Journal of Elasticity最新文献

A complete closed-form solution is derived to the finite plane elasticity problem associated with an elliptical incompressible liquid inclusion embedded in an infinite compressible hyperelastic matrix of harmonic type subjected to uniform remote in-plane Piola stresses. The internal uniform hydrostatic Piola stresses and deformation gradients within the elliptical incompressible liquid inclusion are obtained. The internal uniform hydrostatic tension and hoop stress on the matrix side along the liquid-solid interface for various shapes of the elliptical liquid inclusion and different elastic constants of the matrix under various remote loadings are calculated.

We study the effective properties of a linear elastic or perfectly viscoplastic composite consisting of a soft matrix reinforced by possibly very stiff fibers. The effective material is characterized by the emergence of a discrepancy between the displacement in the fibers and the overall averaged displacement, giving rise to a concentration strain in the matrix. The effective energy stored in the fibers is a combination of stretching, bending and torsional energies. This work completes and corrects results previously obtained by the author and coworkers, who failed to notice the torsional contribution.

Tensile strength characterization of brittle materials by means of uniaxial tensile tests is often unfeasible, as most samples form chips during specimen preparation, leading to unacceptable geometric deviations. For this reason, the disc specimens used in Brazilian tests to determine indirect tensile strength are preferred. Despite its influence on the induced stress field and the location of the failure initiation point, the actual stress distribution along the contact is still under debate. In the present work, the complex variable method is used to develop a new analytical formulation based on the simplest possible shear stress distribution along the disc boundary that fulfils elastic equilibrium. Based on this formulation, an integration method is used to obtain the stress field generated inside specimens—elastic discs—that are subjected to distributed shear forces on their contact rims. An application of this method to the Brazilian test case is performed, proving that shear and frictional forces can be considered simultaneously. Furthermore, a mathematical procedure to simultaneously consider radial and shear stress distributions along the loaded boundary is developed to determine any possible stress field for relevant practical applications. The results confirm that shearing significantly increases stress in the vicinity of the contact area, which may explain the wedge failure pattern sometimes observed in real test specimens. Additionally, the proposed formulation guarantees that if failure is initiated in the centre of the specimen, the applied shear stress distribution no longer influences the indirect tensile strength of the material, although it influences the final test output if failure is initiated at any other point along the vertical diameter.

The elastic properties of dilute solid suspensions with imperfectly bonded inclusions of ellipsoidal shape are estimated. The imperfect bonding is regarded as a sharp interface across which the displacement jumps in proportion to the surface traction. Elastic compliances of the matrix and inclusion phases can exhibit arbitrary anisotropy while that of the bonding exhibits an anisotropy that depends on the interface normal only. A variational framework is employed to generate pairs of elementary bounds, asymptotically exact results, and approximations for the effective elasticity tensor. Each member of the pair differs in the way the bonding compliance is averaged over the interfacial surface: an ‘arithmetic’ mean in one case and a ‘harmonic’ mean in the other case. The results are used to infer the most convenient approximation for a given range of material parameters.

There are many situations where groundwater flow has high flow rates, causing large seepage forces. Examples are flows around highly conductive fractures and tunnels. We present a new analytic element for a tunnel in an elastic medium. We combined the analytic element method for groundwater flow with that for linear elasticity, and include the seepage force as a body force in the linearly elastic model. We represent tunnels and fractures as analytic elements. The solution for the case considered is limited to steady state flow and fluid-to-solid coupling. We present examples of the computed seepage forces around a tunnel and a fracture as well as a comparison with another numerical model.

A multi-scale framework is constructed for the computation of the stiffness tensors of an elastic strain-gradient continuum endowed with an anisotropic microstructure of arbitrarily-shaped particles. The influence of microstructural features on the macroscopic stiffness tensors is demonstrated by comparing the fourth-order, fifth-order and sixth-order stiffness tensors obtained from macro-scale symmetry considerations to the stiffness tensors deduced from homogenizing the elastic response of the granular microstructure. Special attention is paid to systematically relating the particle properties to the probability density function describing their directional distribution, which allows to explicitly connect the level of anisotropy of the particle assembly to local variations in particle stiffness and morphology. The applicability of the multi-scale framework is exemplified by computing the stiffness tensors for various anisotropic granular media composed of equal-sized spheres. The number of independent coefficients of the homogenized stiffness tensors appears to be determined by the number of independent microstructural parameters, which is equal to, or less than, the number of independent stiffness coefficients following from macro-scale symmetry considerations. Since the modelling framework has a general character, it can be applied to different higher-order granular continua and arbitrary types of material anisotropy.

This paper discusses wave propagation in unbounded particle-based materials described by a second-gradient continuum model, recently introduced by the authors, to provide an identification technique. The term particle-based materials denotes materials modeled as assemblies of particles, disregarding typical granular material properties such as contact topology, granulometry, grain sizes, and shapes. This work introduces a center-symmetric second-gradient continuum resulting from pairwise interactions. The corresponding Euler-Lagrange equations (equilibrium equations) are derived using the least action principle. This approach unveils non-classical interactions within subdomains. A novel, symmetric, and positive-definite acoustic tensor is constructed, allowing for an exploration of wave propagation through perturbation techniques. The properties of this acoustic tensor enable the extension of an identification procedure from Cauchy (classical) elasticity to the proposed second-gradient continuum model. Potential applications concern polymers, composite materials, and liquid crystals.

We deal with the Signorini contact problem between two Timoshenko beams. In this work we use the theory of semigroups to show the existence of solutions that decay uniformly to zero. This method is new and more effective than the widely used energy method. This is because in particular we obtain uniform decay of the solutions to zero for any boundary condition. A second important point is that we can take advantage of stabilization results of others linear dynamic systems with different dissipative mechanisms and apply them through our method for Contact Problems (see Sect. 4). Finally, thanks to Lipschitzian perturbations we can generalize the Signorini problem to more general semi linear problems in a simple way (see Sect. 4.3).

Through suitable changes of variables for a typical problem in hyper-elasticity, either in the reference or deformed configurations, one can setup and analyze versions of the same problem in terms of inner or outer maps or variations. Though such kind of transformations are part of the classical background in the Calculus of Variations, we explore under what sets of hypotheses such versions can be shown to have minimizers and be equivalent to the standard form of the problem. Such sets of hypotheses lead naturally to some distinct poly-convex energy densities for hyper-elasticity. Likewise we explore optimality in either of the two forms through a special way to generate one-parameter families of feasible deformations, feasibility including injectivity and non-interpenetration of matter.

The mid-surface scaling invariance of bending strain measures proposed in (Int. J. Solids Struct. 37(39):5517–5528, 2000) is discussed in light of the work of (J. Elast. 146(1):83–141, 2021).