CE 5310 Lecture Notes - Lecture 10: Micrograph, Hysteresis, And1
Document Summary
Three different approaches to model nonlinear mechanical behavior are reviewed here. A micrograph of materials (pristine and damaged concrete) that naturally exhibit mesoscopic defects is shown in fig. Microstructural defects such as dislocations and vacancies give rise to a weak nonlinear mechanical response in materials. Traditionally, this nonlinearity is modelling by expressing stress s in terms of a power series with respect to strain e. in a simple 1 dimensional motion case this can be expressed as (cid:3404)(cid:1831) (cid:2013) (cid:4666)(cid:883)(cid:3398)(cid:2010)(cid:2013)(cid:3398)(cid:2012)(cid:2013)(cid:2870)(cid:3398) (cid:4667) (1) where e is young"s modulus, and are nonlinear elastic parameters of square and cubic order of strain, respectively. 1 is substituted into the wave equation assuming simple harmonic motion, we note that harmonic solutions containing multiple perfect harmonic wave frequencies (having spectral amplitude a2, a3, ) are generated above that with the fundamental frequency (having spectral amplitude a1).
