Time Domain Analysis of Elastic Nonlinearity in Concrete Using Continuous Waves

Concrete and consolidated granular media in general exhibit a strong nonlinear hysteretic elastic behavior when excited by ultrasonic wave perturbations. Due to the sensitivity of their elastic properties to the small changes that can appear in their microstructure, the dynamic stress-strain relationship considered at low strains is affected by the presence of microcracks and hence the progression of damage. Tracking the nonlinear behavior can be made through the dependence on the excitation amplitude of the amplitude of higher order harmonics or of the resonance frequency of the sample. The present chapter shows a time domain analysis of elastic nonlinearity based on the break of the superposition principle when ultrasonic continuous waves are propagating in concrete samples. The latter, which can be of different microstructures (grain sizes, mortar, or polymer matrix), helps to understand the physical mechanisms involved in the different nonlinear elastic responses

Ultrasonic Monitoring of the Interaction between Cement Matrix and Alkaline Silicate Solution in Self-Healing Systems

Alkaline solutions, such as sodium, potassium or lithium silicates, appear to be very promising as healing agents for the development of encapsulated self-healing concretes. However, the evolution of their mechanical and acoustic properties in time has not yet been completely clarified, especially regarding their behavior and related kinetics when they are used in the form of a thin layer in contact with a hardened cement matrix. This study aims to monitor, using linear and nonlinear ultrasonic methods, the evolution of a sodium silicate solution interacting with a cement matrix in the presence of localized cracks. The ultrasonic inspection via linear methods revealed that an almost complete recovery of the elastic and acoustic properties occurred within a few days of healing. The nonlinear ultrasonic measurements contributed to provide further insight into the kinetics of the recovery due to the presence of the healing agent. A good regain of mechanical performance was ascertained through flexural tests at the end of the healing process, confirming the suitability of sodium silicate as a healing agent for self-healing cementitious systems

Exploiting Slow Dynamics Effects for Damage Detection in Concrete

Nonlinear ultrasonic techniques have been developed over the last decades to detect the presence of damage in materials of interest in the field of civil engineering, such as concrete or mortar. The dependence on the strain amplitude of measurable quantities, such as wave velocity, damping factor, resonance frequency, etc. is normally considered a qualitative indicator of the presence of defects at the microstructural level. The experimental approaches proposed have the advantage of being sensitive to small variations in the sample microstructure and are therefore more adapted to detect the presence of small cracks or damaged areas with respect to traditional linear ultrasonic techniques. However, nonlinear methods are difficult to implement, since they usually require a calibrated experimental set-up which also behaves linearly at high amplitudes of excitation. The slow dynamics features, typical of the hysteresis generated by damage, have been given much less attention as a tool for damage detection even though their quantification is often less demanding in terms of an experimental set-up. Here, we provide the first evidence of how recovery, which is part of the slow dynamics process, is sensitive to the presence of damage in concrete samples and thus could be considered as an easy-to-measure nonlinear indicator for Structural Health Monitoring purposes

Proof of concept of a frequency-preserving and time-invariant metamaterial-based nonlinear acoustic diode

Acoustic filters and metamaterials have become essential components for elastic wave control in applications ranging from ultrasonics to noise abatement. Other devices have been designed in this field, emulating their electromagnetic counterparts. One such case is an acoustic diode or rectifier, which enables one-way wave transmission by breaking the wave equation-related reciprocity. Its achievement, however, has proved to be rather problematic, and current realizations display a number of shortcomings in terms of simplicity and versatility. Here, we present the design, fabrication and characterization of a device able to work as an acoustic diode, a switch and a transistor-like apparatus, exploiting symmetry-breaking nonlinear effects like harmonic generation and wave mixing, and the filtering capabilities of metamaterials. This device presents several advantages compared with previous acoustic diode realizations, including versatility, time invariance, frequency preserving characteristics and switchability. We numerically evaluate its efficiency and demonstrate its feasibility in a preliminary experimental realization. This work may provide new opportunities for the practical realization of structural components with one-way wave propagation properties

Power laws and elastic nonlinearity in materials with complex microstructure

Nonlinear ultrasonic methods have been widely used to characterize the microstructure of damaged solids and consolidated granular media. Besides distinguishing between materials exhibiting classical nonlinear behaviors from those exhibiting hysteresis, it could be of importance the discrimination between ultrasonic indications from different physical sources (scatterers). Elastic hysteresis could indeed be due to dislocations, grain boundaries, stick-slip at interfaces, etc. Analyzing data obtained on various concrete samples, we show that the power law behavior of the nonlinear indicator vs. the energy of excitation could be used to classify different microscopic features. In particular, the power law exponent ranges between 1 and 3, depending on the nature of nonlinearity. We also provide a theoretical interpretation of the collected data using models for clapping and hysteretic nonlinearitie

Physical modelling and simulations of tumour growth and angiogenesis: predictions and new hypotheses

The initial stages of tumour growth (avascular phase) are characterised by a low nutrient availability, which soon become a limiting factor for the progression of the neoplasm. Normally a transition to a vascular phase occurs, during which cancer cells stimulate the proliferation of endothelial cells belonging to vessels, hence the formation of new capillaries. The newly formed vascular system rapidly approaches the tumour surface and even infiltrates it, providing additional nutrients which allow further growth (angiogenesis). Blocking the process, might induce tumour to latency, with the consequent implications from therapeutical point of view. In the present contribution we will consider angiogenesis as a case study to show how mathematical models help in the interpretation and quantification of the experimental results

Environmental physical modulation of intrinsic tendency to growth of Multicellular Tumour Spheroids: in silico experiments

Lowering in nutrient local availability and rising in host mechanical rigidity are two distinct boundary conditions that affect the growth of solid a-vascular cancers in similar ways (inhibition of growth). In silico experiments based on a physical-mathematical model can shed light on some of the mechanisms at the basis of these effects and suggest that the self-organizing properties of neoplastic populations are greatly modulated by environmental restrictions