Journal of Elasticity最新文献

We study spontaneous deformations of a ribbon made of nematic polymer networks and activated under the action of a mechanical load. We show that when such ribbons are activated appropriately, the deformations produced can pull back and perform work against the externally applied load. We perform two numerical experiments to demonstrate this effect: (1) the pulling experiment, where the ribbon is pulled longitudinally by a point force, and (2) the bending experiment, where the ribbon is bent out of plane by a terminally applied point force. We quantify the capacity of the ribbon to work against external loads, and compute its dependence on both the ribbon thickness and the imprinted nematic texture (that is, the distribution of the nematic directors across the ribbon’s length). Finally, we compute the efficiency of the activation process. Building on the outcomes of our numerical explorations, we formulate two educated conjectures on how the activation efficiency can in general be improved by acting on both the applied load and the imprinted nematic texture.

This paper proposes a novel procedure to examine the influences of friction, dilatancy, and normal stresses at fault zones on the estimation of seismic moment. For illustrative purposes, the study focuses on a circular frictional dilatant patch located within a frictionless pre-compressed fault zone undergoing relative shear. When dilatancy occurs, the interface beyond the dilatant region may experience separation due to the normal stresses acting on the fault plane, affecting the deformational response of the pre-stressed asperity. This approach allows for an evaluation of the normal stress on the dilatant region, leading to a re-interpretation of the conventional definition of seismic moment. We compare our model against a comprehensive catalog of earthquakes spanning 16 orders of magnitude, utilizing seismologically inferred source properties as well as data from two separate experimental studies that directly measure the shear-dilatant response of shear fractures in both laboratory and field settings. Our findings indicate that friction-induced dilatancy exerts minimal influence on the estimation of seismic moment. However, we emphasize that the discrepancies between our direct measurements and inferred estimates of seismic moment highlight the need for focused campaigns and in situ and on-fault assessments of earthquake mechanics. Plain Language summary. The conventional definition of the Seismic Moment has been central to unifying information from plate tectonics, geology, geodesy, and seismology. It looks at how the ground moves along a fault plane and the strength of the surrounding rocks. However, it often overlooks other factors that might affect this movement, such as the stress on the fault and the local topography that can induce additional physical responses. This study explores how these additional factors, particularly a process called dilatancy, can change our understanding of the seismic moment. The authors found that while these factors do play a role, they have a minimal impact on the traditional definition of seismic moment initially proposed by Aki in 1966.

This article presents two structural constitutive models for collagenous tissues. A salient feature of these models is that they are represented analytically by probability distribution functions that are directly available in standard scientific computing packages. No numerical integration is needed at the user’s end. The models are apt for describing the realistic behavior of collagenous tissues. Most notably, they are able to generate response curves whose slopes are sigmoid. The models can delineate, analytically, the transition from the initial quasi-exponential response to the subsequent non-exponential phase characterized by a sigmoid slope. The constitutive equations have an additive structure, and this structure is leveraged to develop response functions relative to a pre-deformed configuration. The models are evaluated against experimental and simulated response data. Spot-on fits are achieved in all cases. The predictive capability is assessed in the context of biaxial response by fitting a subset of loading paths and predicting the responses of unfitted paths. The models provide indicators of waviness exposure, and these indicators can be used to estimate the trustworthiness of the parameters obtained from regression.

In the plane-stress problem of the classical plate theory, the constant thickness assumption is conventionally used as one of the assumptions in the Kirchhoff-Love hypothesis, which almost becomes a fixed concept for such thin-plate models. However, for some situations of uniformly stretched mid-surface (variable plate thickness), such as the elastic buckling of an in-plane uniformly compressed thin plate, this assumption is a deformation constraint on the plate free surface, thereby increasing the unnecessary anti-deformation stiffness. Herein, by introducing the mean stress and strain into Hooke’s law of a three-dimensional infinitesimal element, transforming the corresponding stress–strain relations, shrinking (dimension-reducing) them, and copying them onto the mid-surface of the plane-stress plate, the corresponding two-dimensional stress–strain relations can be obtained, which include a variable thickness strain. Furthermore, by combining with the corresponding stretching-type geometric relations at the mid-surface, the resultant stretching force on the transverse cross-section can be determined. Simultaneously, the Kirchhoff-Love hypothesis (bending geometric relations) can still be considered applicable to such an already uniformly stretched mid-surface, thereby the cross-section resultant moment relations throughout the thickness can also be determined. Finally, a modified approach is proposed to evaluate the influence of thickness variation on the elastic critical buckling of uniformly compressed thin plates by replacing the flexural stiffness value, which is believed to have a better prediction accuracy.

