Showing papers on "Linear elasticity published in 2020"
TL;DR: In this paper, an alternative method based on Fourier series which avoids meshing and which makes direct use of microstructure images is proposed, which is based on the exact expression of the Green function of a linear elastic and homogeneous comparison material.
Abstract: The local and overall responses of nonlinear composites are classically investigated by the Finite Element Method. We propose an alternate method based on Fourier series which avoids meshing and which makes direct use of microstructure images. It is based on the exact expression of the Green function of a linear elastic and homogeneous comparison material. First, the case of elastic nonhomogeneous constituents is considered and an iterative procedure is proposed to solve the Lippman-Schwinger equation which naturally arises in the problem. Then, the method is extended to non-linear constituents by a step-by-step integration in time. The accuracy of the method is assessed by varying the spatial resolution of the microstructures. The flexibility of the method allows it to serve for a large variety of microstructures. (C) 1998 Elsevier Science S.A.
219 citations
TL;DR: In this paper, a homogenization approach based on asymptotic analysis establishes a connection between these different characteristics at micro- and macro-scales, and guarantees that the additional parameters vanish if the material is purely homogeneous; in other words, it is fully compatible with conventional homogenisation schemes based on spatial averaging techniques.
Abstract: By using modern additive manufacturing techniques, a structure at the millimeter length scale (macroscale) can be produced showing a lattice substructure of micrometer dimensions (microscale). Such a system is called a metamaterial at the macroscale, because its mechanical characteristics deviate from the characteristics at the microscale. Consequently, a metamaterial is modeled by using additional parameters. These we intend to determine. A homogenization approach based on asymptotic analysis establishes a connection between these different characteristics at micro- and macroscales. A linear elastic first-order theory at the microscale is related to a linear elastic second-order theory at the macroscale. Small strains (and, correspondingly, small gradients) are assumed at both scales. A relation for the parameters at the macroscale is derived by using the equivalence of energy at macro- and microscales within a so-called representative volume element (RVE). The determination of the parameters becomes possible by solving a boundary value problem within the framework of the finite element method. The proposed approach guarantees that the additional parameters vanish if the material is purely homogeneous; in other words, it is fully compatible with conventional homogenization schemes based on spatial averaging techniques. Moreover, the proposed approach is reliable, because it ensures that the obtained additional parameters are insensitive to choices of the RVE consisting of a repetition of smaller RVEs depending upon the intrinsic size of the structure.
68 citations
TL;DR: Wang et al. as discussed by the authors proposed a mesh-free method to solve interface problems using the deep learning approach, where two types of PDEs are considered: an elliptic PDE with a discontinuous and high-contrast coefficient, and a linear elasticity equation with discontinuous stress tensor.
45 citations
TL;DR: NNWarp as discussed by the authors reconstructs the force-displacement relation via warping the nodal displacement simulated using a simplistic constitutive model, which can handle a wide range of 3D models of various geometry.
Abstract: NNWarp is a highly re-usable and efficient neural network (NN) based nonlinear deformable simulation framework. Unlike other machine learning applications such as image recognition, where different inputs have a uniform and consistent format (e.g., an array of all the pixels in an image), the input for deformable simulation is quite variable, high-dimensional, and parametrization-unfriendly. Consequently, even though the neural network is known for its rich expressivity of nonlinear functions, directly using an NN to reconstruct the force-displacement relation for general deformable simulation is nearly impossible. NNWarp obviates this difficulty by partially restoring the force-displacement relation via warping the nodal displacement simulated using a simplistic constitutive model–the linear elasticity. In other words, NNWarp yields an incremental displacement fix per mesh node based on a simplified (therefore incorrect) simulation result other than synthesizing the unknown displacement directly. We introduce a compact yet effective feature vector including geodesic , potential and digression to sort training pairs of per-node linear and nonlinear displacement. NNWarp is robust under different model shapes and tessellations. With the assistance of deformation substructuring, one NN training is able to handle a wide range of 3D models of various geometries. Thanks to the linear elasticity and its constant system matrix, the underlying simulator only needs to perform one pre-factorized matrix solve at each time step, which allows NNWarp to simulate large models in real time.
43 citations
TL;DR: In this article, a high-order numerical manifold method (HONMM) which is able to obtain continuous stress/strain field without recourse any stress smoothing operation in the post-processing stage is proposed.
38 citations
15 Apr 2020
TL;DR: In this article, a method of deriving exact solutions to the bi-harmonic equation in the context of elasticity problems is presented, and a number of new solutions are proposed.
Abstract: This reference work offers a method of deriving exact solutions to the biharmonic equation in the context of elasticity problems, and proposes a number of new solutions. Beginning with an in-depth presentation of a general mathematical model, this text proceeds to outline specific applications, extending the developed method to special harmonic problems of mechanics for conjugated domains. All applications are illustrated with numerical examples.
