A 3D fourth order fabric tensor approach of anisotropy in granular media

We propose a micromechanical approach for granular media, with a particular account of the texture-induced anisotropy and of the strain localization rule. The approach is mainly based on the consideration of a fourth order fabric tensor able to capture general anisotropy which can be induced by complex distribution of contacts. Incorporation of this fourth order fabric tensor in a suitable homogenization scheme allows to determine the corresponding macroscopic elastic properties of the granular material. For this purpose, in addition to the classical Voigt upper bound, a new kinematics-based localization rule is proposed. It generalizes the one formulated by Cambou et al. [B. Cambou, Ph. Dubujet, F. Emeriault, F. Sidoroff, Eur. J. Mech. A/Solids 14 (1995) 225–276] in the case of an isotropic contact distribution. The results of the complete model compare well to numerical simulations results when available [C.S. Chang, C.L. Liao, Appl. Mech. Rev. 47 (1 Part 2) (1994) 197–207] (case of isotropic distribution of contacts). Finally, the interest of the fourth order fabric tensor based approach combined with the proposed localization rule is shown for different distributions of contacts by comparing its predictions to those given by a second order fabric tensor approach.     

Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method

A numerical technique for modeling fatigue crack propagation of multiple coplanar cracks is presented. The proposed method couples the extended finite element method (X-FEM) [Int. J. Numer. Meth. Engng. 48 (11) (2000) 1549] to the fast marching method (FMM) [Level Set Methods & Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, Cambridge University Press, Cambridge, UK, 1999]. The entire crack geometry, including one or more cracks, is represented by a single signed distance (level set) function. Merging of distinct cracks is handled naturally by the FMM with no collision detection or mesh reconstruction required. The FMM in conjunction with the Paris crack growth law is used to advance the crack front. In the X-FEM, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity [Comput. Meth. Appl. Mech. Engng. 139 (1996) 289]. This enables the domain to be modeled by a single fixed finite element mesh with no explicit meshing of the crack surfaces. In an earlier study [Engng. Fract. Mech. 70 (1) (2003) 29], the methodology, algorithm, and implementation for three-dimensional crack propagation of single cracks was introduced. In this paper, simulations for multiple planar cracks are presented, with crack merging and fatigue growth carried out without any user-intervention or remeshing.     

Investigation of near-tip displacement fields of a crack normal to and terminating at a bimaterial interface under mixed-mode loading

The displacement fields near the tip of a crack in a bimaterial joint under mixed-mode loading have been investigated by using a highly sensitive moiré interferometry technique. With a scheme adopted for data reduction, the study find that the near-tip displacements due respectively to opening and slipping loads are non-coupled and separable. The study on the parameters characteristic of the crack-tip deformation include: (1) the strength of stress singularity; (2) the angular distribution; and (3) the stress intensity factors K_I and K_II. The characteristic parameters determined experimentally are compared with the theoretical ones for the problem given by Zak and Williams [J. Appl. Mech. 30 (1963) 142], and Chen [Eng. Fract. Mech. 49 (4) (1994) 517].     

Fracture mechanical characterisation of mixed-mode toughness of thermoplast/glass interfaces

According to studies conducted by, e.g. Liechti and Chai [J. Appl. Mech. 58 (1991) 680], Yuuki et al. [Eng. Fract. Mech. 47 (3) (1994) 367] and Ikeda and Miyazaki [Eng. Fract. Mech. 59 (6) (1998) 725], a significant increase of interfacial toughness is observed, whenever the magnitude of the bond tangential shear load of the asymptotic elastic mixed-mode state is increased in either direction. Between these extremes the interfacial toughness curve exhibits a pronounced minimum, which, according to Hutchinson and Suo [Mater. Sci. Eng. A 107 (1989) 135] is believed to represent the so-called intrinsic adhesion, i.e. the failure toughness under pure local mode I loading. Within linear elasticity, the biaxial, singular near-tip solution for an open interface crack may be employed for characterising the local stress state as long as non-linearities such as, e.g. crack-wall contact and plastic flow are contained within a zone small enough compared to the extension of the singular opening-dominated fields. Then, the critical stress state is given in terms of bimaterial stress intensity factors K_1,c, K_2,c and the fracture toughness under mixed-mode loading may be expressed in terms of the critical energy release rate as a function of the mode-mixity ψ=tan⁻¹K_2,c/K_1,c. The stress intensities have to be extracted from a stress analysis of the specimen under the critical load, which in the present work is performed by means of an FE-model of the loaded sample.     

