Minimum theorems in 3D incremental linear elastic fracture mechanics

The crack propagation problem for linear elastic fracture mechanics has been studied by several authors exploiting its analogy with standard dissipative systems theory (see e.g. Nguyen in Appl Mech Rev 47, 1994, Stability and nonlinear solid mechanics. Wiley, New York, 2000; Mielke in Handbook of differential equations, evolutionary equations. Elsevier, Amsterdam, 2005; Bourdin et al. in The variational approach to fracture. Springer, Berlin, 2008). In a recent publication (Salvadori and Carini in Int J Solids Struct 48:1362–1369, 2011) minimum theorems were derived in terms of crack tip “quasi static velocity” for two-dimensional fracture mechanics. They were reminiscent of Ceradini’s theorem (Ceradini in Rendiconti Istituto Lombardo di Scienze e Lettere A99, 1965, Meccanica 1:77–82, 1966) in plasticity. Following the cornerstone work of Rice (1989) on weight function theories, Leblond et al. (Leblond in Int J Solids Struct 36:79–103, 1999; Leblond et al. in Int J Solids Struct 36:105–142, 1999) proposed asymptotic expansions for stress intensity factors in three dimensions—see also Lazarus (J Mech Phys Solids 59:121–144, 2011). As formerly in 2D, expansions can be given a Colonnetti’s decomposition (Colonnetti in Rend Accad Lincei 5, 1918, Quart Appl Math 7:353–362, 1950) interpretation. In view of the expression of the expansions proposed in Leblond (Int J Solids Struct 36:79–103, 1999), Leblond et al. (Int J Solids Struct 36:105–142, 1999) however, symmetry of Ceradini’s theorem operators was not evident and the extension of outcomes proposed in Salvadori and Carini (Int J Solids Struct 48:1362–1369, 2011) not straightforward. Following a different path of reasoning, minimum theorems have been finally derived.     

Twenty Years of Magnon Bose Condensation and Spin Current Superfluidity in 3He-B

20 years ago a new quantum state of matter was discovered and identified (Borovik-Romanov et al. in JETP Lett. 40:1033, 1984; 45:124, 1987; 47:478, 1988; Fomin in JETP Lett. 40:1037, 1984; Borovik-Romanov et al. in Sov. Phys. JETP 61:1199, 1985; Fomin in Sov. Phys. JETP 61:1207, 1985; Bunkov et al. in JETP Lett. 43:168, 1986). The observed dynamic quantum state of spin precession in superfluid ³He-B bears the properties of spin current superfluidity, Bose condensation of spin waves—magnons, off-diagonal long-range order and related phenomena of quantum coherence.     

Permutation decoding of codes from generalized Paley graphs

The generalized Paley graphs $\text{ GP }(q,k)$ GP ( q , k ) are a generalization of the well-known Paley graphs. Codes derived from the row span of adjacency and incidence matrices from Paley graphs have been studied in Ghinellie and Key (Adv Math Commun 5(1):93–108, 2011) and Key and Limbupasiriporn (Congr Numer 170:143–155, 2004). We examine the binary codes associated with the incidence designs of the generalized Paley graphs obtaining the code parameters $[\frac{qs}{2}, q-1, s]$ [ q s 2 , q - 1 , s ] or $[qs, q-1,2s]$ [ q s , q - 1 , 2 s ] where $s=\frac{q-1}{k}$ s = q - 1 k . By finding explicit PD-sets we show that these codes can be used for permutation decoding.     

