Nonequilibrium phenomena in damaged media and their effects on the elastic properties

Abstract

Concrete, particularly if damaged, exhibits a peculiar nonlinear elastic behavior, which is mainly due to the coupling between nonequilibrium and nonlinear features, the two of which are intrinsically connected. More specifically, the formulation of a constitutive equation able to properly predict the dynamic behavior of damaged concrete is made difficult by the concomitant presence of two mechanisms: The modification of the microstructure of the medium and the transition to a new elastic state caused by a finite amplitude excitation (conditioning). Memory of that new state is kept when the excitation is removed, before relaxation back to the original elastic state takes place. Indeed, besides accounting for linear and nonlinear parameters, a realistic constitutive equation to be used in reliable prediction models should take into account nonequilibrium effects. Specific parameters, sensitive to finite amplitude excitations, should be introduced to provide information about conditioning effects. In this paper, experimental results indicating that nonlinearity of damaged concrete is memory-dependent will be presented and the implications of such findings in the development of physical models, with relevant outcomes for the characterization of hysteretical features, will be discussed.

Pump and probe waves in dynamic acousto-elasticity: Comprehensive description and comparison with nonlinear elastic theories

“…9 of Ref. 37). This result seems relevant with the increasing offset, but contradictory with the decrease in odd harmonics.…”

“…24,36,38 In Ref. 37, authors show that longer the conditioning, the higher is the global measured nonlinearity (fundamental þ harmonics; Fig. 9 of Ref.…”

Anisotropy of dynamic acoustoelasticity in limestone, influence of conditioning, and comparison with nonlinear resonance spectroscopy

“…The relaxation time is material dependent, it also depends on the amplitude and the duration of the conditioning vibration. 11,13,14 While the LF strain amplitude is varied from 3 Â 10 À7 to 2:8 Â 10 À5 , the strain amplitude created by a US pulse is on the order of 10 À8 . Therefore, US pulses are assumed to propagate linearly.…”

“…10 The extent of this reversible acoustically induced conditioning was found to be dependent on both the amplitude and the duration of the excitation. 13,14 Nonetheless the physical mechanisms at stake are not clearly identified yet. 11 Another manifestation of the high elastic nonlinearity exhibited by rocks is the acoustoelastic effect (also called stress-induced anisotropy of elasticity).…”

Nonlinear elastic response of thermally damaged consolidated granular media

“…The observed phenomenology includes hysteresis in the stress-strain constitutive equation, [1][2][3] excitation amplitude-dependent resonance frequencies, [4][5][6] the generation of harmonics, 7 the loss of validity of the superposition 8,9 and reciprocity 10 principles, and conditioning/relaxation phenomena. [11][12][13][14] Nonlinear elasticity parameters measured in various types of experiments are very sensitive to changes in the microstructure, including changes due to damage processes, e.g., cracking. Therefore, nonlinear elasticity measurements have been exploited for non-destructive detection and characterization of the microstructural evolution due to both intrinsic processes 15,16 and damage-related ones.…”