•Suture shapes were automatically generated using a line descriptor method.•Analytical and finite element models were developed to determine the pullout response and maximum tensile stress in the ...suture materials.•The material response can be tuned with geometrical parameters like interlocking angle θ0, plateau length d/R0, and radii ratio R0/R1.•Coefficient of friction between suture interfaces also plays an important role in the material response.•A ``brute force'' optimization scheme showed that to optimize the maximum strength and energy absorption, it is preferable to use lo friction coefficient for all types of sutures.
Hard structural elements in nature are often joined with sutures lines, as seen in human skull, cephalopods or turtle shell. These sutures can arrest cracks, and can provide flexibility for respiration, locomotion or growth. In this paper we introduce a morphometric method to capture the complex shape of sutured interfaces using only a few parameters. The method is simple, and can capture relatively complex suture geometries with re-entrants, interlocking features. The study starts with a simple jigsaw-like model which is enriched with additional features (plateau regions in dovetail-like sutures, multiple locking sites). For each case, closed form and finite elements solutions are developed to capture the full nonlinear pullout response and to predict the maximum stress (and potential fracture) in the solid material. These models were then used to identify the geometries and interface properties (friction) that lead to optimum combinations of strength and energy absorption. Suture designs that reduced frictional stress with low coefficient of friction or with multiple contact points were the most efficient. The results can serve as guidelines to design and optimization of non-adhesive sutures with arbitrary shapes made of arc of circles and lines. We found that the best designs involve low coefficient of friction, which raises an interesting hypothesis on the function of the protein layer in natural sutured lines: This soft layer could act as “lubricant” to prevent the fracture of the solid structures.
We study the formation and propagation of nonlinear stress waves in 3D woodpile elastic metamaterials consisting of vertically stacked slender cylindrical rods. We find the nonlinear waveforms ...transmitted through the woodpile architectures under impact are highly sensitive to their design parameters, particularly stacking distances and angles in 3D assemblies. We numerically and experimentally demonstrate that the woodpile system can localize, modulate, and ultimately attenuate propagating nonlinear waves in an efficient manner without relying on material damping. We also show the feasibility of constructing metamaterials with a simultaneous characteristic of high damping and high stiffness by using the controllable wave dispersion in the woodpile structures. These woodpile metamaterials offer enhanced degrees of freedom in manipulating stress waves, thereby offering a new way to design efficient impact protectors with high stiffness.
This paper presents a novel form-finding algorithm for tensegrity structures that is based on the finite element method. The required data for the form-finding is the topology of the structure, ...undeformed bar lengths, total cable length, prestress of cables and stiffness of bars. The form-finding is done by modifying the single cable lengths such that the total cable length is preserved and the potential energy of the system is minimized. Two- and three-dimensional examples are presented that demonstrate the excellent performance of the proposed algorithm.
A new boundary element model for transient dynamic analysis of 2D structures is presented. The dual reciprocity method (DRM) is reformulated for the 2D elastodynamics by using the multiquadric radial ...basis functions (MQ). The required kernels for displacement and traction particular solutions are derived. Some terms of these kernels are found to be singular; therefore, a new smoothing technique is proposed to solve this problem. Hence, the limiting values of relevant kernels are computed. The validity and strength of the proposed formulation are demonstrated throughout several numerical applications. It is proven from the results that the present formulation is more stable than the traditional DRM, which uses the conical (1
+
R) function, especially in predicting results in the far time zone.
Element-free Galerkin (EFG) methods are presented and applied to static and dynamic fracture problems. EFG methods, which are based on moving least-square (MLS) interpolants, require only nodal data; ...no element connectivity is needed. The description of the geometry and numerical model of the problem consists only of a set of nodes and a description of exterior boundaries and interior boundaries from any cracks. This makes the method particularly attractive for growing crack problems, since only minimal remeshing is needed to follow crack growth. In moving least-square interpolants, the dependent variable at any point is obtained by minimizing a function in terms of the nodal values of the dependent variable in the domain of influence of the point. Numerical examples involving fatigue crack growth and dynamic crack propagation are presented to illustrate the performance and potential of this method.
