Journal of Elasticity最新文献

In this paper, we present the first study of plane-strain problems within the framework of complete thermo-flexoelectric theory, incorporating strain-gradient elasticity, direct and converse flexoelectricity, as well as thermoelasticity. We derive the exact solutions for three typical thermoelastic plane strain problems, which are the mechanical-electrical-thermal coupling problem for an infinite-length strip, the mechanical-electrical-thermal coupling problem for a hollow cylinder, and the thermal eigenstrain problem for a cylindrical inclusion. We develop the mixed finite element framework for the plane-strain thermo-flexoelectric problems, benchmarked against the three analytical solutions. This study reveals that the electric field induced by inhomogeneous heating in thermo-flexoelectric solids exhibits a pronounced size effect. Notably, an increase in the strain-gradient length scale parameter diminishes the thermo-flexoelectric effects. This study not only deepens the understanding of the mechanisms of multiphysical fields coupling in thermo-flexoelectric solids, but also provides insights for designing nano thermo-electric converters based on the principle of thermo-flexoelectricity.

A thermodynamically consistent theory for finite deformation size-dependent elastic-inelastic response of a Cosserat material with a deformable director triad ({mathbf{d}}_{i}) and a single absolute temperature (theta ) has been developed by the direct approach. A unique feature of the proposed theory is the Eulerian formulation of constitutive equations, which do not depend on arbitrariness of reference or intermediate configurations or definitions of total and plastic deformation measures. Inelasticity is modeled by an inelastic rate tensor in evolution equations for microstructural vectors. These microstructural vectors model elastic deformations and orientation changes of material anisotropy. General hyperelastic anisotropic constitutive equations are proposed with simple forms in terms of derivatives of the Helmholtz free energy, which depends on elastic deformation variables that include elastic deformations of the directors relative to the microstructural vectors. An important feature of the model is that the gradients of the elastic director deformations in the balances of director momentum control size dependence and are active for all loadings. Analytical solutions of the small deformation equations for simple shear are obtained for elastic response and strain-controlled cyclic loading of an elastic-viscoplastic material.

The primary objective of this study is to investigate the stochastic plasma-mechanical-elastic wave propagation at the boundary of an elastic half-space in a semiconductor material using photo-thermoelasticity theory. The novelty of this work lies in the combination of stochastic simulation with temperature-dependent electrical conductivity and variable thermal conductivity, applied to a two-dimensional (2D) electromagnetic problem based on the electron-hole interaction model. Unlike previous studies, this work incorporates white noise as the randomness factor, providing a more realistic representation of random processes in semiconductor materials. The normal mode analysis technique is used to derive both deterministic and stochastic wave behaviors, focusing on short-time dynamics. The results, which are numerically analyzed and graphically represented, provide new insights into the differential behavior of stochastic versus deterministic distributions in magneto-photo-thermoelastic wave propagation, contributing to a more comprehensive understanding of semiconductor behavior under random influences.

In 1978, Murdoch presented a direct second-gradient hyperelastic theory for thin shells in which the strain-energy density associated with a deformation (boldsymbol{eta }) of a surface (mathcal{S}) is allowed to depend constitutively on the three kinematical descriptors (boldsymbol{C}), (boldsymbol{H}), and (boldsymbol{F}^{scriptscriptstyle top }boldsymbol{G}), where (boldsymbol{F}=text{Grad} _{scriptscriptstyle mathcal{S}} boldsymbol{eta }), (boldsymbol{C}=boldsymbol{F}^{scriptscriptstyle top }boldsymbol{F}), (boldsymbol{H}=boldsymbol{F}^{scriptscriptstyle top }boldsymbol{L}_{ scriptscriptstyle mathcal{S}'}boldsymbol{F}) is the covariant pullback of the curvature tensor (boldsymbol{L}_{scriptscriptstyle mathcal{S}'}) of the deformed surface (mathcal{S}'), and (boldsymbol{G}=text{Grad} _{scriptscriptstyle mathcal{S}} boldsymbol{F}). On the other hand, in Koiter’s direct thin-shell theory, the strain-energy density depends constitutively on only (boldsymbol{C}) and (boldsymbol{H}). Due to the popularity of Koiter’s theory, the second-order tensors (boldsymbol{C}) and (boldsymbol{H}) are well understood and have been extensively characterized. However, the third-order tensor (boldsymbol{F}^{scriptscriptstyle top }boldsymbol{G}) in Murdoch’s theory is largely overlooked in the literature. We address this gap, providing a detailed characterization of (boldsymbol{F}^{scriptscriptstyle top }boldsymbol{G}). We show that for (boldsymbol{eta }) twice continuously differentiable, (boldsymbol{F}^{scriptscriptstyle top }boldsymbol{G}) depends solely on (boldsymbol{C}) and its surface gradient (text{Grad} _{scriptscriptstyle mathcal{S}}boldsymbol{C}) and does not depend on (boldsymbol{L}_{scriptscriptstyle mathcal{S}'}). For the special case of a conformal deformation, we find that a suitably defined strain measure corresponding to (boldsymbol{F}^{scriptscriptstyle top }boldsymbol{G}) depends only the conformal stretch and its surface gradient. For the further specialized case of an isometric deformation, this strain measure vanishes. An orthogonal decomposition of (boldsymbol{F}^{scriptscriptstyle top }boldsymbol{G}) reveals that it belongs to a ten-dimensional subspace of the space of third-order tensors and embodies two independent types of non-local phenomena: one related to the spatial variations in the stretching of (mathcal{S}') and the other to the curvature of (mathcal{S}).

