Kink-fold onset and development based on the maximum strength theorem

The structure of interest occupies initially a rectangular-shaped domain and is composed of a laminated material with weak interfaces defining the horizontal bedding. It is subjected to a compressive lateral force parallel to the bedding. The postulated fold kinematics relies on the existence of a kink band with two parallel sharp boundaries, or hinges, separating two rigid blocks. One block moves upward, the other sideways, by distances defining the fold amplitude and the horizontal shortening, respectively. Internal work is assumed to be done only along the hinges and the weak interfaces. The orientations of the hinges (hinge dip) and of the beds within the kink band (kink dip) are optimised for every fold amplitude to provide the least upper bound on the compressive force according to the maximum strength theorem.It is shown that the fold onset requires the introduction of a compaction mechanism for the hinges. The kink initiates as a sub-vertical compaction band of finite thickness equal to the bed thickness times the sine of the friction angle over the bedding. During the first phase of the fold development, the kink band rotates with the property that the sum of the kink dip and the hinge dip is always complementary to the friction angle over the bedding. Each bed along the hinges sees the activation of two deformation mechanisms: compaction and opening. The boundary between the regions over each bed where they are activated migrates from the bottom of the bed—pure compaction at the onset—towards a position at 90% of the bed thickness—development dominantly controlled by opening. The second phase of the fold development is marked by a thickening of the kink band with minor evolution of the dips. This two-phase development leads to a sharp decrease of the compressive load from the onset, a minimum as the two dips are approximately equal and then a moderate increase in applied load. In conclusion, it is noted that such combination of postulated fold kinematics and the application of the maximum strength theorem to optimise the structure could be generalised to folding in the presence of ramps, providing a useful tool to comprehend the mechanics of fold-and-thrust belts and of accretionary wedges.     

Kink band instability in layered structures

A recent two-dimensional prototype model for the initiation of kink banding in compressed layered structures is extended to embrace the two propagation mechanisms of band broadening and band progression. As well as interlayer friction, overburden pressure and layer bending energy, the characteristics of transverse layer compressibility and foundation stiffness are now included. Experiments on constrained layers of paper show good agreement with the predictions of angle of orientation, kink band width and post-kink load-deflection response obtained from the model.     

The microbuckling failure of Dyneema~? composites under compression

Two grades of Dyneema~?composite laminates with the commercial designations of HB26 and HB50 were cut into blocks with or without an edge crack and compressed in the longitudinal fiber direction. The cracked and uncracked specimens show similar compressive responses including failure pattern and failure load. The two grades of Dyneema~? composites exhibits different failure modes: a diffuse, sinusoidal buckling pattern for Dyneema~? HB50 due to its weak matrix constituent and a kink band for Dyneema~? HB26 due to its relatively stronger matrix constituent. An effective finite element model is used to simulate the collapse of Dyneema~? composites, and the sensitivity of laminate compressive responses to the overall effective shear modulus, interlaminar shear strength, thickness and imperfection angle are investigated. The change of failure mode from kink band to sinusoidal buckling pattern by decreasing the interlaminar shear strength is validated by the finite element analyses.     

Dynamic response of a rigid plastic simply supported imperfect beam subjected to a uniform intense dynamic loading

This paper proposes a theoretical analysis for the dynamic response of a rigid perfectly plastic simply supported beam with an imperfection in the midspan cross-section under uniform step, pulse, and impulsive loading when support is assumed to be free to move inward. The complete solutions for an entire dynamic response process are given and the relationship between the distribution of energy dissipated at plastic hinges and the parameter of imperfection is also discussed.     

