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We propose in this paper analytical and numerical models that describe the in-plane uniaxial elastic properties (Young's moduli and Poisson's ratios) of a honeycomb structure with curved walls. We perform a parametric analysis of the mechanical performance of this honeycomb also by taking into account the different types of deformations acting inside the cell walls. The curved wall honeycomb possesses higher magnitudes of the Poisson's ratio ν12 in the auxetic configuration compared to classical center symmetric configuration with straight cell wall. The presence of the curvature also allows creating configurations with positive Poisson's ratio even for negative internal cell angles, and makes this honeycomb design attractive for mechanical tailoring. [ABSTRACT FROM AUTHOR]

SUMMARY A new finite heterogeneous element consisting of sliced microstructures (FHES) is applied in a multi-scale technique. The FHES represents a heterogeneous material with microscopic constituents without homogenization or microscopic finite element analysis. A representative volume element extracted from a heterogeneous structure is thinly sliced. Each slice is modeled as a combined spring to calculate properties of the FHES. Each FHES has the same number of nodes as an ordinary finite element, and the macroscopic analysis cost is the same as that for ordinary finite element analysis. However, the FHES retains information about the microscopic material layout (i.e., the distribution of a material's property) in itself that is lost during homogenization. In the proposed approach, materials are not homogenized. The FHES does not have a constant (homogenized) material property and can 'change stiffness' depending on its deformation behavior. This reduces error due to coarse-graining and allows us to calculate the macroscopic deformation behavior with sufficient accuracy even if a large gradient of strain is generated in the macroscopic field. The novelty of the research is the development of rational heterogeneous finite elements. The paper presents the theory behind the FHES and its practical application to a linear elastic problem. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper reports some numerical experiments on the effectivity of the Zienkiewicz-Zhu error estimate (1987) and comparisons of two adaptive mesh generators: ADMESH, developed by Jin and Wiberg (1990) and MAD2D by Peraire et al. (1987) and Zhu et al. (1990-91). From the experiments we observe that: (1) without any empirical correction, the effectivity of the error estimate for linear triangular elements is good if post-processed continuous stresses are obtained by adequately using an iterative stress recovery procedure (Zienkiewicz et al., 1985), and is also acceptable by using a simple `averaging' procedure; (2) these two mesh generators are basically comparable. [ABSTRACT FROM AUTHOR]

Applications of inexact Newton and inexact Newton-like solvers are described and analysed for the solution of non-linear systems arising in the numerical solution of problems of elastoplasticity. Both explicit and return mapping incremental finite element algorithms are considered. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Microstructured plates, consisting of various conventional and re-entrant cells, are numerically constructed and analyzed for their effective elastic properties under in-plane deformation. The finite element numerical method is adopted. The calculated effective Poisson's ratios of the plates are found to be in the range between −1 and 1, in consistency with the theory of two-dimensional elasticity. Auxetic angles need to be greater than about 20° in order to obtain negative Poisson's ratio. Increasing the auxetic angles reduces the effective pure shear modulus. Elastically anisotropic characteristics of the homogenized plate are analyzed with the calculated effective Young's modulus, Poisson's ratio, and pure shear modulus. [ABSTRACT FROM AUTHOR]

The problem of nonlinear bending of a curved tube made of incompressible rubber-like material is considered. The tube shaped like a portion of a thin-walled toroidal shell between two radial planes is inflated by pressure and then subjected to in-plane bending moments. To investigate nonlinear response and stability of the tube under these loading conditions, a finite-element approach is proposed. A special shell finite element is formulated under the assumption of uniform deformation along the tube length. The effect of wrinkling on nonlinear response of the tube is described using the tension-field theory. A change in the inflating pressure resulting from deformation of the tube due to bending is taken into account in the formulation of the governing equations. The effect of pressure on the bending stiffness, stability, and deformations of a curved tube is examined and discussed. [ABSTRACT FROM AUTHOR]

In this article the multiplicative decomposition of the deformation gradient into one part constrained in the direction of the axis of anisotropy and one part describing the directional deformation is proposed. This leads to a clear division of the deformation and stress states in the direction of anisotropy and a remaining part. The decomposition is explained in detail and a constitutive model of hyper-elasticity is proposed for the case of transversal isotropy, where the behavior of the model is investigated with the aid of simple analytical examples. The model is also investigated for inhomogeneous deformation states using high-order finite elements based on hierarchical shape functions showing the sensitivity of the accuracy of the results in the case of anisotropic media. [ABSTRACT FROM AUTHOR]

SUMMARY Anisotropic elastic materials, such as the homogenized model of a fiber-reinforced matrix, can display near rigidity under certain applied stress-the resulting strains are small compared with the strains that would occur for other stresses of comparable magnitude. The anisotropic material could be rigid under hydrostatic pressure if the material were incompressible, as in isotropic elasticity, but also for other stresses. Some commonly used finite elements are effective in dealing with incompressibility, but are ill-equipped to handle materials that lock under non-hydrostatic stress states (e.g., uniformly reduced serendipity and Q1/Q0 B-bar hexahedra). The failure of the original B-bar method is attributed to the assumption that the mode of deformation to be relieved is one of near incompressibility. The remedy proposed here is based on the spectral decomposition of the compliance matrix of the material. The spectrum can be interpreted to separate nearly-rigid and flexible modes of stress and strain, which leads naturally to a generalized selective reduced integration. Furthermore, the spectral decomposition also enables a three-field elasticity formulation that results in a B-bar method that is effective for general anisotropic materials with an arbitrary nearly-rigid mode of deformation.Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: The Elastic Multi‐Body Simulation (EMBS) is the state‐of‐the‐art method when dealing with elastic deformations of components in complex mechanical systems. But the required FE‐model representing the elastic structure contains several uncertainties concerning geometry, local and directional stiffness as well as damping phenomena. A mandatory Model Order Reduction (MOR) embodies further approximation errors. Due to the drawbacks of the conventional procedure, a novel approach is suggested, where the data of the elastic body model is directly gained from the results of an Experimental Modal Analysis (EMA). Therefore, the measured data is transferred to the Standard Input Data (SID) format by means of the software MORPACK (Model Order Reduction PACKage). The novel approach yields several challenges for which adequate solutions are presented. The feasibility is demonstrated at the example of an U‐section. The accuracy in the higher frequency range can be increased, which is especially important for vibro‐acoustic simulations. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]