A comparative study between two smoothing strategies for the simulation of contact with large sliding

The numerical simulation of contact problems is still a delicate matter especially when large transformations are involved. In that case, relative large slidings can occur between contact surfaces and the discretization error induced by usual finite elements may not be satisfactory. In particular, usual elements lead to a facetization of the contact surface, meaning an unavoidable discontinuity of the normal vector to this surface. Uncertainty over the precision of the results, irregularity of the displacement of the contact nodes and even numerical oscillations of contact reaction force may result of such discontinuity. Among the existing methods for tackling such issue, one may consider mortar elements (Fischer and Wriggers, Comput Methods Appl Mech Eng 195:5020–5036, 2006; McDevitt and Laursen, Int J Numer Methods Eng 48:1525–1547, 2000; Puso and Laursen, Comput Methods Appl Mech Eng 93:601–629, 2004), smoothing of the contact surfaces with additional geometrical entity (B-splines or NURBS) (Belytschko et al., Int J Numer Methods Eng 55:101–125, 2002; Kikuchi, Penalty/finite element approximations of a class of unilateral contact problems. Penalty method and finite element method, ASME, New York, 1982; Legrand, Modèles de prediction de l’interaction rotor/stator dans un moteur d’avion Thèse de doctorat. PhD thesis, École Centrale de Nantes, Nantes, 2005; Muñoz, Comput Methods Appl Mech Eng 197:979–993, 2008; Wriggers and Krstulovic-Opara, J Appl Math Mech (ZAMM) 80:77–80, 2000) and, the use of isogeometric analysis (Temizer et al., Comput Methods Appl Mech Eng 200:1100–1112, 2011; Hughes et al., Comput Methods Appl Mech Eng 194:4135–4195, 2005; de Lorenzis et al., Int J Numer Meth Eng, in press, 2011). In the present paper, we focus on these last two methods which are combined with a finite element code using the bi-potential method for contact management (Feng et al., Comput Mech 36:375–383, 2005). A comparative study focusing on the pros and cons of each method regarding geometrical precision and numerical stability for contact solution is proposed. The scope of this study is limited to 2D contact problems for which we consider several types of finite elements. Test cases are given in order to illustrate this comparative study.     

Homological models for semidirect products of finitely generated Abelian groups

Let G be a semidirect product of finitely generated Abelian groups. We provide a method for constructing an explicit contraction (special homotopy equivalence) from the reduced bar construction of the group ring of G, ${\overline{B}(\mathsf{\textstyle Z\kern-0.4em Z}[G])}$ , to a much smaller DGA-module hG. Such a contraction is called a homological model for G and is used as the input datum in the methods described in álvarez et?al. (J Symb Comput 44:558–570, 2009; 2012) for calculating a generating set for representative 2-cocycles and n-cocycles over G, respectively. These computations have led to the finding of new cocyclic Hadamard matrices (álvarez et al. in 2006).     

A finite element analysis of the bending and the bendability of metallic sheets

The main objective of this paper is to study the bendability of metallic sheets by using the finite element method. In this aim, two variants of an advanced Gurson-Tvergaard-Needleman model [1, 2] are implemented in the home made FE code LAGAMINE [3, 4] and coupled with the Thomason model to predict the coalescence of voids. This advanced model is an extension of the original one to take into account of the plastic anisotropy and the mixed (isotropic + kinematic) hardening of the matrix. The difference between the two variants is related to the modeling of the damage evolution. As the advanced model is used to study the bending process, its yield function is slightly modified in order to take into account the loadings with negative triaxiality ratios. These present implementations are used to simulate the pure bending process and to predict the bendability of dual phase (DP) steel. The combined effect of an initial geometrical imperfection and damage evolution on the bendability is also studied.     

Goal-oriented explicit residual-type error estimates in XFEM

A goal-oriented a posteriori error estimator is derived to control the error obtained while approximately evaluating a quantity of engineering interest, represented in terms of a given linear or nonlinear functional, using extended finite elements of $Q1$ type. The same approximation method is used to solve the dual problem as required for the a posteriori error analysis. It is shown that for both problems to be solved numerically the same singular enrichment functions can be used. The goal-oriented error estimator presented can be classified as explicit residual type, i.e. the residuals of the approximations are used directly to compute upper bounds on the error of the quantity of interest. This approach therefore extends the explicit residual-type error estimator for classical energy norm error control as recently presented in Gerasimov et al. (Int J Numer Meth Eng 90:1118–1155, 2012a). Without loss of generality, the a posteriori error estimator is applied to the model problem of linear elastic fracture mechanics. Thus, emphasis is placed on the fracture criterion, here the $J$ -integral, as the chosen quantity of interest. Finally, various illustrative numerical examples are presented where, on the one hand, the error estimator is compared to its finite element counterpart and, on the other hand, improved enrichment functions, as introduced in Gerasimov et al. (2012b), are discussed.     

Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS

In this paper we focus on a class of applications involving surface vessels moving at high speeds, or ??planing??. We introduce a Fridsma planing hull benchmark problem, and simulate it using the finite-element-based ALE-VMS (Bazilevs et?al. in Math Models Methods Appl Sci 2012; Takizawa et?al. in Arch Comput Methods Eng 19: 171?C225, 2012) approach. The major reasons for selecting this problem is the relative simplicity of the hull geometry and the existence of high-quality experimental data used for the purposes of validation. The ALE-VMS approach is formulated in the context of the Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) (Tezduyar in Arch Comput Methods Eng 8:83?C130, 2001; Akin et?al. in Comput Fluids 36:2?C11, 2007; Cruchaga et?al. in Int J Numer Methods Fluids 54:1021?C1031, 2007), where the level set technique is used for capturing the air?Cwater interface, and the Arbitrary Lagrangian Eulerian (ALE) method is employed to track the interface between the fluid and structure. In this work, the planing hull structure is treated as a six-degree-of-freedom rigid object. The computational results obtained for the Fridsma hull, which include convergence of the trim angle and drag under mesh refinement, match well with the experimental data.     

Quantized Vortex State in hcp Solid 4He

The quantized vortex state appearing in the recently discovered new states in hcp ⁴He since their discovery (Kim and Chan, Nature, 427:225–227, 2004; Science, 305:1941, 2004) is discussed. Special attention is given to evidence for the vortex state as the vortex fluid (VF) state (Anderson, Nat. Phys., 3:160–162, 2007; Phys. Rev. Lett., 100:215301, 2008; Penzev et al., Phys. Rev. Lett., 101:065301, 2008; Nemirovskii et al., arXiv:0907.0330, 2009) and its transition into the supersolid (SS) state (Shimizu et al., arXiv:0903.1326, 2009; Kubota et al., J. Low Temp. Phys., 158:572–577, 2010; J. Low Temp. Phys., 162:483–491, 2011). Its features are described. The historical explanations (Reatto and Chester, Phys. Rev., 155(1):88–100, 1967; Chester, Phys. Rev. A, 2(1):256–258, 1970; Andreev and Lifshitz, JETP Lett., 29:1107–1113, 1969; Leggett, Phys. Rev. Lett., 25(22), 1543–1546, 1970; Matsuda and Tsuneto, Prog. Theor. Phys., 46:411–436, 1970) for the SS state in quantum solids such as solid ⁴He were based on the idea of Bose Einstein Condensation (BEC) of the imperfections such as vacancies, interstitials and other possible excitations in the quantum solids which are expected because of the large zero-point motions. The SS state was proposed as a new state of matter in which real space ordering of the lattice structure of the solid coexists with the momentum space ordering of superfluidity. A new type of superconductors, since the discovery of the cuprate high T _c superconductors, HTSCs (Bednorz and Mueller, Z. Phys., 64:189, 1986), has been shown to share a feature with the vortex state, involving the VF and vortex solid states. The high T _c s of these materials are being discussed in connection to the large fluctuations associated with some other phase transitions like the antiferromagnetic transition in addition to that of the low dimensionality. The supersolidity in the hcp solid ⁴He, in contrast to the new superconductors which have multiple degrees of freedom of the Cooper pairs with spin as well as angular momentum freedom, has a unique feature of possessing possibly only the momentum fluctuations and vortex ring excitations associated with the possible low dimensional fluctuations of the subsystem(s). The high onset temperature of the VF state can be understood by considering thermally excited low D quantized vortices and it may be necessary to seek low dimensional sub-systems in hcp He which are hosts for vortices.     

