Journal of Elasticity最新文献

We formulate a direct theory for fiber-reinforced elastic shells. Our framework utilizes the Cosserat theory of elasticity to model both the shell-like nature of the structure and the embedded fiber response. To this end, we merge the multiple-director theory of Cosserat continua with the additional constraint that the fibers convect as material curves on the surface. The virtual power statement furnishes the equilibrium equations. We also present a coordinate-free formulation and close with a discussion of material symmetry.

We generalize a recent theory of bending of thin micropolar plates by incorporating surface effects through the modeling of plate surfaces as adjacent two-dimensional micropolar elastic bodies. By incorporating both elastic surface effects and the micropolar elastic behavior of the plate, the proposed model is capable of taking into account the contribution of high surface-to-volume ratios as well as the influence of microstructural mechanics at micro/nano scales. We determine the fundamental solution of the resulting system of equations and establish uniqueness results for the corresponding Dirichlet and Neumann boundary value problems. Moreover, we provide a numerical example to demonstrate the efficiency of the model in representing the size-dependence arising from various factors that incorporate characteristic lengths. Furthermore, we showcase the sensitivity of the results to different types of characteristic lengths present in the model.

Fiber orientation tensors (FOT) are widely used to approximate statistical orientation distributions of fibers within fiber-reinforced polymers. The design process of components made of such fiber-reinforced composites is usually accompanied by a virtual process chain. In this virtual process chain, process-induced FOT are computed in a flow simulation and transferred to the structural simulation. Within the structural simulation, effective macroscopic properties are identified based on the averaged information contained in the FOT. Solving the field equations in flow simulations as well as homogenization of effective stiffnesses necessitates the application of a closure scheme, computing higher-order statistical moments based on assumptions. Additionally, non-congruent spatial discretizations require an intermediate mapping operation. This mapping operation is required, if the discretization, i.e., mesh, of the flow simulation differs from the discretization of the structural simulation. The main objective of this work is to give an answer to the question: Does the sequence of closure and mapping influence the achieved results? It will turn out, that the order influences the result, raising the consecutive question: Which order is beneficial? Both questions are addressed by deriving a quantification of the closure-related uncertainty. The two possible sequences, mapping followed by closure and closure followed by mapping, yield strongly different results, with the magnitude of the deviation even exceeding the magnitude of a reference result. Graphical consideration reveals that for both transversely isotropic and planar FOT-input, invalid results occur if the mapping takes place prior to closure. This issue is retrieved by orientation averaging stiffness tensors. As a by-product, we explicitly define for the first time the admissible parameter space of orthotropic fourth-order fiber orientation tensors and define a distance measure in this parameter space.

A new scheme for hyperelastic material is developed based on applying the argument of calculus variation to two-factor multiplicative decomposition of the deformation gradient. Then, Piola–Kirchhoff stress is coupled with internal balance equation. Strain energy function is expressed in terms of principal invariants of the deformation gradient decomposed counterparts. Recent work introduces a strain energy function in terms of principal stretches of the deformation gradient multiplicatively decomposed counterparts directly. Hence, a new reformulation of Piola–Kirchhoff stress and internal balance equation are provided. This work focuses on developing the mathematical framework to calculate the elasticity tensor for material model formulated in terms of decomposed principal stretches. This paves the way for future implementation of these classes of material model in FE formulation.

Stretch-based constitutive models for isotropic hyperelastic materials as alternatives to the classical strain invariant models have been the subject of considerable recent attention largely motivated by application to modelling the mechanical response of soft tissues. One such four-parameter constitutive model was proposed recently by Anssari-Benam (J. Elast. 153:219–244, 2023) for incompressible isotropic hyperelastic soft materials. The model was deemed to be comprehensive in that several well-known strain-energies may be recovered for some particular and limiting values of some of the parameters. The model is a generalization of several related simpler models based on microstructural considerations that have been shown to match well with experimental data for a wide variety of soft materials. In particular, the celebrated one-term Ogden model is obtained as a special case. Here we examine the response of the new model for the problem of pure torsion for a solid circular cylinder with particular emphasis on the Poynting effects governing the lengthening or shortening of the cylinder.

This paper develops a novel set of displacement temperature potential functions to solve the thermoelastodynamic problems in functionally graded transversely isotropic media subjected to thermal source. For this purpose, three-dimensional heat and wave equations are considered to obtain the displacement temperature equations of motion for functionally graded materials. In the present study, a systematic method is used to decouple the elasticity and heat equations. Hence one sixth-order differential equation and two second-order differential equations are obtained. Completeness of the solution is proved using a retarded logarithmic Newtonian potential function for functionally graded transversely isotropic domain. To verify the obtained solution, in a simpler case, potential functions are generated for homogeneous transversely isotropic media that coincide with respective equations. Presented potential functions can be used to solve the problems in various media like infinite and semi-infinite space, beams and columns, plates, shells, etc., with arbitrary boundary conditions and subjected to arbitrary mechanical and thermal loads.

In this paper, we present a comprehensive investigation of stress propagation in a two-dimensional elastic circular disk. To accurately describe the displacements and stress fields within the disk, we employ a scalar and vector potential approach, representing them as sums of Bessel functions. The determination of the coefficients for these expansions is accomplished in the Laplace space, where we compare the boundary conditions. By converting the inverse Laplace transforms into complex integrals using residue calculus, we successfully derive explicit expressions for the displacements and stress fields. Notably, these expressions encompass primary, secondary, and surface waves, providing a thorough characterization of the stress propagation phenomena within the disk. Our findings contribute to the understanding of mechanical behavior in disk-shaped components and can be valuable in the design and optimization of such structures across various engineering disciplines.