Numerical investigation of sensing and energy harvesting performance of 0-3 and triply periodic minimal surface-based K0.475Na0.475Li0.05(Nb0.92Ta0.05Sb0.03)O3 and polyethylene piezocomposite: A comparative study

The present paper is devoted to conducting a comparative study on the sensing and energy harvesting performance of a 0-3 and triply periodic minimal surface (TPMS)-based piezocomposite with [Formula: see text] ( KNLNTS) material as piezoelectric inclusions and polyethylene as the matrix material. Different types of TPMS are reported in literature like Neovius, Fischer-Koch S, Schwarz CLP, Schoen Gyroid, Schoen IWP, Schwarz Primitive, etc. In the present study, Schwarz primitive TPMS is considered. Representative volume elements (RVEs) with four different volume fractions are generated and the finite element simulations are performed to compute the effective elastic and piezoelectric properties. The homogenization technique is used to calculate the effective properties. The calculated values of the effective properties are further used to calculate the sensing voltage between the electrodes and harvested power across the resistance. The effective elastic and piezoelectric properties increase with an increase in volume fraction of the piezoelectric inclusions resulting in a higher sensing voltage and power. Significant improvement in the effective elastic and piezoelectric properties of TPMS-based piezocomposite was observed. TPMS-based piezocomposite exhibited superior performance as compared to their 0-3 counterparts.

On upper semicontinuity of the Allen–Cahn twisted eigenvalues

We give an asymptotic upper bound for the kth twisted eigenvalue of the linearized Allen–Cahn operator in terms of the kth eigenvalue of the Jacobi operator, taken with respect to the minimal surface arising as the asymptotic limit of the zero sets of the Allen–Cahn critical points. We use an argument based on the notion of second inner variation developed in Le (On the second inner variations of Allen–Cahn type energies and applications to local minimizers. J. Math. Pures Appl. (9) 103 (2015) 1317–1345).

Computable Constants for Korn’s Inequalities on Riemannian Manifolds

A method is presented for the explicit construction of the non-dimensional constant occurring in Korn’s inequalities for a bounded two-dimensional Riemannian differentiable simply connected manifold subject to Dirichlet boundary conditions. The method is illustrated by application to the spherical cap and minimal surface.