All the existing works on the mechanics and physics of magnetoelectroelastic solids are based on the only available set of constitutive equations in which the stress, electric displacement, and magnetic induction are expressed in terms of the strain, electric field, and magnetic field. In this paper, we provide other forms of the constitutive equations and the thermodynamic potential corresponding to each form. The mathematical properties of the thermodynamic potentials and the relations between the material constants are discussed.

No abstract

In this paper, we develop a mean field Mori-Tanaka model ͓T. Mori and K. Tanaka, Acta. Metall. 21, 571 ͑1973͔͒ to calculate the effective magnetoelectroelastic moduli of matrix-based multiferroic composites, emphasizing the effects of shape and orientation distribution of second phase particles that have not been investigated before. Through a systematic study, it is observed that laminated composites are optimal for magnetoelectric coefficient a 11 , while fibrous composites are optimal for a 33 . In addition, these coupling coefficients are maximum when the second phase particles are aligned. It is also postulated that the large discrepancy between theoretical predictions and experimental measurements for magnetoelectric coefficients of multiferroic composites previously reported is partly due to the orientation distribution of second phase particles, which has not been considered before in theoretical modeling. When our calculations take the orientation distribution of second phase particles into account with appropriate texture coefficient, good agreement with experimental data is observed.

a b s t r a c tA peeling model is proposed to analyze the peeling properties of bio-mimetic nano-films using the finite element method (FEM) and theoretical approach. The influences of the nano-film's adhesion length, thickness, elastic modulus, roughness and peeling angle on the peeling force were considered as well as the effect of the viscoelastic behavior. It has been found that the effective adhesion length, at which the peeling force attained maximum, was much smaller than the real length of nano-films; and the shear force dominated in the case of smaller peeling angles, whereas, the normal force dominated at larger peeling angles. The total peeling force decreased with an increasing peeling angle. Two limiting values of the peeling-off force can be found in the viscoelastic model, which corresponds to the smaller and larger loading rate cases. The effects of nano-film thickness and Young's modulus on peeling behaviors were also discussed. The results obtained are helpful for understanding the micro-adhesion mechanisms of biological systems, such as geckos.

SUMMARYBased on finite element formulations for the strain gradient theory of microstructures, a convergence criterion for the C 0-1 patch test is introduced, and a new approach to devise strain gradient finite elements that can pass the C 0-1 patch test is proposed. The displacement functions of several plane triangular elements, which satisfy the C 0 continuity and weak C 1 continuity conditions are evaluated by the C 0-1 patch test. The difference between the proposed C 0-1 patch test and the C 0 constant stress and C 1 constant curvature patch tests is elucidated.An 18-DOF plane strain gradient triangular element (RCT9+RT9), which passes the C 0-1 patch test and has no spurious zero energy modes, is proposed. Numerical examples are employed to examine the performance of the proposed element by carrying out the C 0-1 patch test and eigenvalue test. The proposed element is found to be without spurious zero energy modes, and it possesses higher accuracy compared with other strain gradient elements.

No abstract

A simple triangular 9 DOF plate bending element for analysis of thick and thin plate is presented in this paper. This element is constructed by the following procedure:(i) the variation functions of the rotation and shear strain along each side of the element are determined using Timoshenko's beam theory; and (ii) the rotation, curvature and shear strain ®elds in the domain of the element are then determined using the technique of improved interpolation.The proposed element, denoted by ARS-T9, is robust and free of shear locking and, thus, it can be employed to analyze very thin plate. Numerical examples show that the proposed element is a high performance element for thick and thin plates.

No abstract