Stress and strain control via level set topology optimization

Abstract

This paper presents a level set topology optimization method for manipulation of stress and strain integral functions in a prescribed region (herein called sub-structure) of a linear elastic domain. The method is able to deviate or concentrate the flux of stress in the sub-structure by optimizing the shape and topologies of the boundaries outside of that region. A general integral objective function is proposed and its shape sensitivities are derived. For stress isolation or maximization, a von Mises stress integral is used and results show that stresses in the sub-structure can be drastically reduced. For strain control, a strain integral combined with a vector able to select the component of the strain is used. A combination of both can be used to minimize deformation of a prescribed direction. Numerical results show that strain can be efficiently minimized or maximized for a wide range of directions. The proposed methodology can be applied to stress isolation of highly sensitive non strain-based sensors, design for failure, maximization of mechanical strain and strain direction control for strain-based sensors and microdevices.

Topology Optimization and 3D printing of Large Deformation Compliant Mechanisms for Straining Biological Tissues

“…Development (amount and location) of stress/strain in a structure significantly depends upon its geometrical features and the loading conditions. In TO, one can find approaches that impose stress constraints (Duysinx and Bendsøe, 1998;Luo et al, 2013;da Silva et al, 2019), and also, on stress isolation at predefined regions within the design domain (Li and Wang, 2014;Luo et al, 2017;Picelli et al, 2018). Our aim here is not to isolate strain (Picelli et al, 2018) in the design domain but rather to achieve a target strain level in the biological tissue substrates using optimized compliant mechanisms.…”