Effects of spatial grain orientation distribution and initial surface topography on sheet metal necking

The finite element method is used to numerically simulate localized necking in AA6111-T4 under stretching. The measured EBSD data (grain orientations and their spatial distributions) are directly incorporated into the finite element model and the constitutive response at an integration point is described by the single crystal plasticity theory. We assume that localized necking is associated with surface instability, the onset of unstable growth in surface roughening. It is demonstrated that such a surface instability/necking is the natural outcome of the present approach, and the artificial initial imperfection necessitated by the macroscopic M–K approach [Marciniak and Kuczynski (1967). Int. J. Mech. Sci. 9, 609–620] is not relevant in the present analysis. The effects of spatial orientation distribution, material strain rate sensitivity, texture evolution, and initial surface topography on necking are discussed. It is found that localized necking depends strongly on both the initial texture and its spatial orientation distribution. It is also demonstrated that the initial surface topography has only a small influence on necking.     

Effects of texture on shear band formation in plane strain tension/compression and bending

In this study, effects of typical texture components observed in rolled aluminum alloy sheets on shear band formation in plane strain tension/compression and bending are systematically studied. The material response is described by a generalized Taylor-type polycrystal model, in which each grain is characterized in terms of an elastic–viscoplastic continuum slip constitutive relation. First, a simple model analysis in which the shear band is assumed to occur in a weaker thin slice of material is performed. From this simple model analysis, two important quantities regarding shear band formation are obtained: i.e. the critical strain at the onset of shear banding and the corresponding orientation of shear band. Second, the shear band development in plane strain tension/compression is analyzed by the finite element method. Predictability of the finite element analysis is compared to that of the simple model analysis. Third, shear band developments in plane strain pure bending of a sheet specimen with the typical textures are studied. Regions near the surfaces in a bent sheet specimen are approximately subjected to plane strain tension or compression. From this viewpoint, the bendability of a sheet specimen may be evaluated, using the knowledge regarding shear band formation in plane strain tension/compression. To confirm this and to encompass overall deformation of a bent sheet specimen, including shear bands, finite element analyses of plane strain pure bending are carried out, and the predicted shear band formation in bent specimens is compared to that in the tension/compression problem. Finally, the present results are compared to previous related studies, and the efficiency of the present method for materials design in future is discussed.     

双材料单伸臂叠合梁的界面滑移与自振特性分析

将叠合梁划分为接触区和分离区,接触区界面间的摩擦作用会对叠合梁的滑移、刚度和自振频率产生影响.本文给出了单伸臂叠合梁在均布荷载和集中力作用下,考虑叠合界面摩擦作用的滑移应变和滑移分布的表达式;推导了考虑叠合界面间摩擦力及摩擦力产生的抵抗弯矩共同作用下的截面刚度.假设梁按等波长和等刚度两种形式自由振动,运用传递矩阵法推导...     

Atomistic damage mechanisms during hypervelocity projectile impact on AlN: A large-scale parallel molecular dynamics simulation study

Atomistic mechanisms of damage initiation during hypervelocity (15 km/s) impact on an AlN coating is investigated using parallel molecular-dynamics simulations involving 209 million atoms. On impact a strong shock wave is generated, which then splits into an elastic precursor and a structural phase transformation (SPT) waves, the latter driving a wurtzite to rocksalt structural transition. During its development, the SPT wave induces plastic processes in the intact wurtzite material, which in turn facilitate the nucleation and growth of brittle cracks. Specifically, the interface between the transformed (rocksalt) and untransformed (wurtzite) regions acts as a source of nanocavities and kink bands. They further interact with stress release waves reflected from the back surface and create cracks in mode I, from the nanocavities, and in mode II, from the kink band superdislocation boundary. Stresses are evaluated using a stoichiometric-preserving formula for virial local averages on inhomogeneous binary systems. Defects are analyzed using shortest-path ring statistics.     

Kink band propagation in layered structures

Confined layered structures in layer-parallel compression exhibit kink band deformation that has an associated severe initial instability. However, once the first kink band forms the system restabilizes and the bands then propagate in two mechanisms: band broadening and band progression. Previous work on triggering the initial instability and band broadening is now extended to include band progression. A new model for this propagation mechanism that successfully accounts for the modulating restabilizing response is presented and quantitative comparisons with the physical experiments yield excellent results.     