The phase retrieval problem: a spectral parameter power series approach

This paper presents the application of the spectral parameter power series method [Pauli, Math Method Appl Sci 33:459–468 (2010)] for constructing the Green’s function for the elliptic operator $-\nabla \cdot I\nabla $ in a rectangular domain $\varOmega \subset \mathbb R ^{2}$ , where $I$ admits separation of variables. This operator appears in the transport-of-intensity equation (TLE) for undulatory phenomena, which relates the phase of a coherent wave with the axial derivative of its intensity in the Fresnel regime. We present a method for solving the TIE with Dirichlet boundary conditions. In particular, we discuss the case of an inhomogeneous boundary condition, a problem that has not been addressed specifically in other works, under the restricted assumption that the intensity $I$ admits separation of variables. Several simulations show the validity of the method.     

Convolutional Goppa codes defined on fibrations

We define a new class of Convolutional Codes in terms of fibrations of algebraic varieties generalizing our previous constructions of Convolutional Goppa Codes (Domínguez Pérez et?al. in AAECC 15:51?C61, 2004 [1]; Mu?oz Porras et?al. in IEEE Trans. Inform. Theory 52(1):340?C344, 2006; [16]). This general approach allow us to give convolutional codes with maximal error correction capability (Maximum Distance Separable).     

Theoretical Analysis of Neutron and X-ray Scattering Data on 3He

X-ray scattering experiments on bulk liquid ³He (Albergamo et al. in Phys. Rev. Lett. 99:205301, 2007; Schmets and Montfrooij in Phys. Rev. Lett. 100:239601, 2008; Albergamo et?al. in Phys. Rev. Lett. 100:239602, 2008) have indicated the possibility of the existence of a sharp collective mode at large momentum transfers. We address this issue within a manifestly microscopic theory of excitations in a Fermi fluid that can be understood as proper generalization of the time-honored theory of Jackson, Feenberg, and Campbell (Jackson in Phys. Rev. A 8:1529, 1973; Feenberg in Theory of Quantum Fluids, 1969; Chang and Campbell in Phys. Rev. B 13:3779, 1976) of excitations in ⁴He. We show that both neutron and X-ray data can be well explained within a theory where the high momentum excitations lie in fact inside the particle-hole continuum. ??Pair fluctuations?? contribute a sharpening of the mode compared to the random phase approximation (RPA). When the theoretical results are convoluted with the experimental resolution, the agreement between theory and X-ray data is quite good.     

The benefit of fractional derivatives in modelling the dynamics of filler-reinforced rubber under large strains: a comparison with the Maxwell-element approach

The dynamic properties of rubber-like materials are characterised by a significant dependence on the predeformation and the frequency. The focus of this paper is to represent the frequency and predeformation dependent dynamic behaviour of a carbon-black filled SBR rubber with 40 phr amount of filler using the concept of fractional derivatives. Thus, we introduce a constitutive approach of finite fractional viscoelasticity which is suitable to approximate the dynamic material properties with respect to the storage and the loss modulus. The constitutive approach is based on a proposal of [18] which was modified by a deformation dependent relaxation function in a previous work [46] to represent the dependence of the dynamic modulus on the predeformation and the frequency. The constitutive approach in [46] is based on the classical theory of finite viscoelasticity and formulated in the frequency domain. In this work, the approach of [46] will be extended by the concept of fractional derivatives and compared to the classical one. Thus, the classical and the extended fractional constitutive models are firstly introduced and the complex modulus tensors of both models are derived. It should be mentioned that both constitutive approaches are firstly formulated in the time domain. This formulation is necessary to satisfy the thermodynamical consistency. In order to conduct vibration analyses of elastomer structures with high computational efficiency, the equations are then transferred to the frequency domain. To this end, the constitutive model is geometrically linearised in the neighbourhood of a large and temporally constant predeformation. The incremental strain tensor varies harmonically and its amplitude has to be small. Furthermore, parameter identification of both approaches is done on the basis of quasi-static and dynamic investigations of the carbon-black filled SBR rubber. The numerical results of the parameter identification of the classical and the fractional model are compared to each other with respect to the number of necessary material parameters and the quality of the approximation. Finally, the numerical implementation of the frequency domain formulation into the finite element code MSC Marc on the basis of the proposal of [28] will be presented.     