Beamlike solutions for fully anisotropic elastic tubes of arbitrary closed cross section are derived following the exact beam theory introduced recently by Ladevèze and Simmonds Comptes Rendus Acad. ...Sci. Paris 322 (1996) 455; Eur. J. Mech., A/Solids 17 (1998) 377. Instead of using finite elements to compute the various operators that appear, here the linear shell theory of Koiter A consistent first approximation in the general theory of thin elastic shells, The Theory of Thin Elastic Shells, Proc. IUTAM Sympos. Delft, Koiter, W.T. (Ed.), North-Holland, Amsterdam, 1959, p. 12 and Sanders An improved first-approximation theory for thin shells, (1959) NASA Rept. No. 24 is used to exploit the relative thinness of the tube. Analytical, beamlike solutions (the analogues of Saint–Venant solutions in three-dimensional elasticity) are obtained which contain relative errors of O(
h/
R), where
h is the shell thickness and
R is some cross sectional radius. These errors are of the same order of magnitude as those contained unavoidably in the stress–strain relations of any first-approximation shell theory. In addition, beamlike stress–strain relations are obtained which express an overall bending strain vector and an overall extensional-shear strain vector in terms of the net traction and moment at any section. Numerical results are presented for tubes with elliptic cross sections. This work generalizes the analysis of Reissner and Tsai J. Appl. Mech. 39 (1972) 148 by considering external surface loads and by allowing for overall transverse shearing forces in addition to a net axial force and complements the asymptotic analysis of Berdichevsky et al. Comp. Eng. 2 (1992) 411 by allowing the tube to be of any length.
A new three-dimensional variable-order singular boundary element has been constructed for stress analysis of three-dimensional interface cracks and internal material junctions. The singular fields in ...the vicinity of crack front or junction have been accurately represented by the singular elements by taking account the variable order of singularities and the angular profiles of field variables. Both the singular stress fields and displacement fields are independently formulated by the element’s shape functions. Different kinds of displacement formulations are investigated. The formulation combining singular and linear terms is found to be the most accurate one. The mixed-mode stress intensity factors are treated as nodal unknowns. The variation of stress intensity factors along the line of singularity can be obtained directly from the final system of equations and thus no post processing, such as three-dimensional J-integral or domain integral, is necessary. Numerical examples involving stress singularity, such as penny-shaped cracks in homogeneous and dissimilar material interface, plates with through-thickness cracks, and a dissimilar inclusion, are investigated. The analysis results are in good agreement with those reported in the literature.
A macroscopic yield or failure criterion is derived for fiber composite materials. The derivation decomposes naturally into two modes of yield/failure, one being matrix dominated, the other being ...fiber dominated, thus there are two governing criteria. The resulting forms are quadratic in the components of the average stress tensor with two material parameters for each mode of yield/failure. The physical context of the formulation is that of aligned fiber systems with a polymeric matrix phase under high fiber concentration conditions.
The closed-form solutions to the compressive stiffness of elastic layers bonded between rigid plates are derived through theoretical analyses for the layers of infinite-strip, circular and square ...shapes. Based on the two kinematics assumptions, the governing equations for the mean pressure are established from the equilibrium equations and the bulk modulus equation. Satisfying the stress boundary conditions, the pressure functions are solved and the formulae for the compressive stiffness are derived. The compressive stiffnesses calculated from these formulae are extremely close to the results obtained from the finite element method for an extensive range of shape factor and Poisson's ratio.
A method to model the thermoelastic response of flat laminated composites using a large radius axisymmetric hollow layered cylinder model is presented. An axisymmetric concentric cylinder model and a ...flat laminate model, each based on Reissner's variational principle with equilibrium stress fields, are compared. The stress components and the governing equations of the axisymmetric concentric cylinder formulation for a cylinder of infinite radius are shown analytically to be equivalent to the flat laminate formulation. Numerical results for the axisymmetric free edge stress field are shown to be nearly identical to the flat laminate free edge stress field solution. Selected results for the elastic stress fields and energy release rates in composite laminates with free edge and/or internal delaminations and transverse cracking are presented.
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