36 citations
TL;DR: In this article, two novel chiral block lattice topologies are conceived having interesting auxetic and acoustic behavior, which are made up of a periodic repetition of square or hexagonal rigid and heavy blocks connected by linear elastic interfaces, whose chirality results from an equal rotation of the blocks with respect to the line connecting their centroids.
33 citations
TL;DR: In this paper, a new set of novel crack-tip elements for analysis of interface cracks in linear elastic composite bimaterials by using the boundary element method (BEM) is presented.
32 citations
TL;DR: In this paper, a lattice volume fraction distribution optimization method is proposed to reduce the thermal distortion in metal additive manufacturing. But the optimization problem is formulated as an unconstrained minimization problem.
28 citations
TL;DR: In this paper, Hankel integral transforms are applied to solve the time-harmonic vertical vibration of a flexible circular foundation by using variational methods to demonstrate the influence of soil anisotropy, poroelasticity, foundation flexibility, depth of embedment and frequency of excitation on the vertical dynamic response of foundation and the force transmitted to soil.
28 citations
TL;DR: In this paper, a combined experimental and constitutive modeling framework is proposed for the development and validation of concentration-dependent 3D hyperelastic models for hydrogels in a concentration range of 0.4-4% w/v.
TL;DR: In this paper, a general loading condition is considered and the rods are regarded as hyperelastic bodies composed of a homogeneous isotropic material, and the finite displacement fields and deformation gradients are derived under the hypothesis of homogeneous deformations.
Abstract: This paper deals with the equilibrium problem of von Mises trusses in nonlinear elasticity. A general loading condition is considered and the rods are regarded as hyperelastic bodies composed of a homogeneous isotropic material. Under the hypothesis of homogeneous deformations, the finite displacement fields and deformation gradients are derived. Consequently, the Piola-Kirchhoff and Cauchy stress tensors are computed by formulating the boundary-value problem. The equilibrium in the deformed configuration is then written and the stability of the equilibrium paths is assessed through the energy criterion. An application assuming a compressible Mooney-Rivlin material is performed. The equilibrium solutions for the case of vertical load present primary and secondary branches. Although, the stability analysis reveals that the only form of instability is the snap-through phenomenon. Finally, the finite theory is linearized by introducing the hypotheses of small displacement and strain fields. By doing so, the classical solution of the two-bar truss in linear elasticity is recovered.
TL;DR: In this article, a virtual element method based on the Hellinger-Reissner variational principle was proposed for 3D linear elasticity problems, and a convergence and stability analysis was developed and confirmed the theoretical predictions via some numerical tests.
TL;DR: It is shown that the leading-order term of the perturbed elastic wave field is determined by the Neumann-Poincare operator associated to the Lam\'e system and the polariton resonance for the elastic system is studied.
Abstract: This paper is concerned with the analysis of surface polariton resonance for nanoparticles in linear elasticity. With the presence of nanoparticles, we first derive the perturbed displacement field...
TL;DR: In this paper, a wave function expansion method is used to solve the scattering and dynamic stress concentration around the elliptic cavity in the full plane under steady state linear elastic stationary incident SH wave with arbitrary angle.
TL;DR: In this article, an analytical plane strain solution is proposed for lined circular tunnels under non-hydrostatic initial stress field, assuming rock mass as a viscoelastic material obeying Burgers model, while concrete lining is supposed to have linear elastic behavior.
TL;DR: In this article, a scaled boundary finite element method (SBFEM) is used for transient vibro-acoustic analysis of plates and shells, where only the bottom surface of the shell is discretized with finite elements while the solution along the thickness is expressed analytically as a Pade expansion.
TL;DR: In this article, a new multipoint stress mixed finite element method for linear elasticity with weakly enforced stress symmetry on simplicial grids was developed, motivated by the multipoint flux mixed finite elements.
Abstract: We develop a new multipoint stress mixed finite element method for linear elasticity with weakly enforced stress symmetry on simplicial grids. Motivated by the multipoint flux mixed finite element ...
TL;DR: In this article, a nonlocal linear elastic fracture formulation based on a discrete layer approach and an interface model to study cracked nanobeams is presented, which uses the stress-driven nonlocal theory of elasticity to account for the size-dependency in the constitutive equations, and the Bernoulli-Euler beam theory to define the kinematic field.
TL;DR: The results show that the proposed half-plane boundary element method has an appropriate accuracy for analyzing seismic inclusion problems and can be recommended to geotechnical/mechanical engineers for transient analysis of different topographic features, seismic isolation and composite materials.
