An implicit dual-based approach to couple peridynamics with classical continuum mechanics

A general local/nonlocal implicit coupling technique called the dual-based approach is proposed to couple peridynamics (PD) with classical continuum mechanics. In the present method, physical information is transmitted mutually from local to nonlocal regions through the coupling elements; no transition region is introduced. For different mesh discretizations, two coupling methods are achieved with simplicity and effectivity. To obtain the stiffness matrix of the coupled model, without loss of generality, the implicit dual-horizon ordinary state-based peridynamic model is proposed, in which the linearization of dual-horizon ordinary state-based PD is derived and the dual assembly algorithm of the peridynamic stiffness matrix is developed. It will be seen that the implicit dual-based coupling approach provides a new implicit coupling method that is easy to implement and makes full use of the internal connection between PD and classical continuum mechanics. Several numerical examples involving static crack propagation are investigated, and the satisfactory results show both quantitative and qualitative agreement with either the analytic solution or the available experiment.     

A unified formulation for continuum mechanics applied to fluid–structure interaction in flexible tubes

This paper outlines the development of a new procedure for analysing continuum mechanics problems with a particular focus on fluid–structure interaction in flexible tubes. A review of current methods of fluid–structure coupling highlights common limitations of high computational cost and solution instability. It is proposed that these limitations can be overcome by an alternative approach in which both fluid and solid components are solved within a single discretized continuum domain. A single system of momentum and continuity equations is therefore derived that governs both fluids and solids and which are solved with a single mesh using finite volume discretization schemes. The method is validated first by simulating dynamic oscillation of a clamped elastic beam. It is then applied to study the case of interest—wave propagation in highly flexible tubes—in which a predicted wave speed of 8.58 m/s falls within 2% of an approximate analytical solution. The method shows further good agreement with analytical solutions for tubes of increasing rigidity, covering a range of wave speeds from those found in arteries to that in the undisturbed fluid. Copyright © 2005 John Wiley & Sons, Ltd.     

A non‐local continuum damage approach to model dynamic crack branching

Dynamic crack‐branching instabilities in a brittle material are studied numerically by using a non‐local damage model. PMMA is taken as our model brittle material. The simulated crack patterns, crack velocities, and dissipated energies compare favorably with experimental data gathered from the literature, as long as the critical strain for damage initiation as well as the parameters for a rate‐dependent damage law are carefully selected. Nonetheless, the transition from a straight crack propagation to the emergence of crack branches is very sensitive to the damage initiation threshold. The transition regime is thus a particularly interesting challenge for numerical approaches. We advocate using the present numerical study as a benchmark to test the robustness of alternative non‐local numerical approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

Investigation of the response of an aluminium plate subjected to repeated low velocity impact using a continuum damage mechanics approach

Experimental investigation of repeated impacts on aluminium plates is performed using drop weights impacting from either constant or variable heights. In repeated impacts of constant and variable heights, the effect of plasticity is noticeable on the specimens in the very first impact. The effect of strain hardening is observed at higher impact numbers. Stiffness of plates is decreased by initiation and propagation of cracks in the specimens. Finally, perforation and penetration occur at the ultimate consecutive impacts. Numerical simulations of repeated impacts are also conducted using continuum damage mechanics by Abaqus software. Lemaitre's model is used as the damage model, and the code is written in Vumat subroutine. The effect of initial uniaxial and biaxial tensile stress on the plates is considered in repeated impacts, and it is concluded that plates with initial tensile uniaxial stress at transverse edges have maximum values of contact force and absorbed energy.     

A stress-influence-function with adaptive strength feature approach for stress constrained continuum topology optimization via small-loop sequential strategy

Recently, the stress-influence-function (SIF) approach is presented for stress constrained continuum topology optimization. The SIF approach provides an alternative for continuum topology optimization with stress constraints. However, the SIF approach is not good at controlling the maximum stress of the elements compared to the conventional approach. In the study, the stress-influence-function with adaptive strength feature (SIF-ASF) approach via small-loop sequential strategy is proposed to achieve better control on the maximum elemental stress. First, the stress constrained continuum topology optimization formulation is given and the SIF approach is briefly introduced. Then the SIF-ASF approach is proposed for stress constrained continuum topology optimization, in which the strength feature in the stress influence function is adjusted in each iterative step of the optimization process. The adjoint-vector based sensitivity analysis to the design variables is further discussed. Three numerical examples are given to illustrate the applicability and validity of the proposed SIF-ASF approach. It is shown that the proposed SIF-ASF approach can achieve better control on the maximum elemental stress than the SIF approach. Moreover, the proposed SIF-ASF approach may obtain a lighter structure than the conventional approach.     

