Multiscale static and dynamic mechanical study of the Turritella terebra and Turritellinella tricarinata seashells.

Marine shells are designed by nature to ensure mechanical protection from predators and shelter for molluscs living inside them. A large amount of work has been done to study the multiscale mechanical properties of their complex microstructure and to draw inspiration for the design of impact-resistant biomimetic materials. Less is known regarding the dynamic behaviour related to their structure at multiple scales. Here, we present a combined experimental and numerical study of the shells of two different species of gastropod sea snail belonging to the Turritellidae family, featuring a peculiar helicoconic shape with hierarchical spiral elements. The proposed procedure involves the use of micro-computed tomography scans for the accurate determination of geometry, atomic force microscopy and nanoindentation to evaluate local mechanical properties, surface morphology and heterogeneity, as well as resonant ultrasound spectroscopy coupled with finite element analysis simulations to determine global modal behaviour. Results indicate that the specific features of the considered shells, in particular their helicoconic and hierarchical structure, can also be linked to their vibration attenuation behaviour. Moreover, the proposed investigation method can be extended to the study of other natural systems, to determine their structure-related dynamic properties, ultimately aiding the design of bioinspired metamaterials and of structures with advanced vibration control.

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.

Proof of Concept for an Ultrasensitive Technique to Detect and Localize Sources of Elastic Nonlinearity Using Phononic Crystals.

The appearance of nonlinear effects in elastic wave propagation is one of the most reliable and sensitive indicators of the onset of material damage. However, these effects are usually very small and can be detected only using cumbersome digital signal processing techniques. Here, we propose and experimentally validate an alternative approach, using the filtering and focusing properties of phononic crystals to naturally select and reflect the higher harmonics generated by nonlinear effects, enabling the realization of time-reversal procedures for nonlinear elastic source detection. The proposed device demonstrates its potential as an efficient, compact, portable, passive apparatus for nonlinear elastic wave sensing and damage detection.

Modeling dynamic acousto-elastic testing experiments: validation and perspectives.

Materials possessing micro-inhomogeneities often display a nonlinear response to mechanical solicitations, which is sensitive to the confining pressure acting on the sample. Dynamic acoustoelastic testing allows measurement of the instantaneous variations in the elastic modulus due to the change of the dynamic pressure induced by a low-frequency wave. This paper shows that a Preisach-Mayergoyz space based hysteretic multi-state elastic model provides an explanation for experimental observations in consolidated granular media and predicts memory and nonlinear effects comparable to those measured in rocks.

Comparison between PUN and Tofts models in the quantification of dynamic contrast-enhanced MR imaging.

Dynamic contrast-enhanced study in magnetic resonance imaging (DCE-MRI) is an important tool in oncology to visualize tissues vascularization and to define tumour aggressiveness on the basis of an altered perfusion and permeability. Pharmacokinetic models are generally used to extract hemodynamic parameters, providing a quantitative description of the contrast uptake and wash-out. Empirical functions can also be used to fit experimental data without the need of any assumption about tumour physiology, as in pharmacokinetic models, increasing their diagnostic utility, in particular when automatic diagnosis systems are implemented on the basis of an MRI multi-parametric approach. Phenomenological universalities (PUN) represent a novel tool for experimental research and offer a simple and systematic method to represent a set of data independent of the application field. DCE-MRI acquisitions can thus be advantageously evaluated by the extended PUN class, providing a convenient diagnostic tool to analyse functional studies, adding a new set of features for the classification of malignant and benign lesions in computer aided detection systems. In this work the Tofts pharmacokinetic model and the class EU1 generated by the PUN description were compared in the study of DCE-MRI of the prostate, evaluating complexity of model implementation, goodness of fitting results, classification performances and computational cost. The mean R² obtained with the EU1 and Tofts model were equal to 0.96 and 0.90, respectively, and the classification performances achieved by the EU1 model and the Tofts implementation discriminated malignant from benign tissues with an area under the receiver operating characteristic curve equal to 0.92 and 0.91, respectively. Furthermore, the EU1 model has a simpler functional form which reduces implementation complexity and computational time, requiring 6 min to complete a patient elaboration process, instead of 8 min needed for the Tofts model analysis.

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

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.

Break of reciprocity principle due to localized nonlinearities in concrete.

The effects of localized nonlinearities on the reciprocity principle in the context of ultrasounds and nonlinear elasticity are discussed in this paper. Experiments will be presented to prove that a localized crack in a concrete beam causes a break of reciprocity in the ultrasonic response to a mechanical excitation. The link between non-reciprocity and asymmetry in the nonlinear response will be demonstrated and discussed as a tool for NonDestructive Evaluation.

Detection and location of cracks using loss of reciprocity in ultrasonic waves propagation.

The reciprocity theorem is a general statement valid for elastic media, and it has been applied to the solution of elastic wave equations, transducers calibration, time reversal acoustics, etc. However, localized nonlinear scatterers are expected to break reciprocity even though the effect is, in several cases, negligible. Here the dependence of the reciprocity break on the presence of a localized damage and the influence of its relative position has been experimentally investigated. It will be shown that the break of reciprocity, usually considered a disadvantage, can be exploited as an imaging tool for localized cracks detection.

Phenomenological universalities: a novel tool for the analysis of dynamic contrast enhancement in magnetic resonance imaging.