Many biological materials exhibit the ability to actively deform, essentially due to a complex chemical interaction involving two proteins, actin and myosin, in the myocytes (the muscle cells). While the mathematical description of passive materials is well-established, even for large deformations, this is not the case for active materials, since capturing its complexities poses significant challenges. This paper focuses on the mathematical modeling of active deformation of biological materials, guided by the important example of skeletal muscle tissue. We will consider an incompressible and transversely isotropic material within a hyperelastic framework. Our goal is to design constitutive relations that agree with uniaxial experimental data whenever possible. Finally, we propose a novel model based on a coercive and polyconvex elastic energy density for a fiber-reinforced material; in this model, active deformation occurs solely through a change in the reference configuration of the fibers, following the mixture active strain approach. This model assumes a constant active parameter, preserving the good mathematical features of the original model while still capturing the essential deformations observed in experiments.

In this paper we explore the influence of magnetisation on the deformation of planar ferromagnetic elastic ribbons. We begin the investigation by deriving the leading-order magnetic energy associated with a curved planar ferromagnetic elastic ribbon. The sum of the magnetic and the elastic energy is the total energy of the ribbon. We derive the equilibrium equations by taking the first variation of the total energy. We then systematically determine and analyse solutions to these equilibrium equations under various canonical boundary conditions. We also determine the stability of the equilibrium solutions. Comparing our findings with the well-studied Euler’s elastica provides insights into the magnetic effects on the deformation behaviour of elastic ribbons. Our analysis contributes to a deeper understanding of the interplay between magnetisation and the mechanical response of planar ferromagnetic structures, and offers valuable insights for both theoretical and practical applications.

This paper analytically investigates the vertical dynamic response of a rigid strip foundation on layered unsaturated media. Using the triphasic Biot-type model and extended precise integration method, we derive the flexibility coefficient for layered unsaturated media. On this basis, by introducing the Bessel function series of the first kind, the dual integral equations of the mixed boundary value problem in this study are transformed into a set of linear equations. Finally, we obtain explicit expressions for the contact stress and vertical compliance, which are used to evaluate the soil-structure interaction. After the proposed solution is verified, several parameters are presented to study the impacts of the stratification, soil thickness, saturation degree, air-entry value and dimensionless frequency.

A nonlocal model for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. Evolution from the elastic to the inelastic phase depends on material strength. Existence and uniqueness of the displacement-failure set pair follow from an initial value problem describing the evolution. The displacement-failure pair satisfies energy balance. The length of nonlocality (epsilon ) is taken to be small relative to the domain in (mathbb{R}^{d}), (d=2,3). The strain is formulated as a difference quotient of the displacement in the nonlocal model. The two point force is expressed in terms of a weighted difference quotient and delivers an evolution on a subset of (mathbb{R}^{d}times mathbb{R}^{d}). This evolution provides an energy balance between external energy, elastic energy, and damage energy including fracture energy. For any prescribed loading the deformation energy resulting in material failure over a region (R) is uniformly bounded as (epsilon rightarrow 0). For fixed (epsilon ), the failure energy is discovered to be is nonzero for (d-1) dimensional regions (R) associated with flat crack surfaces. Calculation shows, this failure energy is the Griffith fracture energy given by the energy release rate multiplied by area for (d=3) (or length for (d=2)). The nonlocal field theory is shown to recover a solution of Naiver’s equation outside a propagating flat traction free crack in the limit of vanishing spatial nonlocality. The theory and simulations presented here corroborate the recent experimental findings of (Rozen-Levy et al. in Phys. Rev. Lett. 125(17):175501, 2020) that cracks follow the location of maximum energy dissipation inside the intact material. Simulations show fracture evolution through the generation of a traction free internal boundary seen as a wake left behind a moving strain concentration.

We analytically study finite torsional and extensional deformations of rubberlike material circular cylinders with the two material moduli in the Mooney–Rivlin relation assumed to be continuous functions of the undeformed radius. It is shown that under null resultant axial load on the end faces the cylinder length increases upon twisting. Furthermore, when the two moduli are affine functions of the radius the inhomogeneity parameters can be found to have the maximum shear stress occur at a pre-determined interior point. Whereas the radial stress is finite at the center of a cross-section of a homogeneous material cylinder, it may have large values for an inhomogeneous material cylinder. The closed-form solutions provided herein for the two moduli having affine, power-law and exponential functions of the radius should benefit numerical analysts verify their algorithms and engineers design soft material robots for improving their performance under torsional loads.