TL;DR: Numerical analysis for an industrial part is carried out, defining the material GF-PA6 as elastic and isotropic with constant Young's compression modulus according to ISO standard 604, and simulations and experimental tests show good accuracy.
Abstract: This manuscript presents an experimental and numerical analysis of the mechanical structural behavior of Nylstrong GF-PA6, a plastic material manufactured using FDM (fused deposition modeling) technology for a compression uniaxial stress field. Firstly, an experimental test using several test specimens fabricated in the Z and X-axis allows characterizing the elastic behavior of the reinforced GF-PA6 according to the ISO 604 standard for uniaxial compression stress environments in both Z and X manufacturing orientations. In a second stage, an experimental test analyzes the structural behavior of an industrial part manufactured under the same conditions as the test specimens. The experimental results for the test specimens manufactured in the Z and X-axis present differences in the stress-strain curve. Z-axis printed elements present a purely linear elastic behavior and lower structural integrity, while X-axis printed elements present a nonlinear elastic behavior typical of plastic and foam materials. In order to validate the experimental results, numerical analysis for an industrial part is carried out, defining the material GF-PA6 as elastic and isotropic with constant Young’s compression modulus according to ISO standard 604. Simulations and experimental tests show good accuracy, obtaining errors of 0.91% on the Z axis and 0.56% on the X-axis between virtual and physical models.
TL;DR: In this paper, the authors developed a numerical methodology for the calculation of mode-I R-curves of brittle and elastoplastic lattice materials, and revealed the impact of lattice topology, relative density and constituent material behavior on the toughening response of 2D isotropic lattices.
Abstract: We develop a numerical methodology for the calculation of mode-I R-curves of brittle and elastoplastic lattice materials, and unveil the impact of lattice topology, relative density and constituent material behavior on the toughening response of 2D isotropic lattices. The approach is based on finite element calculations of the J-integral on a single-edge-notch-bend (SENB) specimen, with individual bars modeled as beams having a linear elastic or a power-law elasto-plastic constitutive behavior and a maximum strain-based damage model. Results for three 2D isotropic lattice topologies (triangular, hexagonal and kagome) and two constituent materials (representative of a brittle ceramic (silicon carbide) and a strain hardening elasto-plastic metal (titanium alloy)) are presented. We extract initial fracture toughness and R-curves for all lattices and show that (i) elastic brittle triangular lattices exhibit toughening (rising R-curve), and (ii) elasto-plastic triangular lattices display significant toughening, while elasto-plastic hexagonal lattices fail in a brittle manner. We show that the difference in such failure behavior can be explained by the size of the plastic zone that grows upon crack propagation, and conclude that the nature of crack propagation in lattices (brittle vs ductile) depends both on the constituent material and the lattice architecture. While results are presented for 2D truss-lattices, the proposed approach can be easily applied to 3D truss and shell-lattices, as long as the crack tip lies within the empty space of a unit cell.
TL;DR: In this article, the anisotropic characteristics of the effective stress coefficient for sandstone under different true triaxial stress and pore pressure conditions were investigated, and the results showed that effective stress coefficients exhibited anisotropy due to the different principal strains in three directions and the annessotropy of pore structure, and it is closely linked with the pore fluid flowing through highly compressible clay aggregates.
TL;DR: In this article, the authors proposed a nonlinear stress-strain constitutive equation in the form of a function of time and cycles simultaneously, which combines both time and cycle-dependent nature of fatigue phenomena in an integrated formulation.
TL;DR: In this article, the role of the plastic spin in free energy and the dissipation of a crack tip was investigated and a generalised Jintegral was defined and employed to determine the power of the singularity.
TL;DR: In this paper, the stability, elastic moduli and deformation behavior of graphene-based diamond-like phases are examined by molecular dynamics simulations and three important criteria are considered to study stability of the structure within applied methods.
TL;DR: In this article, a finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented, which is a minimal enhancement of classical crystal/J 2 plasticity that fundamentally accounts for polar/excess dislocations at the mesoscale.
TL;DR: A computationally efficient modeling approach for the accurate evaluation of process-induced deformations and residual stresses in composite parts is presented in this paper, where a family of refined one-dimensional kinematic models, developed in the framework of the Carrera Unified Formulation, has been used to predict the accurate through-thickness deformation of layered structures during the manufacturing process.
TL;DR: In this article, a physics-based analytical model is proposed to accurately and rapidly predict the in-process thermal stress in an additively manufactured (AM) part, where a moving point heat source approach is employed to predict the temperature field.
TL;DR: In this work, both experimental and simulation results are used to study the discrete effects of both experimental parameters and varying lattice anisotropy across the orientation space, on orientation determination accuracy.