Authors:Tobias Preclik; Sebastian Eibl; Ulrich Rüde Abstract: Abstract Formulating a consistent theory for rigid-body dynamics with impacts is an intricate problem. Twenty years ago Stewart published the first consistent theory with purely inelastic impacts and an impulsive friction model analogous to Coulomb friction. In this paper we demonstrate that the consistent impact model can exhibit multiple solutions with a varying degree of dissipation even in the single-contact case. Replacing the impulsive friction model based on Coulomb friction by a model based on the maximum dissipation principle resolves the non-uniqueness in the single-contact impact problem. The paper constructs the alternative impact model and presents integral equations describing rigid-body dynamics with a non-impulsive and non-compliant contact model and an associated purely inelastic impact model maximizing dissipation. An analytic solution is derived for the single-contact impact problem. The models are then embedded into a time-stepping scheme. The macroscopic behaviour is compared to Coulomb friction in a large-scale granular flow problem. PubDate: 2017-10-12 DOI: 10.1007/s00466-017-1486-0

Authors:Jörg Schröder; Markus von Hoegen; Patrizio Neff Abstract: Abstract In this paper we propose an anisotropic extension of the isotropic exponentiated Hencky energy, based on logarithmic strain invariants. Unlike other elastic formulations, the isotropic exponentiated Hencky elastic energy has been derived solely on differential geometric grounds, involving the geodesic distance of the deformation gradient \({{\varvec{F}}}\) to the group of rotations. We formally extend this approach towards anisotropy by defining additional anisotropic logarithmic strain invariants with the help of suitable structural tensors and consider our findings for selected case studies. PubDate: 2017-10-06 DOI: 10.1007/s00466-017-1466-4

Authors:Gang Pang; Songsong Ji; Yibo Yang; Shaoqiang Tang Abstract: Abstract Using an alternative source decomposition, we propose new exact boundary conditions on numerical boundary of a square lattice for out-of-plane motion over the whole space. A set of recurrence relations are found for the resulting kernel functions, hence allow their efficient and accurate evaluation with a system of ordinary differential equations. Stability of the boundary conditions is proved rigorously. Numerical results illustrate effective suppression for spurious wave reflection, and elimination of corner effects. This approach may be extended to other lattice structures and in higher dimensions. PubDate: 2017-10-05 DOI: 10.1007/s00466-017-1488-y

Authors:Sahuck Oh; Chung-Hsiang Jiang; Chiyu Jiang; Philip S. Marcus Abstract: Abstract We present a new, general design method, called design-by-morphing for an object whose performance is determined by its shape due to hydrodynamic, aerodynamic, structural, or thermal requirements. To illustrate the method, we design a new leading-and-trailing car of a train by morphing existing, baseline leading-and-trailing cars to minimize the drag. In design-by-morphing, the morphing is done by representing the shapes with polygonal meshes and spectrally with a truncated series of spherical harmonics. The optimal design is found by computing the optimal weights of each of the baseline shapes so that the morphed shape has minimum drag. As a result of optimization, we found that with only two baseline trains that mimic current high-speed trains with low drag that the drag of the optimal train is reduced by \(8.04\%\) with respect to the baseline train with the smaller drag. When we repeat the optimization by adding a third baseline train that under-performs compared to the other baseline train, the drag of the new optimal train is reduced by \(13.46\%\) . This finding shows that bad examples of design are as useful as good examples in determining an optimal design. We show that design-by-morphing can be extended to many engineering problems in which the performance of an object depends on its shape. PubDate: 2017-10-03 DOI: 10.1007/s00466-017-1482-4

