Neumann exterior wave propagation problems: computational aspects of 3D energetic Galerkin BEM

In this work, we consider as model problem an exterior 3D wave propagation Neumann problem reformulated in terms of a space–time hypersingular boundary integral equation with retarded potentials. This latter is set in the so-called energetic weak form, recently proposed in Aimi et al. (Int J Numer Methods Eng 80:1196–1240, 2009; CMES 58:185–219, 2010), regularized as in Frangi (Int J Numer Methods Eng 45:721–740, 1999) and then approximated by the Galerkin boundary element method. Details on the discretization phase and, in particular, on the computation of integrals, double in time and double in space, constituting the elements of the final linear system matrix are given and analyzed. Various numerical results and simulations are presented and 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.     

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.     

Continuum phase field modeling of dynamic fracture: variational principles and staggered FE implementation

The modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations of complex crack topologies including branching. This drawback can be overcome by a diffusive crack modeling based on the introduction of a crack phase field as proposed in Miehe et?al. (Comput Methods Appl Mech Eng 19:2765?C2778, 2010a; Int J Numer Meth Eng 83:1273?C1311, 2010b), Hofacker and Miehe (Int J Numer Meth Eng, 2012). In this work, we summarize basic ingredients of a thermodynamically consistent, variational-based model of diffusive crack propagation under quasi-static and dynamic conditions. It is shown that all coupled field equations, in particular the balance of momentum and the gradient-type evolution equation for the crack phase field, follow as the Euler equations of a mixed rate-type variational principle that includes the fracture driving force as the mixed field variable. This principle makes the proposed formulation extremely compact and provides a perfect basis for the finite element implementation. We then introduce a local history field that contains a maximum energetic crack source obtained in the deformation history. It drives the evolution of the crack phase field. This allows for the construction of an extremely robust operator split scheme that updates in a typical time step the history field, the crack phase field and finally the displacement field. We demonstrate the performance of the phase field formulation of fracture by means of representative numerical examples, which show the evolution of complex crack patterns under dynamic loading.     

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.     

Thermodynamics and thermal decomposition for shape memory effects with crystallization based on dissipation and logarithmic strain

The present effort provides a 3-D thermodynamic framework generalizing the 1-D modeling of 2-way shape memory materials described by Westbrook et al. (J. Eng. Mater. Technol. 312:041010, 2010) and Chung et al. (Macromolecules 41:184–192, 2008), while extending the strain-induced crystallization and shape memory approaches of Rao and Rajagopal (Interfaces Free Bound. 2:73–94, 2000; Int. J. Solids Struct. 38:1149–1167, 2001), Barot and Rao (Z. Angew. Math. Phys. 57:652–681, 2006), and Barot et al. (Int. J. Eng. Sci. 46:325–351, 2008) to include finite thermal expansion within a logarithmic strain basis. The free energy of newly-formed orthotropic crystallites is assumed additive, with no strains in their respective configurations of formation. A multiplicative decomposition is assumed for the assumed thermoelastic orthotropic expansional strains of the respective crystallites. The properties of the crystallites are allowed to depend both on current temperature and their respective temperatures of formation. The entropy production rate relation is written in the frame rotating with the logarithmic spin and produces stress and entropy relations incorporating the integrated configurational free energies, and a driving term for the crystallization analogous to that obtained by the previous studies of Rao et al. The salient attributes of the 1-D modeling of Westbrook et al. are recovered, and applications are discussed.     

Frictional mortar contact for finite deformation problems with synthetic contact kinematics

In this paper we present a mortar based method, for frictional two dimensional contact problems. It is based on the work by Tur et al. (Comput Methods Appl Mech Eng 198(37–40):2860–2873, 2009) and uses the same concentrated integration scheme as well as a non regularized tangential contact formulation based on Lagrange multipliers only. We abstract the contact kinematics to a rather synthetic formulation. Therefore we are able to use two different methods of defining the normal field on the discretized surface normal: The popular method of averaged non-mortar side normal and the rather simple non continuous mortar side normal field. The problem is solved with a fixed point Newton–Raphson procedure and for both normal fields the full linearizations are derived. With numerical examples we show the performance of the more concise formulation of the non averaged non continuous mortar side normal field.     

Transverse deflection of a clamped mild-steel plate

The theory of plastic flow by extended slip (Acta Mech 223:655–668, 2012; Philos Mag A 91:3343–3357, 2011; Z Angew Math Mech 84:266–279, 2004; Q J Mech Appl Math 52:645–662, 1999) is applied to a problem of bi-axial strain: the transverse plastic deflection, by means of a flat-ended punch, of a clamped plate of mild-steel. Two new theorems concerned with the Mechanics of Plates are presented. It is shown that, if the static shear yield stress of the plate material remains independent of strain, then the load–deflection relation for the punch, in the case of quasi-static punching of a plate clamped along a closed arbitrary contour, obeys an exactly linear theoretical relation. This prediction is then confirmed by experiments carried out at quasi-static rates of loading with thin plates of hot-rolled mild-steel. It is demonstrated by experiment, in the case of concentric circular punch and clamp contours, that the load–deflection relation for the punch remains linear to within <1 % provided that the maximum principal strain within the free domain of the plate does not exceed the yield-point elongation strain of the mild-steel concerned.     