半刚接钢框架内填RC 墙结构简化分析模型

该文提出了一种用于分析半刚接钢框架内填RC 墙结构(简称PSRCW)滞回性能的简化分析模型(即斜向板带模型),基于混凝土应力-应变关系给出了斜向板带的轴力-位移关系曲线,采用Pivot 塑性滞回模型模拟斜向板带的力学行为。采用有限元方法分析了板带恢复力模型、板带数量及倾角对PSRCW 结构斜向板带模型的影响,结果表明Pivot 塑性滞回模型可较好地模拟斜向板带的滞回性能,可采用7 条以上板带及40°~50°之间板带倾角描述PSRCW 结构的整体性能。应用该简化模型对有关试件进行了滞回性能模拟,并与试验结果比较,两者吻合良好。     

Micromechanics-based viscoelastic damage model for particle-reinforced polymeric composites

The objective of this study is to develop a micromechanics-based viscoelastic damage model that can predict the overall viscoelastic behavior of particle-reinforced polymeric composites undergoing damage. The emphasis here is that the present model successfully combines a rate-dependent viscoelastic constitutive model and a damage model. The Laplace transform based on the Boltzmann superposition principle and the ensemble-volume averaged method suggested by Ju and Chen (Acta Mech 103:103–121, 1994a; Acta Mech 103:123–144, 1994b) are extended toward effective viscoelastic properties. Further, the probability of the distribution function of Weibull (J Appl Mech 18:293–297, 1951) is adopted to describe a damage model that is dependent on damage parameters. A series of numerical simulations including parametric studies, and experimental comparisons are carried out to give insight into the potential capacity of the present micromechanics-based viscoelastic damage framework.     

Application of the theory of representation to describe yielding of anisotropic aluminum alloys

In this paper a rigorous method to extend any isotropic yield criterion such as to describe any type of material symmetry is developed. Using this approach, extensions of Drucker’s [J. Appl. Mech. 16 (1949) 349] isotropic yield criterion to transverse isotropy, cubic symmetries, and orthotropy are presented. Comparison with representative sets of data show that the present theory can successfully describe anisotropy of both the plastic strain ratio and yield of aluminum thin sheets as well as the yield anisotropy of extruded bars.     

Progressive damage modeling in fiber-reinforced materials

This paper presents an anisotropic damage model suitable for predicting failure and post-failure behavior in fiber-reinforced materials. In the model the plane stress formulation is used and the response of the undamaged material is assumed to be linearly elastic. The model is intended to predict behavior of elastic-brittle materials that show no significant plastic deformation before failure. Four different failure modes – fiber tension, fiber compression, matrix tension, and matrix compression – are considered and modeled separately. The onset of damage is predicted using Hashin’s initiation criteria [Hashin Z, Rotem A. A fatigue failure criterion for fiber-reinforced materials. J Compos Mater 1973;7:448; Hashin Z. Failure criteria for unidirectional fiber composites. J Appl Mech 1980;47:329–34] and the progression of damage is controlled by a new damage evolution law, which is easy to implement in a finite element code. The evolution law is based on fracture energy dissipation during the damage process and the increase in damage is controlled by equivalent displacements. The issues related to numerical implementation, such as mesh sensitivity and convergence in the softening regime, are also addressed.     

Thermoelastic composites with columnar microstructure and cylindrically anisotropic phases. Part I: Exact results

A wide class of composite materials, which are in this paper referred to as having columnar microstructure, posses the microgeometrical characteristic that the constituent phases are homogeneous along one and only one direction. This class includes as an important subclass all the composites consisting of a homogeneous matrix reinforced by aligned parallel continuous homogeneous fibers. In the present work, considering a transversely isotropic composite with columnar microstructure and with cylindrically anisotropic phases, a number of exact results are established for effective thermoelastic moduli by modelling the composite as a nested composite cylinder assemblage. The results obtained in this work extend those of Hashin and Rosen [Z. Hashin, B.W. Rosen, The elastic moduli of fiber-reinforced materials, ASME J. Appl. Mech. 31 (1964) 223–232] and Hashin [Z. Hashin, Thermoelastic properties and conductivity of carbon/carbon fiber composites, Mech. Mater. 8 (1990) 293–308].     