Dynamic contrast enhancement in magnetic resonance imaging (DCE-MRI) is a promising tool for the clinical diagnosis of tumors, whose implementation may be improved through the use of suitable hemodynamic models. If one prefers to avoid assumptions about the tumor physiology, empirical fitting functions may be adopted. For this purpose, in this paper we discuss the exploitation of a recently proposed phenomenological universalities (PUN) formalism. In fact, we show that a novel PUN class may be used to describe the time-signal intensity curves in both healthy and tumoral tissues, discriminating between the two cases and thus potentially providing a convenient diagnostic tool. The proposed approach is applied to analysis of the DCE-MRI data relative to a study group composed of ten patients with spine tumors.

Oscillations in growth of multicellular tumour spheroids: a revisited quantitative analysis.

OBJECTIVES: Multicellular tumour spheroids (MTS) provide an important tool for study of the microscopic properties of solid tumours and their responses to therapy. Thus, observation of large-scale volume oscillations in MTS, reported several years ago by two independent groups (1,2), in our opinion represent a remarkable discovery, particularly if this could promote careful investigation of the possible occurrence of volume oscillations of tumours 'in vivo'. MATERIALS AND METHODS: Because of high background noise, quantitative analysis of properties of observed oscillations has not been possible in previous studies. Such an analysis can be now performed, thanks to a recently proposed approach, based on formalism of phenomenological universalities (PUN). RESULTS: Results have provided unambiguous confirmation of the existence of MTS volume oscillations, and quantitative evaluation of their properties, for two tumour cell lines. Proof is based not only on quality of fitting of the experimental datasets, but also on determination of well-defined values of frequency and amplitude of the oscillations for each line investigated, which would not be consistent with random fluctuation. CONCLUSIONS: Biological mechanisms, which can be directly responsible for observed oscillations, are proposed, which relates also to recent work on related topics. Further investigations, both at experimental and at modelling levels, are also suggested. Finally, from a methodological point of view, results obtained represent further confirmation of applicability and usefulness of the PUN approach.

Concurrent growth of phenotypic features: a phenomenological universalities approach.

Different physical features of an organism are often measured concurrently, because their correlations can be used as predictors of longevity, future health, or adaptability to an ecological niche. Since, in general, we do not know a priori if the temporal variations in the measured quantities are causally related, it may be useful to have a method that could help us to identify possible correlations and to obtain parameters that may vary from population to population. In this paper we develop a procedure that may detect underlying relationships. We do this by generalizing the recently introduced concept of phenomenological universalities to the complex field. In this generalization, allometric growth is described by a complex function, whose real and imaginary parts represent two phenotypic traits of the same organism. As particular solutions of the resulting problem, we obtain generalizations of the Gompertz and the von Bertalanffy-West growth equations. We then apply the procedure to two biological systems in order to show how to determine the existence of mutual interference between trait variations.

Generalization of Berreman's model to the case of large amplitude of the grooves.

We generalize Berreman's model to the case qA > or = 1 , where q is the wave vector of the surface structure and A its amplitude, to describe the alignment induced by a solid surface on a nematic liquid crystal. We show that, by taking into account correctly the elastic contribution to the surface energy connected with the surface topography, the effective surface energy is smaller than the one determined by Berreman, where the limiting surface is assumed flat and qA << 1 . The analysis is performed by assuming that the anchoring energy on the surface is strong, i.e., nematic molecules in contact with the limiting surface are tangent to it, for any bulk distortion. The generalization to the weak anchoring case is also presented.

A multilevel approach to cancer growth modeling.

Cancer growth models may be divided into macroscopic models, which describe the tumor as a single entity, and microscopic ones, which consider the tumor as a complex system whose behavior emerges from the local dynamics of its basic components, the neoplastic cells. Mesoscopic models (e.g. as based on the Local Interaction Simulation Approach [Delsanto, P.P., Mignogna, R., Scalerandi, M., Schechter, R., 1998. In: Delsanto, P.P. Saenz, A.W. (Eds.), New Perspectives on Problems in Classical and Quantum Physics, vol. 2. Gordon & Breach, New Delhi, p. 5174]), which explicitly consider the behavior of cell clusters and their interactions, may be used instead of the microscopic ones, in order to study the properties of cancer biology that strongly depend on the interactions of small groups of cells at intermediate spatial and temporal scales. All these approaches have been developed independently, which limits their usefulness, since they all include relevant features and information that should be cross-correlated for a deeper understanding of the mechanisms involved. In this contribution we consider multicellular tumor spheroids as biological reference systems and propose an intermediate model to bridge the gap between a macroscopic formulation of tumor growth and a mesoscopic one. Thus we are able to establish, as an important result of our formalism, a direct correspondence between parameters characterizing processes occurring at different scales. In particular, we analyze their dependence on an important limiting factor to tumor growth, i.e. the extra-cellular matrix pressure. Since the macro and meso-models stem from totally different roots (energy conservation and clinical observations vs. cell groups dynamics), their consistency may be used to validate both approaches. It may also be interesting to note that the proposed formalism fits well into a recently proposed conjecture of growth laws universality.

A 2D spring model for the simulation of ultrasonic wave propagation in nonlinear hysteretic media.

A two-dimensional (2D) approach to the simulation of ultrasonic wave propagation in nonclassical nonlinear (NCNL) media is presented. The approach represents the extension to 2D of a previously proposed one dimensional (1D) Spring Model, with the inclusion of a PM space treatment of the intersticial regions between grains. The extension to 2D is of great practical relevance for its potential applications in the field of quantitative nondestructive evaluation and material characterization, but it is also useful, from a theoretical point of view, to gain a better insight of the interaction mechanisms involved. The model is tested by means of virtual 2D experiments. The expected NCNL behaviors are qualitatively well reproduced.