A simplified implementation of a gradient-enhanced damage model with transient length scale effects

Gradient-enhanced damage models with constant gradient activity suffer from spurious damage growth at high deformation levels. This issue was resolved by Geers et al. (Comput Methods Appl Mech Eng 160(1–2):133–153, 1998) by expressing the gradient activity parameter as a function of the local equivalent strain at the expense of adding one set of degrees of freedom to those of the standard model. In this contribution, a new formulation of the gradient-enhanced damage model with variable length scale is presented which eliminates the need for the extra set of degrees of freedom. The merits of the proposed formulation are demonstrated, and the choice of the damage evolution law and its impact on the model performance are discussed.     

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.     

A note on oblique water entry

A minor error in Howison et al. (J. Eng. Math. 48:321–337, 2004) obscured the fact that the points at which the free surface turns over in the solution of the Wagner model for the oblique impact of a two-dimensional body are directly related to the turnover points in the equivalent normal impact problem. This note corrects some of the earlier results given in Howison et al. (J. Eng. Math. 48:321–337, 2004) and discusses the implications for the applicability of the Wagner model.     

Reduction of the number of material parameters by ANN approximation

Modern industrial standards require advanced constitutive modeling to obtain satisfactory numerical results. This approach however, is causing significant increase in number of material parameters which can not be easily obtained from standard and commonly known experimental techniques. Therefore, it is desirable to introduce procedure decreasing the number of the material parameters. This reduction however, should not lead to misunderstanding the fundamental physical phenomena. This paper proposes the reduction of the number of material parameters by using ANN approximation. Recently proposed viscoplasticity formulation for anisotropic solids (metals) developed by authors is used as an illustrative example. In this model one needs to identify 28 material parameters to handle particular metal behaviour under adiabatic conditions as reported by Glema et al (J Theor Appl Mech 48:973–1001, 2010), (Int J Damage Mech 18:205–231, 2009) and Sumelka (Poznan University of Technology, Poznan, 2009). As a result of proposed approach, authors decreased the number of material parameters to 19.     

A new yield surface distortion model based on Baltov and Sawczuk’s model

In the present study, a new distortion yield surface model is proposed to represent compatible results with experimental observations. The proposed yield surface model is determined numerically during tension–torsion loadings by considering a kinematic hardening model and monotonic loading paths. The experimental results of yield surface determination (Khan et al. in Int J Plast 26:1432–1441, 2010; Naghdi et al. in ASME J. Appl Mech 25:201–209, 1957) represent the nosed and flattened regions in the loading and reverse loading directions, respectively. But, the Baltov and Sawczuk’s yield surface model can only predict nosed or flattened shape in both loading and reversed loading directions, depending on the sign of their model constant. Thus, the elliptic Baltov and Sawczuk’s yield surface is modified by changing the sign of this parameter continuously from loading to reverse loading direction. Relations and convexity of the new model are obtained and discussed. The new model is able to predict properly the shape of the yield surface. The experimental results are in a satisfactory agreement with the new yield surface distortion model predictions.     

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.     

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.     

Remarks on the generalized cyclotomic sequences of length 2p^{m}

This paper presents some nonrandom distribution properties of two generalized cyclotomic binary sequences of length $2p^{m}$ constructed by Zhang et al. (Appl Algebra Eng Commun Comput 21:93?C108, 2010). Using these properties we further study the $k$ -error linear complexity and autocorrelation of these sequences. For some small values of $k$ , the upper bounds on the $k$ -error linear complexity are derived, which are far less than their linear complexity. Finally the bounds on the autocorrelation of these sequences are also presented. Our results show that there exist some drawbacks in application of these two sequences.     

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.     

Degree of cure-dependent modelling for polymer curing processes at small-strain. Part I: consistent reformulation

A physically-based small strain curing model has been developed and discussed in our previous contribution (Hossain et al. in Comput Mech 43:769–779, 2009a) which was extended later for finite strain elasticity and viscoelasticity including shrinkage in Hossain et al. (Comput Mech 44(5):621–630, 2009b) and in Hossain et al. (Comput Mech 46(3):363–375, 2010), respectively. The previously proposed constitutive models for curing processes are based on the temporal evolution of the material parameters, namely the shear modulus and the relaxation time (in the case of viscoelasticity). In the current paper, a thermodynamically consistent small strain constitutive model is formulated that is directly based on the degree of cure, a key parameter in the curing (reaction) kinetics. The new formulation is also in line with the earlier proposed hypoelastic approach. The curing process of polymers is a complex phenomenon involving a series of chemical reactions which transform a viscoelastic fluid into a viscoelastic solid during which the temperature, the chemistry and the mechanics are coupled. Part I of this work will deal with an isothermal viscoelastic formulation including shrinkage effects whereas the following Part II will give emphasis on the thermomechanical coupled approach. Some representative numerical examples conclude the paper and show the capability of the newly proposed constitutive formulation to capture major phenomena observed during the curing processes of polymers.     

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/).