Authors:L. Chen; Y. M. Cheng Abstract: Abstract In this paper, the complex variable reproducing kernel particle method (CVRKPM) for solving the bending problems of isotropic thin plates on elastic foundations is presented. In CVRKPM, one-dimensional basis function is used to obtain the shape function of a two-dimensional problem. CVRKPM is used to form the approximation function of the deflection of the thin plates resting on elastic foundation, the Galerkin weak form of thin plates on elastic foundation is employed to obtain the discretized system equations, the penalty method is used to apply the essential boundary conditions, and Winkler and Pasternak foundation models are used to consider the interface pressure between the plate and the foundation. Then the corresponding formulae of CVRKPM for thin plates on elastic foundations are presented in detail. Several numerical examples are given to discuss the efficiency and accuracy of CVRKPM in this paper, and the corresponding advantages of the present method are shown. PubDate: 2017-09-23 DOI: 10.1007/s00466-017-1484-2

Authors:Julian Kochmann; Stephan Wulfinghoff; Lisa Ehle; Joachim Mayer; Bob Svendsen; Stefanie Reese Abstract: Abstract Recently, two-scale FE-FFT-based methods (e.g., Spahn et al. in Comput Methods Appl Mech Eng 268:871–883, 2014; Kochmann et al. in Comput Methods Appl Mech Eng 305:89–110, 2016) have been proposed to predict the microscopic and overall mechanical behavior of heterogeneous materials. The purpose of this work is the extension to elasto-viscoplastic polycrystals, efficient and robust Fourier solvers and the prediction of micromechanical fields during macroscopic deformation processes. Assuming scale separation, the macroscopic problem is solved using the finite element method. The solution of the microscopic problem, which is embedded as a periodic unit cell (UC) in each macroscopic integration point, is found by employing fast Fourier transforms, fixed-point and Newton–Krylov methods. The overall material behavior is defined by the mean UC response. In order to ensure spatially converged micromechanical fields as well as feasible overall CPU times, an efficient but simple solution strategy for two-scale simulations is proposed. As an example, the constitutive behavior of 42CrMo4 steel is predicted during macroscopic three-point bending tests. PubDate: 2017-09-20 DOI: 10.1007/s00466-017-1476-2

Authors:Jan Jaśkowiec Abstract: Abstract The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times. PubDate: 2017-09-19 DOI: 10.1007/s00466-017-1479-z

Authors:Dustin R. Jantos; Philipp Junker; Klaus Hackl Abstract: Abstract Modern high-performance materials have inherent anisotropic elastic properties. The local material orientation can thus be considered to be an additional design variable for the topology optimization of structures containing such materials. In our previous work, we introduced a variational growth approach to topology optimization for isotropic, linear-elastic materials. We solved the optimization problem purely by application of Hamilton’s principle. In this way, we were able to determine an evolution equation for the spatial distribution of density mass, which can be evaluated in an iterative process within a solitary finite element environment. We now add the local material orientation described by a set of three Euler angles as additional design variables into the three-dimensional model. This leads to three additional evolution equations that can be separately evaluated for each (material) point. Thus, no additional field unknown within the finite element approach is needed, and the evolution of the spatial distribution of density mass and the evolution of the Euler angles can be evaluated simultaneously. PubDate: 2017-09-18 DOI: 10.1007/s00466-017-1483-3

Authors:I. A. Rodrigues Lopes; F. M. Andrade Pires; F. J. P. Reis Abstract: Abstract A mixed parallel strategy for the solution of homogenization-based multi-scale constitutive problems undergoing finite strains is proposed. The approach aims to reduce the computational time and memory requirements of non-linear coupled simulations that use finite element discretization at both scales (FE \(^2\) ). In the first level of the algorithm, a non-conforming domain decomposition technique, based on the FETI method combined with a mortar discretization at the interface of macroscopic subdomains, is employed. A master–slave scheme, which distributes tasks by macroscopic element and adopts dynamic scheduling, is then used for each macroscopic subdomain composing the second level of the algorithm. This strategy allows the parallelization of FE \(^2\) simulations in computers with either shared memory or distributed memory architectures. The proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the Newton–Raphson scheme. Several examples are presented to demonstrate the robustness and efficiency of the proposed parallel strategy. PubDate: 2017-09-15 DOI: 10.1007/s00466-017-1472-6

