Piezoresistive device optimization using topological derivative concepts

Abstract

A piezoresistive sensor is composed of a piezoresistive membrane attached to a flexible plate. The piezoresistive material is anisotropic, and its electrical properties change when subjected to mechanical stresses. In this work, the topology design of a piezoresistive pressure sensor is addressed. More specifically, an optimization technique based on topological sensitivity analysis is proposed in order to obtain the optimized distribution of piezoresistive material over the plate. In most of the works regarding topological sensitivity analysis, isotropic materials are considered. However, the problem of conductivity in an anisotropic non-homogeneous domain has been recently addressed, and a closed form for the topological derivative associated to the energy shape functional has been presented. In this work, on the other hand, a closed form for the topological derivative associated with a multi-objective shape functional related to the steady-state anisotropic current density diffusion problem is presented. To illustrate the applicability of the closed formula and the proposed optimization procedure, numerical examples regarding the conceptual design of piezoresistive sensors, considering distinct optimization parameters and boundary conditions in the conductivity problem, are presented.