Nonlinear dynamic analysis of bra fitting using finite element models

Abstract

This thesis aimed to investigate the viscoelastic behavior of the breasts in free vibration and running using a theoretical mathematical model and to develop a 3D FE model to predict the 3D contact area, deformation, and stress distribution between the soft breast and bra. To describe the obvious difference in the vibration characteristics above and below the static equilibrium position, a new piecewise mass-spring-damper model of a breast was developed with theoretical equations to derive the in-vivo spring constants and damping coefficients of breasts from free-falling breast experiments and validated with bare-breasted running experiment. It was found that all the damping ratio, spring constants, damping coefficients of the breasts at the positions above the static equilibrium were significantly smaller than those of the below (p<0.05) in the paired-sample t-test. With the derived spring constants and damping coefficients, a forced vibration model was developed for bare-breasted running to study the kinetic characteristic of breasts in terms of displacement, velocity, acceleration and force. It was observed that the maximum vertical breast force during a cycle period ranged from 0.8N-27.6N. To predict the 3D contact area, deformation, and stress distribution between the soft breast and bra, an FE contact model was developed in Marc. The results showed peak von Mises stresses was 1 MPa on the center front, the bottom, and the outer region of the cups. The maximum von Mises stress of straps and the underband are 0.125 MPa and 0.300 MPa respectively that were smaller, probably because the straps and underband were more extensible. The derived contact pressure was also validated in an order of 1 kPa magnitude. This research has established a basis for future biomechanical studies of bra fitting with the scientific understanding of breast free vibration, bared-breast running and the interaction between the breasts and bra. This research constitutes the initial steps down the path to achieve this.