Authors:Oliver Schmitt; Paul Steinmann Abstract: Abstract We introduce a manufacturing constraint for controlling the minimum member size in structural shape optimization problems, which is for example of interest for components fabricated in a molding process. In a parameter-free approach, whereby the coordinates of the FE boundary nodes are used as design variables, the challenging task is to find a generally valid definition for the thickness of non-parametric geometries in terms of their boundary nodes. Therefore we use the medial axis, which is the union of all points with at least two closest points on the boundary of the domain. Since the effort for the exact computation of the medial axis of geometries given by their FE discretization highly increases with the number of surface elements we use the distance function instead to approximate the medial axis by a cloud of points. The approximation is demonstrated on three 2D examples. Moreover, the formulation of a minimum thickness constraint is applied to a sensitivity-based shape optimization problem of one 2D and one 3D model. PubDate: 2017-09-14 DOI: 10.1007/s00466-017-1477-1

Authors:K. P. Baxevanakis; C. Mo; M. Cabal; A. Kontsos Abstract: Abstract Strain localization bands (SLBs) that appear at early stages of deformation of magnesium alloys have been recently associated with heterogeneous activation of deformation twinning. Experimental evidence has demonstrated that such “Lüders-type” band formations dominate the overall mechanical behavior of these alloys resulting in sigmoidal type stress–strain curves with a distinct plateau followed by pronounced anisotropic hardening. To evaluate the role of SLB formation on the local and global mechanical behavior of magnesium alloys, an integrated experimental/computational approach is presented. The computational part is developed based on custom subroutines implemented in a finite element method that combine a plasticity model with a stiffness degradation approach. Specific inputs from the characterization and testing measurements to the computational approach are discussed while the numerical results are validated against such available experimental information, confirming the existence of load drops and the intensification of strain accumulation at the time of SLB initiation. PubDate: 2017-09-14 DOI: 10.1007/s00466-017-1480-6

Authors:Tao Jin; Hashem M. Mourad; Curt A. Bronkhorst; Veronica Livescu Abstract: Abstract We present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. A material stability analysis is used to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems. PubDate: 2017-09-13 DOI: 10.1007/s00466-017-1470-8

Authors:Yuval Tal; Bradford H. Hager Abstract: Abstract This paper presents a mortar-based finite element formulation for modeling the dynamics of shear rupture on rough interfaces governed by slip-weakening and rate and state (RS) friction laws, focusing on the dynamics of earthquakes. The method utilizes the dual Lagrange multipliers and the primal–dual active set strategy concepts, together with a consistent discretization and linearization of the contact forces and constraints, and the friction laws to obtain a semi-smooth Newton method. The discretization of the RS friction law involves a procedure to condense out the state variables, thus eliminating the addition of another set of unknowns into the system. Several numerical examples of shear rupture on frictional rough interfaces demonstrate the efficiency of the method and examine the effects of the different time discretization schemes on the convergence, energy conservation, and the time evolution of shear traction and slip rate. PubDate: 2017-09-09 DOI: 10.1007/s00466-017-1475-3

Authors:Jin He; Harold S. Park Abstract: Abstract We present a computational method that can be applied to capture surface stress and surface tension-driven effects in both stiff, crystalline nanostructures, like size-dependent mechanical properties, and soft solids, like elastocapillary effects. We show that the method is equivalent to the classical Young–Laplace model. The method is based on converting surface tension and surface elasticity on a zero-thickness surface to an initial stress and corresponding elastic properties on a finite thickness shell, where the consideration of geometric nonlinearity enables capturing the out-of-plane component of the surface tension that results for curved surfaces through evaluation of the surface stress in the deformed configuration. In doing so, we are able to use commercially available finite element technology, and thus do not require consideration and implementation of the classical Young–Laplace equation. Several examples are presented to demonstrate the capability of the methodology for modeling surface stress in both soft solids and crystalline nanostructures. PubDate: 2017-09-02 DOI: 10.1007/s00466-017-1474-4