A note on cyclic codes from APN functions

Cyclic codes, as linear block error-correcting codes in coding theory, play a vital role and have wide applications. Ding (SIAM J Discret Math 27(4):1977–1994, 2013), Ding and Zhou (Discret Math, 2014) constructed a number of classes of cyclic codes from almost perfect nonlinear (APN) functions and planar functions over finite fields and presented some open problems on cyclic codes from highly nonlinear functions. In this paper, we consider two open problems involving the inverse APN function $f(x)=x^{q^m-2}$ and the Dobbertin APN function $f(x)=x^{2^{4i}+2^{3i}+2^{2i}+2^{i}-1}$ . From the calculation of linear spans and the minimal polynomials of two sequences generated by these two classes of APN functions, the dimensions of the corresponding cyclic codes are determined and lower bounds on the minimum weight of these cyclic codes are presented. Actually, we present a framework for the minimal polynomial and linear span of the sequence $s^{\infty }$ defined by $s_t={\mathrm {Tr}}((1+\alpha ^t)^e)$ , where $\alpha $ is a primitive element in ${\mathrm {GF}}(q)$ . These techniques can also be applied to other open problems in Ding (SIAM J Discret Math 27(4):1977–1994, 2013), Ding and Zhou (Discret Math, 2014).     

An extension of the noncommutative Bergman’s ring with a large number of noninvertible elements

For a prime number \(p\) , Bergman (Israel J Math 18:257–277, 1974) established that \(\mathrm {End}(\mathbb {Z}_{p} \times \mathbb {Z}_{p^{2}})\) is a semilocal ring with \(p^{5}\) elements that cannot be embedded in matrices over any commutative ring. In an earlier paper Climent et al. (Appl Algebra Eng Commun Comput 22(2):91–108, 2011), the authors presented an efficient implementation of this ring, and introduced a key exchange protocol based on it. This protocol was cryptanalyzed by Kamal and Youssef (Appl Algebra Eng Commun Comput 23(3–4):143–149, 2012) using the invertibility of most elements in this ring. In this paper we introduce an extension of Bergman’s ring, in which only a negligible fraction of elements are invertible, and propose to consider a key exchange protocol over this ring.     

Reply: On Role of Symmetries in Kelvin Wave Turbulence

In the Ref. (Lebedev and L’vov in J. Low Temp. Phys. 161, 2010, doi:10.1007/s10909-010-0215-2), this issue, two of us (VVL and VSL) considered symmetry restriction on the interaction coefficients of Kelvin waves and demonstrated that linear in small wave vector asymptotic, obtained analytically, is not forbidden, as Kosik and Svistunov (KS) expect by naive reasoning. Here we discuss this problem in additional details and show that theoretical objections by KS, presented in Ref. (Kozik and Svistunov in J. Low Temp. Phys. 161, 2010, doi:10.1007/s10909-010-0242-z), this issue, are irrelevant and their recent numerical simulation, presented in Ref. (Kozik and Svistunov in arXiv:1007.4927v1, 2010) is hardly convincing. There is neither proof of locality nor any refutation of the possibility of linear asymptotic of interaction vertices in the KS texts, Refs. (Kozik and Svistunov in J. Low Temp. Phys. 161, 2010, doi:10.1007/s10909-010-0242-z; arXiv:1006.0506v1, 2010). Therefore we can state again that we have no reason to doubt in this asymptote, that results in the L’vov–Nazarenko energy spectrum of Kelvin waves.     