The atomistic‐continuum hybrid taxonomy and the hybrid‐hybrid approach

The hybrid taxonomy — a means of characterizing different atomistic‐continuum methods on the basis of the type of information exchanged between the atomistic and the continuum solver — is introduced. The formulation of the taxonomy raises a new hybrid possibility, called a ‘hybrid‐hybrid’ method. Some examples of hybrid‐hybrid simulations for dense fluids are discussed and validated against full molecular dynamics results. Copyright © 2014 John Wiley & Sons, Ltd.     

A unified approach to damage accumulation and fatigue crack growth

An approach is proposed to the theory of fatigue cracks propagation based on the following postulate: a growing crack at least once in a cycle becomes a nonequilibrium one (in the Griffith's sense) under the condition that the resistance to crack growth is calculated with an account of damage accumulated at the crack tip during the loading history. The theory is used for nonuniaxial stress states including jumplike growth, stops, kinking and branching phenomena. The general structure of differential equations is discussed for the averaged crack growth rate under nonuniaxial loading.     

A boundary density evolutionary topology optimization of continuum structures with smooth boundaries

Based on the variable density method, this article proposes a boundary density evolutionary topology optimization method. The method uses a material interpolation model without penalization. Combined with the density grading filtering method, an optimal topology with only 0/1 cells can be obtained. Compared with the solid isotropic microstructures with penalization method (SIMP), no penalty factor is required in the material interpolation model; compared with the evolutionary structural optimization method (ESO), intermediate-density elements are allowed in the optimization process, but the concept of gradually removing the low-utilization materials near the boundary in the ESO method is retained. After the optimal result is obtained, the structural boundary element is processed by the level set of nodal strain energy, and the optimization result with smooth boundaries similar to the level set method (LSM) can be obtained. The proposed method has the superiority of the variable density method, and it also combines the advantages of the evolutionary method and the level set method, so which is named as boundary density evolution (BDE) method. The four static and one dynamic optimization examples illustrate the stability and efficiency of the proposed method.     

基于连续损伤力学的复合材料单剪螺栓连接强度估算策略

针对中国缺少T800级复合材料螺栓连接设计参数的问题,发展一种综合连续损伤力学（CDM）和工程算法的单剪连接强度估算策略,以替代试验,降低研究周期和成本。在该强度估算策略中,首先建立试件的CDM有限元模型,通过数值模拟得到单剪螺栓连接的设计参数,包括单剪挤压强度修正系数、无缺口层合板拉伸强度和应力集中减缓因子等。随后根据上述参数,建立工程算法,估算复合材料单剪螺栓连接的最终挤压强度。结果表明:通过该策略得到的T800级复合材料螺栓连接设计参数和强度估算结果与试验结果有较好的一致性,说明该强度估算策略的可行性。      

A unified parametric design approach to structural shape optimization

This paper presents a general parametric design approach for 2-D shape optimization problems. This approach has been achieved by integrating practical design methodologies into numerical procedures. It is characterized by three features: (i) automatic selection of a minimum number of shape design variables based on the CAD geometric model; (ii) integration of sequential convex programming algorithms to solve equality constrained optimization problems; (iii) efficient sensitivity analysis by means of the improved semi-analytical method. It is shown that shape design variables can be either manually or systematically identified with the help of equality constraints describing the relationship between geometric entities. Numerical solutions are performed to demonstrate the applicability of the proposed approach. A discussion of the results is also given:     

A unified stochastic framework for robust topology optimization of continuum and truss-like structures

In this article, a unified framework is introduced for robust structural topology optimization for 2D and 3D continuum and truss problems. The uncertain material parameters are modelled using a spatially correlated random field which is discretized using the Karhunen–Loève expansion. The spectral stochastic finite element method is used, with a polynomial chaos expansion to propagate uncertainties in the material characteristics to the response quantities. In continuum structures, either 2D or 3D random fields are modelled across the structural domain, while representation of the material uncertainties in linear truss elements is achieved by expanding 1D random fields along the length of the elements. Several examples demonstrate the method on both 2D and 3D continuum and truss structures, showing that this common framework provides an interesting insight into robustness versus optimality for the test problems considered.     

Optical trapping with modified exponential decay in optical waveguides via dressed continuum

Simultaneous interaction of two side-coupled waveguides with the dressed continuum represented by a linear waveguide array causes cross-coupling between the two evanescent decay-channels and results in the phenomenon of trapping of the light field in the spatial domain during propagation through the waveguide system. For specific parameter values, it has been shown that the trapping effect is possible for all relative positions of the waveguides side-coupled to the dressed continuum. The model also demonstrates non-exponential decay characteristics of the optical field amplitudes in the waveguides. Depending on the values of the propagation mismatch, the nonlinearity arising in the decay-rate characteristics exhibits features like optical Zeno and anti-Zeno effects.     

