Linear Elastic Anisotropic Materials Research Articles

A powerful matrix formalism for stress singularities in anisotropic multi-material corners. Homogeneous (orthogonal) boundary and interface conditions

A computational code based on a semianalytic procedure for the determination of the characteristic exponents and the singular stress and displacement fields in multi-material corners is developed. Linear elastic anisotropic materials under generalized plane strain state are considered. This code is a universal computational tool able to analyze both open and closed (periodic) corners, composed of one or multiple materials with isotropic, transversely isotropic or orthotropic constitutive laws, covering both mathematically non-degenerate and degenerate materials in the framework of Stroh formalism. In multi-material corners, material junctions with perfectly bonded or frictionless sliding interfaces can be studied. The considered homogeneous boundary conditions cover stress free and fixed faces, or faces with some restricted or allowed direction of displacements, defined either in the reference frame aligned with the cylindrical coordinate system or in an inclined reference frame. The code is developed in MATLAB and it is based on the Stroh matrix formalism for anisotropic elasticity, the concept of transfer matrix for single material wedges, and on the matrix formalism for homogeneous (orthogonal) boundary conditions. The comparison of the characteristic exponents obtained by the present code and by the solution of closed-form eigenequations available in the literature, has a two-fold objective, first to exhaustively check the general computational implementation of the matrix formalism presented, and second to check the closed-form expressions of eigenequations for relevant specific cases published in the literature.

Topology and material orientation optimization based on evolution equations

AbstractMany modern high‐performance materials have inherent anisotropic elastic properties and its local material orientation can be considered to be an additional design variable for the topology optimization [1–3]. We extend our previous model for topology optimization with variational controlled growth [4–6] for linear elastic anisotropic materials, for which the material orientation is introduced as an additional design variable. We solve the optimization problem purely with the principles of thermodynamics by minimizing the Gibbs energy. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Extreme conditions of elastic constants and principal axes of anisotropy

This paper describes the derivation of extreme conditions of each elasticity coefficient (Young’s modulus, shear modulus, et al.,) for the general case of linear-elastic anisotropic materials. The stationarity conditions are obtained, and they determine the orthogonal coordinate systems being the principal axes of anisotropy, where the number of independent elasticity constants decreases from 21 to 18 and, in some cases of anisotropy, to 15 or lower. The example of a material with cubic symmetry is given.

Unified analytical expressions of the three-dimensional fundamental solutions and their derivatives for linear elastic anisotropic materials

Novel unified analytical displacement and stress fundamental solutions as well as the higher order derivatives of the displacement fundamental solutions for three-dimensional, generally anisotropic and linear elastic materials are presented in this paper. Adequate integral expressions for the displacement and stress fundamental solutions as well as the higher order derivatives of the displacement fundamental solutions are evaluated analytically by using the Cauchy residue theorem. The resulting explicit displacement fundamental solutions and their first and second derivatives are recast into convenient analytical forms which are valid for non-degenerate, partially degenerate, fully degenerate and nearly degenerate cases. The correctness and the accuracy of the novel unified and closed-form three-dimensional anisotropic fundamental solutions are verified by using some available analytical expressions for both transversely isotropic (non-degenerate or partially degenerate) and isotropic (fully degenerate) linear elastic materials.

Experimental investigation of the mechanical properties of neoprene coated nylon woven reinforced composites

In this study, the mechanical behaviour of neoprene coated nylon woven fabric composites was assessed using biaxial loading based on hydraulic bulge test method and uniaxial tensile method at varied environmental testing conditions. Results indicating failure modes, ultimate strengths and strains from the uniaxial testing of the composites were compared and recommendations for application of the composite material in structural design are reported. A through thickness approximate homogeneous modulus from the weft and warp uniaxial tests results of the membrane for a simple linear elastic anisotropic material model was used in ABAQUS finite element software to simulate the bulge test experiments. Results from the numerical analysis were found to replicate the bulge experiments to a first approximation. This approach offers useful application for the FE modelling and design of offshore inflatable structures made of coated woven fabrics which are typified by large size and complex geometries, as it reduces computational cost and potentially eliminates the need for a complex material description involving detailed theoretical derivations and advanced programming to implement.

An attempt to separate elastic strain energy density of linear elastic anisotropic materials based on strains considerations

A promising new effort toward the decomposition of the elastic strain energy density of linear elastic anisotropic materials into a dilatational and a distortional part is presented. By assuming that volume changes must keep the material symmetries unchanged, a new physical perspective is presented and interesting definitions are drawn. This new perspective necessitates the introduction of a strain parameter m characteristic of the material’s anisotropy. This strain parameter besides easing the calculation of the dilatational and distortional energetic terms additionally accounts for the directional sensitivity of anisotropic materials.

Solid-mechanics finite element simulations of the draping of fabrics: a sensitivity analysis

Abstract This paper covers numerical investigations of the draping of woven fabrics into a “hat” shape, combining a hemispherical cup with a wide flat rim. A mechanical approach is adopted using finite element analysis (FEA) methodology. In this, the fabric is considered as a solid sheet with mechanical properties and friction properties. In this study, a linear elastic anisotropic material model describes the deformation of fabrics. An explicit dynamic finite element analysis is applied and systematic parametric numerical studies are presented, which incorporate investigations of the effects of numerical parameters, material properties and processing conditions on the draping of fabrics. More specifically, the effects of the following variables and parameters are included: number of elements, number of time increments in the dynamic FEA analysis, punch speed, shear and tensile moduli of fabric, coefficient of friction for all interfaces and level of load on the fabric holder.

Experimental and theoretical studies of columns under axial impact

The dynamic response of columns loaded by an impulsive axial compression was studied experimentally and theoretically. Approximate criteria for determination of dynamic buckling are discussed and applied. The investigation was carried out on clamped specimens, made of metals and composite materials, loaded impulsively by a striking mass. In the theoretical study Rayleigh-type beam equations are assumed for a geometrically imperfect column of a linear-elastic anisotropic material. A numerical solution, by a finite-difference approach, yields buckling behavior which correlates well with the experimental results. It is shown that initial geometrical imperfection, duration of impulse and effective slenderness have a major influence on the buckling loads whereas the effect of the material is secondary. The major effects are presented in a form that can guide the designer.