Prediction of ductile fracture in tension by bifurcation,localization, and imperfection analyses

In this investigation, it is shown that the onset of ductile fracture in tension can be interpreted as the result of a supercritical bifurcation of homogeneous deformation and that this fact can be applied to predict ductile fracture initiation of materials with general imperfections or flaws. We focus on one dimensional quasi-static simple tension for rate-independent isotropic plastic materials. For deformation beyond the bifurcation point, multiple equilibrium paths appear. The homogeneous deformation, as one of the equilibrium paths, loses stability while the inhomogeneous paths are stable, thus indicating the occurrence of strain localization. This investigation also provides a physical example for the application of the Lambert W function in material localization analyses. Material instability is treated as the instability of a static system with dynamic perturbation. We also address the presence of microvoids in a power law plastic material as an unfolding of the supercritical pitchfork bifurcation. The imperfect system, idealized as spherical voids within the plastic matrix, is analyzed using the familiar Gurson model which is based on the presumption of a randomly voided material and characterized by the volume fraction of voids. If, in addition, the sizes of the microvoids are known, this then provides a length scale for the imperfection zone. In this manner, relevance to the sample size effects of strain-to-failure for ductile fracture initiation is addressed by considering separate zones with variations in void volume fractions. Fracture initiation predictions are presented and compare very well to existing experimental results.     

Engineering measures for preventing upheaval buckling of buried submarine pipelines

In-service hydrocarbons must be transported at high temperature and high pressure to ease the flow and to prevent the solidification of the wax fraction.The high temperature and high pressure will induce the additional stress in the pipeline,which results in the upheaval buckling of the pipeline.If such expansion is resisted,e.g.,by the frictional effects of the foundation soil over a kilometer or of a pipeline,the compressive axial stress will be set up in the pipe-wall.When the stress exceeds the constraint of the foundation soil on the pipeline,suddenly-deforming will occur to release the internal stress,similar to the sudden deformation of the strut due to stability problems.The upheaval buckling may jeopardize the structural integrity of the pipeline.Therefore,effective engineering measures against this phenomenon play an important role in the submarine pipeline design.In terms of the pipeline installation and protection measures commonly used in Bohai Gulf,three engineering measures are investigated in great details.An analytical method is introduced and developed to consider the protection effect of the anti-upheaval buckling of the pipeline.The analysis results show that the amplitude of the initial imperfection has a great effect on the pipeline thermal upheaval buckling.Both trenching and burial and discrete dumping are effective techniques in preventing the pipeline from buckling.The initial imperfection and operation conditions of the pipelines determine the covered depth and the number of layers of the protection measures.     

Limit analysis of masonry vaults by means of curved shell finite elements and homogenization

The study of masonry vaults should take into account the essentials of the material “masonry” – i.e. heterogeneity, almost no resistance to tension combined with a good compressive strength and a high friction coefficient, as well as the overall importance of the geometry for achieving the equilibrium.In this paper, a new six-noded triangular curved element, specifically developed for the kinematic limit analysis of masonry shells, is presented. Plastic dissipation is allowed only at the interfaces (generalized cylindrical hinges) between adjoining elements for combined membrane actions, bending moment, torsion and out-of-plane shear, as it is required for the analysis of thick (Reissner–Mindlin) shells. An upper bound of the collapse load is so obtained, since, looking at the dual formulation, the admissibility of the stress state is imposed only at the element boundaries. Masonry strength domain at each interface between contiguous triangular elements is evaluated resorting to a suitable upper bound FE homogenization procedure. The model is assessed through several numerical simulations on a number of masonry shells experimentally tested until collapse. In particular, the dependence of the collapse multiplier on the mesh and on the material parameters (sensitivity analysis) is thoroughly discussed.     