A continuum approach to magnon-phonon couplings—I: General equations,background solution

It is proposed to study the magnon-phonon couplings, exhibited in elastic ferromagnetic bodies, on the basis of a purely continuum approach and its related mathematical methods. The present part of the work is mostly devoted to establishing the equations that govern weak-field dynamical disturbances by the method of superimposition. More precisely, having defined an ideal, mechanically unloaded and field-free reference configuration, with respect to which the material behaves isotropical]y, we built up an initial configuration which corresponds to a stationary rigid-body, one-ferromagnetic domain state by applying an intense magnetic field and appropriate mechanical loadings on the boundary of the body. This initial state induces hexagonal symmetry for the dynamical properties to be studied in Part II in a neighborhood of this state. Viscosity and spin-lattice relaxation processes are accounted for, and the case of weakly elastically anisotropic bodies is commented upon.     

A trust region-based approach to optimize triple response systems

This article presents a new computing procedure for the global optimization of the triple response system (TRS) where the response functions are non-convex quadratics and the input factors satisfy a radial constrained region of interest. The TRS arising from response surface modelling can be approximated using a nonlinear mathematical program that considers one primary objective function and two secondary constraint functions. An optimization algorithm named the triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the non-degenerate TRS. In TRSALG, the Lagrange multipliers of the secondary functions are determined using the Hooke–Jeeves search method and the Lagrange multiplier of the radial constraint is located using the trust region method within the global optimality space. The proposed algorithm is illustrated in terms of three examples appearing in the quality-control literature. The results of TRSALG compared to a gradient-based method are also presented.     

A Monte Carlo simulation approach to the availability assessment of multi-state systems with operational dependencies

This paper deals with multi-state systems (MSS), whose performance can settle on different levels, e.g. 100%, 80%, 50% of the nominal capacity, depending on the operative conditions of the constitutive multi-state elements. Examples are manufacturing, production, power generation and gas and oil transportation systems. Often in practice, MSS are such that operational dependencies exist between the system state and the state of its components. For example, in a production line of nodal series structure, with no buffers between the nodes, if one of the nodes throughput changes (e.g. switches from 100% to 50% due to a deterministic or stochastic transition of one of its components), the other nodes must be reconfigured (i.e. their components must deterministically change their states) so as to provide the same throughput.In this paper, we present a Monte Carlo simulation technique which allows modelling the complex dynamics of multi-state components subject to operational dependencies with the system overall state. A correlation method is tailored to model the automatic change of state of the relevant components following a change in one of the system nodes. The proposed technique is verified on a simple case study of literature.     

A continuum damage model applied to high-temperature fatigue lifetime prediction of a martensitic tool steel

High‐temperature operational conditions of hot work tool steels induce several thermomechanical loads. Depending on the processes, (i.e. forging, die casting or extrusion), stress, strain, strain rate and temperature levels applied on the material are nevertheless very different. Thus, lifetime prediction models need to be able to take into account a broad range of working conditions. In this paper, a non‐isothermal continuum damage model is identified for a widely used hot work tool steel AISI H11 (X38CrMoV5) with a nominal hardness of 47 HRc. This investigation is based on an extensive high‐temperature, low‐cycle fatigue database performed under strain rate controlled conditions with and without dwell times in the temperature range 300–600°C . As analysis of experimental results does not reveal significant time‐dependent damage mechanisms, only a fatigue damage component was activated in the model formulation. After normalization, all fatigue results are defined on a master Woehler curve defined by a nonlinear damage model, which allows the parameter identification. Last, a validation stage of the model is performed from thermomechanical fatigue tests.     

A unified approach to predict evaporation losses in evaporative heat exchangers

In this paper, the rules of thumb used to predict evaporation losses in different evaporative heat exchangers are unified. The accurate prediction of all aspects of evaporative heat exchanger behavior is very important. Accurately predicting evaporation losses is significant since water, in this class of heat exchangers, is cooled primarily by evaporation of a portion of the circulating water that causes the concentration of impurities to increase. Furthermore, the design of hybrid cooling towers requires that the amount of evaporation be known. A single correlation is, therefore, developed for this class of heat exchangers that is simple and accurate with a wide range of applicability. The predicted values are in good agreement with experimental values as well as predictions made by reliable mathematical models.