An Integrated Procedure for the Structural Design of a Composite Rotor-Hydrofoil of a Water Current Turbine (WCT)

This paper shows an integrated structural design optimization of a composite rotor-hydrofoil of a water current turbine by means the finite elements method (FEM), using a Serial/Parallel mixing theory (Rastellini et al. Comput. Struct. 86:879–896, 2008, Martinez et al., 2007, Martinez and Oller Arch. Comput. Methods. 16(4):357–397, 2009, Martinez et al. Compos. Part B Eng. 42(2011):134–144, 2010) coupled with a fluid-dynamic formulation and multi-objective optimization algorithm (Gen and Cheng 1997, Lee et al. Compos. Struct. 99:181–192, 2013, Lee et al. Compos. Struct. 94(3):1087–1096, 2012). The composite hydrofoil of the turbine rotor has been design using a reinforced laminate composites, taking into account the optimization of the carbon fiber orientation to obtain the maximum strength and lower rotational-inertia. Also, these results have been compared with a steel hydrofoil remarking the different performance on both structures. The mechanical and geometrical parameters involved in the design of this fiber-reinforced composite material are the fiber orientation, number of layers, stacking sequence and laminate thickness. Water pressure in the rotor of the turbine is obtained from a coupled fluid-dynamic simulation (CFD), whose detail can be found in the reference Oller et al. (2012). The main purpose of this paper is to achieve a very low inertia rotor minimizing the start-stop effect, because it is applied in axial water flow turbine currently in design by the authors, in which is important to take the maximum advantage of the kinetic energy. The FEM simulation codes are engineered by CIMNE (International Center for Numerical Method in Engineering, Barcelona, Spain), COMPack for the solids problem application, KRATOS for fluid dynamic application and RMOP for the structural optimization. To validate the procedure here presented, many turbine rotors made of composite materials are analyzed and three of them are compared with the steel one.     

Simulation of concrete flow in V-funnel test and the proper range of viscosity and yield stress for SCC

The present paper highlights the flow simulation of self consolidating concrete (SCC) in V-funnel test that is used to determine the concrete filling ability and its resistance against segregation. Simulations were performed using a two-dimensional smoothed particle hydrodynamic (SPH) method to determine the discharge time where SCC was considered as a homogeneous Bingham fluid. The numerical predictions are lower than experimental data because of the assumptions of two-dimensional and homogeneous flow. Having the SPH method employed, SCCs with different viscosities and yield stresses were simulated to compare the discharge time with the suggested criteria in EFNARC (2002) and (2005) guidelines. Based on simulations results, the appropriate range of viscosities and yield stresses as well as a relation between rheological properties and discharge time for SCC taking into account EFNARC (2002) and (2005) guidelines are suggested. Using the suggested relations, one can assess the proper SCC filling ability without conducting the V-funnel test.     

The Renewed KU Leuven Pulsed Field Facility

The KU Leuven pulsed magnet facility was established in the sixties by the late Prof. A. Van Itterbeek (Van Itterbeek et al., Appl. Sci. Res., 18:105, 1967, Van Itterbeek et al., Les Champs Magnétiques Intenses, vol. 379, 1966). During the period 1972–1997 the laboratory was directed by Prof. F. Herlach (Witters and Herlach, J. Phys. D, Appl. Phys., 16:255, 1983, Li and Herlach, Meas. Sci. Technol., 6:1035, 1995, Herlach et al., Physica B, 201:542, 1994) who continuously developed the facility further along two lines: improved pulsed-field-coil design and enhanced capabilities for experimentation. From 1998 on, the facility is lead by Prof. V.V. Moshchalkov, in close collaboration with Prof. E.F. Herlach and Prof. J. Vanacken. Recently, the laboratory has been completely renewed; its present configuration is based on the former installation of the High Field Magnet Laboratory at the Radboud University Nijmegen (the Netherlands) (Rosseel et al., IEEE Trans. Appl. Supercond., 16:1664, 2006), which was originally developed in collaboration with the KU Leuven spin-off company METIS (http://www.metis.be/).