed in two directions at an angle π/3 by means of the asymptotic homogenization method. Each periodic cell of the medium is a binary piezoelectric composite wherein both constituents are homogeneous piezoelectric materials with transversely isotropic properties. This paper makes use of some results obtained in Part I. Relatively simple closed-form expressions for the overall properties are obtained by means of potential methods of a complex variable and Weierstrass elliptic and related functions. Schulgasser universal type of relations are derived in a simple new way by means of the homogenized asymptotic method. The number of local problems to get all coefficients is two. The numerical computation of these effective properties is simple.

A computational model of ceramic microstructures subjected to multi-axial dynamic loading

Abstract: A model is presented for the dynamic finite element analysis of ceramic microstructures subjected to multi-axial dynamic loading. This model solves an initial-boundary value problem using a multi-body contact model integrated with interface elements to simulate microcracking at grain boundaries and subsequent large sliding, opening and closing of microcracks. An explicit time integration scheme is adopted to integrate the system of spatially discretized ordinary differential equations. A systematic and parametric study of the effect of interface element parameters, grain anisotropy, stochastic distribution of interface properties, grain size and grain morphology is carried out. Numerical results are shown in terms of microcrack patterns and evolution of crack density, i.e., damage kinetics. The brittle behavior of the microstructure as the interfacial strength decreases is investigated. Crack patterns on the representative volume element vary from grains totally detached from each other to a few short cracks, nucleated at voids, except, for the case of microstructures with initial flaws. Grain elastic anisotropy seems to play an important role in microfracture presenting higher values of crack density than the isotropic case. The computational results also show that decreasing the grain size results in a decrease in crack density per unit area at equal multiaxial dynamic loading. Histograms of crack density distribution are presented for the study of the stochasticity of interface parameters. Finally, a strong dependency with grain shape is observed for different microstructures generated using Voronoi Tessellation. The micromechanical model here discussed allows the study of material pulverization upon unloading. The qualitative and quantitative results presented in this article are useful in developing more refined continuum theories on fracture properties of ceramics.

A new proof that the number of linear elastic symmetries is eight

Abstract: It is shown here that there are exactly eight different sets of symmetry planes that are admissible for an elasticity tensor. Each set can be seen as the generator of an associated group characterizing one of the traditional symmetry classes.

Numerical evaluation of effective elastic properties of graphite fiber tow impregnated by polymer matrix

Abstract: Homogenized elastic material properties are found for a fibrous graphite–epoxy composite system with fibers randomly distributed within a transverse plane section of the composite aggregate using the finite element method. To enhance efficiency of the numerical analysis the real microstructure is replaced by a material representative volume element, represented here by a periodic unit cell consisting of a small number of particles, which statistically resembles the actual composite. Such a unit cell is derived from a simple optimization procedure formulated in terms of various statistical descriptors characterizing the microstructure of the random medium. In the present approach the two-point probability and the second order intensity functions are employed. The upper bound on the macroscopic elastic stiffnesses then follows from the principle of minimum potential energy. The Finite Element Method (FEM) is used to carry out the numerical analysis. Results derived herein confirm applicability of the present approach and suggest that the unit cell, which effectively exploits the knowledge of the material's statistics of the composite, is more reliable then the one constructed simply as a cut of a small part of the real microstructure.

Homogenization method for a discrete-continuum simulation of dislocation dynamics

Abstract: The question of the description of the elastic fields of dislocations and of the plastic strains generated by their motion is central to the connection between dislocation-based and continuum approaches of plasticity. In the present work, the homogenization of the elementary shears produced by dislocations is discussed within the frame of a discrete-continuum numerical model. In the latter, a dislocation dynamics simulation is substituted for the constitutive form traditionally used in finite element calculations. As an illustrative example of the discrete-continuum model, the stress field of single dislocations is obtained as a solution of the boundary value problem. The hybrid code is also shown to account for size effects originating from line tension effects and from stress concentrations at the tip of dislocation pile-ups.

Deformation of thermosetting resins at impact rates of strain. Part I: Experimental study

Abstract: Three thermosetting resins have been tested in compression at strain rates between 10−3 and 5×10 3 s −1 . A smaller number of tests have been performed on the same resins at similar strain rates in tension. The testing technique is described and the results obtained are presented. Significant differences between the three materials were found over the whole range of strain rates. All three exhibited a pronounced strain rate sensitivity. Temperature measurements, performed in compression tests at the higher strain rates, showed evidence of adiabatic heating. This revealed the presence of energy storage mechanisms in both yield and strain–stiffening regimes.

Dynamics of nanoscale pattern formation of an epitaxial monolayer

Abstract: A two-phase monolayer grown on an elastic substrate may form stripes or dots on the scale of nanometers. Sometimes these stripes and dots order into superlattices. This paper reports on a simulation on the basis of a model proposed by the authors recently. The size selection and spatial ordering result from two competing actions: the phase boundary energy tends to coarsen the phases, and the concentration-dependent surface stress tends to refine the phases. A nonlinear diffusion equation couples the concentration field in the epilayer and the stress field in the substrate. The simulation reveals remarkably rich dynamics. An epilayer may evolve into various patterns, suggesting a significant degree of experimental control in growing nanoscale superlattices, just as in growing atomic crystals.

Fracture in mechanism-based strain gradient plasticity

Abstract: In a remarkable series of experiments, Elssner, Korn and Ruehle (Scripta Metall. Mater. 31 (1994) 1037) observed cleavage fracture in ductile materials, a phenomenon that cannot be explained by classical plasticity theories. In this paper we present a study of fracture by the theory of mechanism-based strain gradient (MSG) plasticity (Gao et al., J. Mech. Phys. Solids 47 (1999b) 1239); Huang et al., J. Mech. Phys. Solids 48 (2000a) 99). It is established that, at a distance much larger than the dislocation spacing such that continuum plasticity is applicable, the stress level in MSG plasticity is significantly higher than that in classical plasticity near the crack tip. The numerical results also show that the crack tip stress singularity in MSG plasticity is higher than that in the HRR field, and it exceeds or equals to the square-root singularity. This study provides a means to explain the observed cleavage fracture in ductile material.

Micromechanical modelling of porous materials under dynamic loading

Abstract: The behaviour of porous material under dynamic conditions is assessed by a micromechanical approach. By averaging, a general form for the dynamic macrostress is proposed which recovers the static definition when inertia effects are neglected. In this work, a representative volume element for the porous material is defined as a hollow sphere. Using an approximation of the velocity field and the principle of virtual work, an explicit relationship is found between the macroscopic stress and strain rate. The macrostress tensor is proved to be symmetric, in the present formulation proposed for porous materials. Illustrations are shown for hydrostatic tension or compression and also for axisymmetric loading. In the latter case, the effect of stress triaxiality is captured.