Mechanical properties of nanostructure of biological materials

Natural biological materials such as bone, teeth and nacre are nanocomposites of protein and mineral with superior strength. It is quite a marvel that nature produces hard and tough materials out of protein as soft as human skin and mineral as brittle as classroom chalk. What are the secrets of nature? Can we learn from this to produce bio-inspired materials in the laboratory? These questions have motivated us to investigate the mechanics of protein-mineral nanocomposite structure. Large aspect ratios and a staggered alignment of mineral platelets are found to be the key factors contributing to the large stiffness of biomaterials. A tension-shear chain (TSC) model of biological nanostructure reveals that the strength of biomaterials hinges upon optimizing the tensile strength of the mineral crystals. As the size of the mineral crystals is reduced to nanoscale, they become insensitive to flaws with strength approaching the theoretical strength of atomic bonds. The optimized tensile strength of mineral crystals thus allows a large amount of fracture energy to be dissipated in protein via shear deformation and consequently enhances the fracture toughness of biocomposites. We derive viscoelastic properties of the protein-mineral nanostructure and show that the toughness of biocomposite can be further enhanced by the viscoelastic properties of protein.     

微孔洞生长对板材拉伸过程中变形局部化的影响

本文在作者提出的含孔洞材料下限本构方程的基础上，采用了初始缺陷带模型对微孔洞生长及分布对板材拉伸过程中变形局部影响进行了，分析着重研究了细观损演化规律对变形局部化模式及临界应变的影响，并成功预测了ＡＩＳＩ４３４０钢板材拉伸试件变形局部化换稳为及失稳方向。     

Dynamic crack deflection and penetration at interfaces in homogeneous materials: experimental studies and model predictions

We examine the deflection/penetration behavior of dynamic mode-I cracks propagating at various speeds towards inclined weak planes/interfaces of various strengths in otherwise homogeneous isotropic plates. A dynamic wedge-loading mechanism is used to control the incoming crack speeds, and high-speed photography and dynamic photoelasticity are used to observe, in real-time, the failure mode transition mechanism at the interfaces. Simple dynamic fracture mechanics concepts used in conjunction with a postulated energy criterion are applied to examine the crack deflection/penetration behavior and, for the case of interfacial deflection, to predict the crack tip speed of the deflected crack. It is found that if the interfacial angle and strength are such as to trap an incident dynamic mode-I crack within the interface, a failure mode transition occurs. This transition is characterized by a distinct, observable and predicted speed jump as well as a dramatic crack speed increase as the crack transitions from a purely mode-I crack to an unstable mixed-mode interfacial crack.     

Influence of an Asymmetric Follower Force on the Stationary States of a Double-Link Pendulum

It is studied how the asymmetry of the follower force influences the stationary states of an inverted two-link mathematical pendulum with viscoelastic hinges and the upper end elastically fixed. It is shown that if the parameters of the system change, bifurcations of the stationary states leading to fold and cusp catastrophes become possible     

Forming limit comparisons for FCC and BCC sheets

In this paper, numerical simulations of forming limit diagrams (FLDs) are performed based on a rate-sensitive polycrystal plasticity model together with the Marciniak–Kuczynski (M–K) approach. Sheet necking is initiated from an initial imperfection in terms of a narrow band. The deformations inside and outside the band are assumed to be homogeneous, and conditions of compatibility and equilibrium are enforced across the band interfaces. Thus, the polycrystal model need only be applied to two polycrystal aggregates, one inside and one outside the band. Both FCC and BCC crystals are considered with 12 distinct slip systems for an FCC crystal and 24 distinct slip systems for a BCC crystal. The response of an aggregate comprised of many grains is based on an elastic–viscoplastic Taylor-type polycrystal model. With this formulation, the effects of initial imperfection intensity and orientation, crystal elasticity, strain-rate sensitivity, single slip hardening, and latent hardening on the FLD can be assessed. Identical initial textures are considered for both FCC and BCC polycrystals and the predicted FLDs are compared with each other.     