Numerical models of shear fracture propagation

Two-dimensional numerical models using the displacement discontinuity method and the PATH algorithm show that shear fractures can propagate in three different patterns, depending on the lateral normal stress (LNS). Under 0 or very small LNS they propagate by open wing cracks, as shown in many previous results. Under increasing LNS, the extension consists first of a short wing crack followed by a succession of small closed and open segments forming a stair-step pattern. As the LNS increases, the length of the closed segments increases, thus changing the general orientation of the extension. Under sufficiently high LNS the transition is complete, and propagation takes place as a closed shear fracture. These results provide a remarkable confirmation of the theoretical predictions made by Cherepanov [J. Appl. Math. Mech. (English transl. of Prikl. Mate. Mekh.) 30 (1966) 96]. They also explain the difference between the fracture parameters in tension and in shear.     

Development of plastic strips and fracture in the vicinity of two unequal cracks in a plate

We studied the process of development of plastic strains and fracture in tension of a thin infinite plate with two collinear unequal cracks. An ideally elastoplastic material of the plate satisfies the Tresca condition. We investigated the propagation of narrow plastic strips on the continuation of the cracks by using the well-known method for the simulation of such strips by segments with jumps of displacements satisfying the plasticity condition. We also present a general algorithm for the solution of the problem under consideration. Within the framework of this algorithm, the results for two equal cracks are obtained as a special case. In the case of unequal cracks, we computed the value of loading whose application results in the joining of strips lying between the cracks and deduced equations for the determination of the length of these strips and crack tip opening displacements both at the time of joining of the strips and after this event. The numerical analysis of results demonstrates that the largest strips appear (prior to their joining and opening) between the cracks in the vicinities of the tips of the longer crack. According to the strain criterion, the processes of fracture and joining of the cracks are initiated just at the indicated sites. It is shown that, under a load of 0.6 _t, at the ends of cracks, one observes the initiation of secondary strips following the primary ones and making an angle of 59° with them (just as in the case of a single crack). We also indicate the principal shortcomings of the solution of the problem suggested by Theocaris [Eng. Fract. Mech,18, No. 3, 545–560 (1981)].Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 6, pp. 17–29, November – December, 1995.     

An RVE-based micromechanical analysis of fiber-reinforced composites considering fiber size dependency

An RVE-based micromechanical elastic damage model considering fiber size dependency is presented to predict the effective elastic moduli and interfacial damage evolution in fiber-reinforced composites. To assess the validity of the present model, the predictions based on the proposed micromechanical elastic model are compared with Hashin’s theoretical bounds [Hashin Z. Analysis of properties of fiber composites with anisotropic constituents. J Appl Mech: Trans ASME 1979;46:543–50]. The proposed micromechanical elastic damage model is then exercised under uniaxial loading conditions to show the overall elastic damage behavior of the proposed micromechanical framework and to illustrate fiber size effect on the behavior of the composites. Moreover, comparisons between the present prediction and experimental data are made to further illustrate the capability of the proposed micromechanical framework for predicting the elastic damage behavior of fiber-reinforced composites.     

Theory and finite element computations of a unified cyclic phase transformation model for monocrystalline materials at small strains

After a survey the refined numerical treatment and verification is presented for a rate-independent macroscopic unified PT material model (including mass conservation with respect to phase fractions and covexified free energy) by Govindjee and Miehe (Comput Methods Appl Mech Eng 191:215–238, 2001) for describing SME and SE effects within a linear kinematic setting. Special attention is given to temperature dependent PTs. The material model was implemented into ABAQUS via the UMAT material interface in 2004. Validation of this PT model is carried out with experimental data supplied by Xiangyang et al. (J Mech Phys Solids 48:2163–2182, 2000), using 3D finite element computations. Experimentally gained material data from different sources are used and numerical results of energy barriers for PTs are given. Another feature is the simulation of suppressed shape memory effects by quasiplastic temperature induced PT. Furthermore, a plane strain problem is treated with comparisons of butterfly shaped expansions of martensitic PT and plastic deformation, correspondingly.     

Simulation of solitary waves in a monodisperse granular chain using COMSOL multiphysics: localized plastic deformation as a dissipation mechanism

Solitary wave propagation in a monodisperse granular chain was simulated using the finite element method. The model was built to address a discrepancy between numerical and experimental results from Lazaridi and Nesterenko (J Appl Mech Tech Phys 26(3):405–408 1985). In their work, solitary waves were generated in a chain of particles through impact of a piston, and results were quantified by comparing the chains’ reactions to a rigid wall. Their numerical calculations resulted in a solitary wave with a force amplitude of 83 N, while it was measured experimentally to be 71 N. In the present work, the configuration of the granular chain and piston was duplicated from Lazaridi and Nesterenko (J Appl Mech Tech Phys 26(3):405–408, 1985). Qualitatively similar solitary waves were produced, and von Mises stress values indicated that localized plastic deformation is possible, even at low piston impact velocities. These results show that localized plastic deformation was a likely source of dissipation in experiments performed by Lazaridi and Nesterenko.     