The electroelastic problems of one-dimensional hexagonal piezoelectric quasicrystal materials with a periodic distribution of slant mode-III cracks under anti-plane shear and electromechanical loading are analyzed in this paper. Based on the three electrical boundary conditions at the crack surfaces, electrically permeable, electrically semi-permeable and electrically impermeable condition, the problems are classified as solving singular integral equations by using screw dislocation solutions. For two special cases of coplanar and parallel periodic crack arrays, the closed form solutions for the electroelastic fields, including stress fields, electric fields and tearing displacements, have been determined. The solutions of the singular integral equations for slant cracks can be transformed into the solutions of algebraic equations, the field intensity factors and mechanical strain energy release rates have been determined. The numerical solutions show that the normalized mechanical strain energy release rates increase under the influence of phonon field stress, phason field stress as well as electric fields, indicating that cracks are more likely to propagate in piezoelectric quasicrystal materials. In addition, it is found that the stress fields at the crack tips exhibited singularity, and the variation law of the total energy release rates with the applied electrical loading are also obtained.

Using general solutions of the equilibrium equations of linearized stability theory, transcendental equations for determining the critical strains corresponding to the onset of wrinkling of a thin coating film located on a semibounded substrate are obtained. The substrate/film (bilayer) system is assumed to be under plane strain conditions, and the body materials are nonlinearly elastic with arbitrary structures of elastic potentials. Two variants of the boundary conditions at the interface are considered: perfectly bonded layers and perfectly lubricated layers, corresponding to the “strongest” and “weakest” types of bonding between the bilayer components. Numerical results for determining the critical values of the wrinkling strain are presented for the harmonic potential (compressible bodies, large strains), the quadratic potential (compressible bodies, small strains), the Treloar potential, and the Bartenev–Khazanovich potential (incompressible bodies, large strains). The nature of the dependence of the critical strain and critical wavelength on the elastic constants of the substrate and film materials and on the type of elastic potential was studied. A comparison of the obtained results with known theoretical and experimental results was carried out.

We consider the general theory of 6-parameter shells, in which material points on the midsurface are endowed with 3 translational and 3 rotational degrees of freedom. In this framework, we derive quasiconvexity conditions and rank-one convexity conditions. These inequalities represent necessary conditions for energy minimizers; they are the two-dimensional counterparts of the well-known relaxed convexity conditions in three-dimensional finite elasticity. As a specific feature, the quasiconvexity inequality for shells contains the gradients in the tangent plane of the variation fields associated to deformation and microrotation. Finally, we also deduce the Legendre-Hadamard condition for shells, as a consequence of the rank-one convexity inequality.

Due to the geometric feature and information, increasing investigations have been focused on tangled systems with rich mechanics behaviors. But most of them are limited to single physical intertwining or mathematical knot, which makes it difficult to illustrate the interaction between mechanics and geometry. This work proposes different kinds of elastic tangles with three ropes, in which the mechanics components and geometric properties are obtained. Five topological parameters are derived to show the relation between tangle type and mechanics characteristic. Based on the geometry knot theory, the strength and stability of tangles can be predicted by geometry rules. Moreover, numerical calculation and experiment are performed to support the theoretical prediction. This work wishes to provide guidance for the design and control of systems with complex entanglements and further inspire geometric mechanics of slender flexible elastomers.

Liquid crystal elastomers (LCEs) marry the large deformation response of a cross-linked polymer network with the nematic order of liquid crystals pendent to the network. Of particular interest is the actuation of LCE sheets where the nematic order, modeled by a unit vector called the director, is specified heterogeneously in the plane of the sheet. Heating such a sheet leads to a large spontaneous deformation, coupled to the director design through a metric constraint that is now well-established by the literature. Here we go beyond the metric constraint and identify the full plate theory that underlies this phenomenon. Starting from a widely used bulk model for LCEs, we derive a plate theory for the pure bending deformations of patterned LCE sheets in the limit that the sheet thickness tends to zero using the framework of (Gamma )-convergence. Specifically, after dividing the bulk energy by the cube of the thickness to set a bending scale, we show that all limiting midplane deformations with bounded energy at this scale satisfy the aforementioned metric constraint. We then identify the energy of our plate theory as an ansatz-free lower bound of the limit of the scaled bulk energy, and construct a recovery sequence that achieves this plate energy for all smooth enough midplane deformations. We conclude by applying our plate theory to a variety of examples.