Simulation and interpretation of diffuse mode bifurcation of elastoplastic solids

The diffuse mode bifurcation of elastoplastic solids at finite strain is investigated. The multiplicative decomposition of deformation gradient and the hyperelasto-plastic constitutive relationship are adapted to the numerical bifurcation analysis of the elastoplastic solids. First, bifurcation analyses of rectangular plane strain specimens subjected to uniaxial compression are conducted. The onset of the diffuse mode bifurcations from a homogeneous state is detected; moreover, the post-bifurcation states for these modes are traced to arrive at localization to narrow band zones, which look like shear bands. The occurrence of diffuse mode bifurcation, followed by localization, is advanced as a possible mechanism to create complex deformation and localization patterns, such as shear bands. These computational diffuse modes and localization zones are shown to be in good agreement with the associated experimental ones observed for sand specimens to ensure the validity of this mechanism. Next, the degradation of horizontal sway stiffness of a rectangular specimen due to plane strain uniaxial compression is pointed out as a cause of the bifurcation of the first antisymmetric diffuse mode, which triggers the tilting of the specimen. Last, circular and punching failures of a footing on a foundation are simulated.     

Bending and buckling of a class of nonlinear fiber composite rods

An investigation of the mechanics of bending and buckling is carried out for a class of nonlinear fiber composite rods composed of embedded unidirectional fibers parallel to the rod axis. The specific class of composite considered is one in which the fibers interact with the matrix through a nonlinear Needleman-type cohesive zone [Needleman, A., 1987. A continuum model for void nucleation by inclusion debonding. ASME J. Appl. Mech. 54, 525-531; Needleman, A., 1992. Micromechanical modelling of interfacial decohesion. Ultramicroscopy 40, 203-214]. The primary decohesive mechanism active in bending and buckling of these composite rods is shear slip along the fiber-matrix interfaces allowing the use of a previously developed constitutive relation for antiplane shear response [Levy, A.J., 2000b. The fiber composite with nonlinear interface—part II: antiplane shear. ASME J. Appl. Mech. 67, 733-739]. The formulation requires the specification of a potential interface force-slip law that is assumed to permit interface failure in shear.Four cases of the bending and shearing of beams (concentrated or uniform load on a cantilever or a simply supported beam) are analyzed, each of which exhibits qualitatively distinct response. For certain values of interface parameters, the beam deflection or its gradient at a fixed location can change discontinuously with load. Furthermore, for interface parameter values within a certain range, singular surfaces will exist in uniformly loaded beams where there is a non-uniform distribution of shear stress along the beam length. These singular surfaces divide the beam into regions of maximal and minimal fiber slip and propagate with a rate that varies inversely as the square of the applied load. For other parameter values, singular surfaces will not exist and fiber slip will be diffuse.For the class of nonlinear composite considered, bifurcation and imperfection buckling of pinned-pinned columns is analyzed. For bifurcation buckling, a nonlinear eigenvalue problem is derived and the solution is obtained by Galerkin's method. It is demonstrated that critical loads are influenced by the initial slope, and hence the linear portion, of the interface force-slip relation but the post-buckling response, which in some sense resembles that of plastic buckling, is affected by the entire interface constitutive relation. Imperfection buckling is analyzed in a similar manner by assuming a slight initial curvature of the rod. Sensitivity of the response to imperfection magnitude is discussed as well.     

Electroelastic interaction between piezoelectric screw dislocation and circularly layered inclusion with imperfect interfaces

The interaction between a piezoelectric screw dislocation and an interphase layer in piezoelectric solids is theoretically investigated.Here,the dislocation located at arbitrary points inside either the matrix or the inclusion and the interfaces of the interphase layer are imperfect.By the complex variable method,the explicit solutions to the complex potentials are given,and the electroelastic fields can be derived from them.The image force acting on the dislocation can be obtained by the generalized PeachKoehler formula.The motion of the piezoelectric screw dislocation and its equilibrium positions are discussed for variable parameters.The important results show that,if the inner interface of the interphase layer is imperfect and the magnitude of degree of the interface imperfection reaches the certain value,two equilibrium positions of the piezoelectric screw dislocation in the matrix near the interface are found for the certain material combination which has never been observed in the previous studies(without considering the interface imperfection).