Journal of Elasticity最新文献

We consider a special approach to investigate a mixed boundary value problem (BVP) for the Lamé system of elasticity in the case of three-dimensional bounded domain (varOmega subset mathbb{R}^{3}), when the boundary surface (S=partial varOmega ) is divided into two disjoint parts, (S_{D}) and (S_{N}), where the Dirichlet and Neumann type boundary conditions are prescribed respectively for the displacement vector and stress vector. Our approach is based on the potential method. We look for a solution to the mixed boundary value problem in the form of linear combination of the single layer and double layer potentials with densities supported respectively on the Dirichlet and Neumann parts of the boundary. This approach reduces the mixed BVP under consideration to a system of pseudodifferential equations which do not contain neither extensions of the Dirichlet or Neumann data, nor the Steklov–Poincaré type operator. Moreover, the right hand sides of the resulting pseudodifferential system are vectors coinciding with the Dirichlet and Neumann data of the problem under consideration. The corresponding pseudodifferential matrix operator is bounded and coercive in the appropriate (L_{2})-based Bessel potential spaces. Consequently, the operator is invertible, which implies the unconditional unique solvability of the mixed BVP in the Sobolev space ([W^{1}_{2}(varOmega )]^{3}) and representability of solutions in the form of linear combination of the single layer and double layer potentials with densities supported respectively on the Dirichlet and Neumann parts of the boundary. Using a special structure of the obtained pseudodifferential matrix operator, it is also shown that the operator is invertible in the (L_{p})-based Besov spaces with (frac{4}{3} < p < 4), which under appropriate boundary data implies (C^{alpha })-Hölder continuity of the solution to the mixed BVP in the closed domain (overline{varOmega }) with (alpha =frac{1}{2}-varepsilon ), where (varepsilon >0) is an arbitrarily small number.

Approximations for the elastic properties of dilute solid suspensions with imperfect interfacial bonding are derived and assessed. A variational procedure is employed in such a way that the resulting approximations reproduce exact results for weakly anisotropic but otherwise arbitrarily large interfacial compliances. Two approximations are generated which display the exact same format but differ in the way the interfacial compliance is averaged over the interfaces: the first approximation depends on an ‘arithmetic’ mean while the second approximation depends on a ‘harmonic’ mean. Both approximations allow for arbitrary elastic anisotropy of the constitutive phases but are restricted to suspended inclusions of spherical shape. The approximations are applied to a class of isotropic suspensions and confronted to full-field numerical simulations for assessment. Simulations are performed by means of a Fast Fourier Transform algorithm suitably implemented to handle dilute suspensions with imperfect interfaces. Also included in the comparisons are available results for suspensions with extremely anisotropic bondings. Overall, the ‘harmonic’ approximation is found to be much more precise than the ‘arithmetic’ approximation. The finding is of practical relevance given the widespread use of ‘arithmetic’ approximations in existing descriptions based on modified Eshelby tensors.

This paper proposes a theory that bridges classical analytical mechanics and nonequilibrium thermodynamics. Its intent is to derive the evolution equations of a system from a stationarity principle for a suitably augmented Lagrangian action. This aim is attained for homogeneous systems, described by a finite number of state variables depending on time only. In particular, it is shown that away from equilibrium free energy and entropy are independent constitutive functions.

The objective of this paper is to generalize an Ogden-type model for elastically isotropic response to include elastic-viscoplastic response. The proposed model uses a strain energy function that depends on the total dilatation and the maximum and minimum elastic distortional stretches. A novel feature of the model is that these elastic distortional stretches are expressed in terms of two independent invariants of an elastic distortional deformation tensor that is determined by an evolution equation. The Cauchy stress is determined by derivatives of the strain energy function, the dilatation and the elastic distortional deformation tensor without the need for determining its principal directions. Examples demonstrate the response of the model for hyperelastic response but the proposed formulation can also model a smooth elastic-plastic transition with rate-independent or rate-dependent response with hardening.

We study the homogenization of a linear elastic solid reinforced by a small volume fraction of very stiff fibers. The effective material is characterized by the emergence of concentrations of strain energies around and within the fibers. The former is expressed in terms of the discrepancy appearing between the averaged effective displacements in the fibers and in the matrix, by means of a tensor-valued capacity of the cross-sections of the fibers. The latter corresponds to a combination of stretching, bending and torsional energies, where the torsional contribution is specific to anisotropic constitutive components.

In this work our main objective is to establish various (high frequency-) uniqueness criteria. Initially, we consider (p)-Dirichlet type functionals on a suitable class of measure preserving maps (u: Bsubset mathbb{R}^{2} to mathbb{R}^{2}), (B) being the unit disk, and subject to suitable boundary conditions. In the second part we focus on a very similar situations only exchanging the previous functionals by a suitable class of (p)-growing polyconvex functionals and allowing the maps to be arbitrary.

In both cases a particular emphasis is laid on high pressure situations, where only uniqueness for a subclass, containing solely of variations with high enough Fourier-modes, can be obtained.

Ionic polymer metal composites (IPMCs) consist of an electroactive polymeric membrane, which is plated with metal electrodes and includes a fluid phase of ions in a solvent, whose diffusion allows for actuation and sensing applications. We build on a previous finite-deformation theory of our group that accounts for the cross-diffusion of ions and solvent and couples the mass balances of these species with the stress balance and the Gauss law. Here, we abandon the assumption that the fluid phase is a dilute solution, with benefits on both modelling and computation. A reliable finite element (FE) implementation of electrochemomechanical theories for IPMCs is challenging because the IPMC behaviour is governed by boundary layers (BLs) occurring in tiny membrane regions adjacent to the electrodes, where steep gradients of species concentrations occur. We address this issue by adopting the generalized FE method to discretise the BLs. This allows unprecedented analyses of the IPMC behaviour since it becomes possible to explore it under external actions consistent with applications, beside obtaining accurate predictions with a reasonable computational cost. Hence, we provide novel results concerning the influence of the membrane permittivity on the species profiles at the BLs. Additionally, by leveraging on the mobility matrix, we establish that the initial peak deflection in actuation strongly depends on the constitutive equations for the species transport and discuss the predictions of some experimental results from the literature. Overall, we demonstrate the potential of the proposed model to be an effective tool for the thorough analysis and design of IPMCs.