Authors:J. M. Rodriguez Prieto; J. M. Carbonell; J. C. Cante; J. Oliver; P. Jonsén Abstract: Abstract The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay re-triangulation of the domain, is used to study machining of Ti6Al4V. In this work the method is revised and applied to study the influence of the cutting speed on the cutting force and the chip formation process. A parametric methodology for the detection and treatment of the rigid tool contact is presented. The adaptive insertion and removal of particles are developed and employed in order to sidestep the difficulties associated with mesh distortion, shear localization as well as for resolving the fine-scale features of the solution. The performance of PFEM is studied with a set of different two-dimensional orthogonal cutting tests. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation metal cutting problems with continuous chip and serrated chip formation. PubDate: 2017-09-01 DOI: 10.1007/s00466-017-1442-z

Authors:Q. V. Le; F. Bobaru Abstract: Abstract Peridynamic models are derived by assuming that a material point is located in the bulk. Near a surface or boundary, material points do not have a full non-local neighborhood. This leads to effective material properties near the surface of a peridynamic model to be slightly different from those in the bulk. A number of methods/algorithms have been proposed recently for correcting this peridynamic surface effect. In this study, we investigate the efficacy and computational cost of peridynamic surface correction methods for elasticity and fracture. We provide practical suggestions for reducing the peridynamic surface effect. PubDate: 2017-08-30 DOI: 10.1007/s00466-017-1469-1

Authors:Daniel E. Hurtado; Guillermo Rojas Abstract: Abstract Computer simulations constitute a powerful tool for studying the electrical activity of the human heart, but computational effort remains prohibitively high. In order to recover accurate conduction velocities and wavefront shapes, the mesh size in linear element (Q1) formulations cannot exceed 0.1 mm. Here we propose a novel non-conforming finite-element formulation for the non-linear cardiac electrophysiology problem that results in accurate wavefront shapes and lower mesh-dependance in the conduction velocity, while retaining the same number of global degrees of freedom as Q1 formulations. As a result, coarser discretizations of cardiac domains can be employed in simulations without significant loss of accuracy, thus reducing the overall computational effort. We demonstrate the applicability of our formulation in biventricular simulations using a coarse mesh size of \(\sim \) 1 mm, and show that the activation wave pattern closely follows that obtained in fine-mesh simulations at a fraction of the computation time, thus improving the accuracy-efficiency trade-off of cardiac simulations. PubDate: 2017-08-29 DOI: 10.1007/s00466-017-1473-5

Authors:F. Shi; M. J. S. Lowe; E. A. Skelton; R. V. Craster Abstract: Abstract The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach. PubDate: 2017-08-28 DOI: 10.1007/s00466-017-1471-7

Authors:Tugce Ozturk; Anthony D. Rollett Abstract: Abstract The present study is devoted to the creation of a process–structure–property database for dual phase titanium alloys, through a synthetic microstructure generation method and a mesh-free fast Fourier transform based micromechanical model that operates on a discretized image of the microstructure. A sensitivity analysis is performed as a precursor to determine the statistically representative volume element size for creating 3D synthetic microstructures based on additively manufactured Ti–6Al–4V characteristics, which are further modified to expand the database for features of interest, e.g., lath thickness. Sets of titanium hardening parameters are extracted from literature, and The relative effect of the chosen microstructural features is quantified through comparisons of average and local field distributions. PubDate: 2017-08-22 DOI: 10.1007/s00466-017-1467-3

Authors:P. Broumand; A. R. Khoei Abstract: Abstract This paper presents a general framework for modeling dynamic large deformation contact-impact problems based on the phantom-node extended finite element method. The large sliding penalty contact formulation is presented based on a master-slave approach which is implemented within the phantom-node X-FEM and an explicit central difference scheme is used to model the inertial effects. The method is compared with conventional contact X-FEM; advantages, limitations and implementational aspects are also addressed. Several numerical examples are presented to show the robustness and accuracy of the proposed method. PubDate: 2017-08-20 DOI: 10.1007/s00466-017-1463-7