Compression moulding of SMC: In situ experiments,modelling and simulation

Compression mouldings of commercial SMC were performed with an instrumented industrial press under various process conditions. Results underline the influence of process parameters such as the initial SMC temperature, the axial punch velocity and the geometry of the mould on local normal stress levels. They also show negligible fibre-bundle segregation in the principal plane of the moulded parts. Thereby, a one-phase plug flow shell model is proposed as a direct extension of the plug flow model proposed by M.R. Barone and D.A. Caulk [J Appl Mech 53(191):1986;361–70]. In the present approach, the SMC is considered as a power-law viscous medium exhibiting transverse isotropy. The shell model is implemented into a finite element code especially developed for the simulation of compression moulding of composite materials. Simulation and experimental results are compared, emphasizing the role of the SMC rheology on the overall recorded stress levels. Despite the simplicity of the model, rather good comparisons are obtained.     

On vibrations of thin plates with one-dimensional periodic structure

A new approach to problems of thin plates with a periodic structure along one direction in the planes parallel to the plate midplane is proposed. The model is a certain generalisation of the length-scale models for periodic plates, which make it possible to take into account the effect of periodicity cell size on the dynamics of plates with two-dimensional periodic structure [J. J drysiak, C. Woźniak, J. Theoret. Appl. Mech. 33 (1995) 337–349; J. J drysiak, Eng. Trans. 46 (1998) 73–87]. In order to describe this effect in stationary processes, e.g., a plate stability, and non-stationary processes for one-dimensional periodic plates the generalised model is presented in this paper. In order to show differences between governing equations of the extended model and the model for plates with two-dimensional periodic structure or the homogenised model vibrations problems of one-dimensional periodic plates will be analysed.     

Strain-injection and crack-path field techniques for 3D crack-propagation modelling in quasi-brittle materials

This paper presents a finite element approach for modelling three-dimensional crack propagation in quasi-brittle materials, based on the strain injection and the crack-path field techniques. These numerical techniques were already tested and validated by static and dynamic simulations in 2D classical benchmarks [Dias et al., in: Monograph CIMNE No-134. International Center for Numerical Methods in Engineering, Barcelona, (2012); Oliver et al. in Comput Methods Appl Mech Eng 274:289–348, (2014); Lloberas-Valls et al. in Comput Methods Appl Mech Eng 308:499–534, (2016)] and, also, for modelling tensile crack propagation in real concrete structures, like concrete gravity dams [Dias et al. in Eng Fract Mech 154:288–310, (2016)]. The main advantages of the methodology are the low computational cost and the independence of the results on the size and orientation of the finite element mesh. These advantages were highlighted in previous works by the authors and motivate the present extension to 3D cases. The proposed methodology is implemented in the finite element framework using continuum constitutive models equipped with strain softening and consists, essentially, in injecting the elements candidate to capture the cracks with some goal oriented strain modes for improving the performance of the injected elements for simulating propagating displacement discontinuities. The goal-oriented strain modes are introduced by resorting to mixed formulations and to the Continuum Strong Discontinuity Approach (CSDA), while the crack position inside the finite elements is retrieved by resorting to the crack-path field technique. Representative numerical simulations in 3D benchmarks show that the advantages of the methodology already pointed out in 2D are kept in 3D scenarios.     

Analysis of a delayed fracture criterion for lifetime prediction of viscoelastic polymer materials

In this work a multi-axial yield/failure model for viscoelastic/plastic materials is applied, which was developed by Naghdi and Murch (in J.?Appl. Mech. 30:321?C328, 1963) and later extended and refined by Crochet (in J.?Appl. Mech. 33:327?C334, 1966), to predict long-term creep rupture of polymers. The criterion defines a function, which depends on time, the viscoelastic properties and applied stress, to establish an empirical law with creep yield (fracture). In this work a linear relationship is proposed, defined as a time-dependent failure criterion, which can be applied for extrapolation purposes. A comparative analysis using energy-based failure criteria is performed. It is proved, for the polymers considered in this study, that the proposed time-dependent failure criterion holds for long times. Experimental data are used to illustrate the applicability of this time-dependent failure criterion.