Metallic glasses (MGs) are often perceived as quintessential structural materials due to their superior mechanical properties such as high strength and large elastic limit. In practical applications, service conditions that introduce cyclic variations in stresses and strains are inevitably involved. The fatigue of MGs is thus a topic of research and practical interest. In this review, a brief introduction on MGs, their applications and challenges, is first provided. Next, experimental studies on fatigue behaviors of both macroscopic and nanoscale MGs are summarized. The range of topics covered include the stress-life behavior, fatigue-crack growth behavior, fatigue-fracture morphology, fatigue-failure mechanisms, as well as the effects of chemical composition, cycling frequency, loading condition, and sample size on the fatigue limits. Finally, recent progresses in simulation studies on the fatigue of MGs are discussed, with an emphasis placed on the atomic-level understanding of the fatigue mechanisms.

Cellulose nanopaper, which consists of a porous network of cellulose nanofibrils (CNFs), exhibits excellent mechanical properties with high strength and toughness. The physical mechanisms, including a realizable reduction of defect size in the nanopaper and facile formation/reformation of hydrogen bonds among CNFs, suggest a bottom-up material design strategy to address the conflict between strength and toughness. A thorough exploration of the rich potential of such a design strategy requires a fundamental understanding of its mechanical behavior. In this review, we supply a comprehensive perspective on advances in cellulose nanopaper mechanics over the most recent two decades from the three aspects of mechanical properties, structure–property relationship and microstructure-based mechanical modeling. We discuss the effects of size, orientation, polymerization degree, and isolate origins of CNFs; density or porosity and humidity of nanopaper; and hemicellulose and lignin on the mechanical properties of cellulose nanopaper. We also discuss the similarities and differences in the microstructure, mechanical properties, and toughening mechanisms between cellulose nanopaper and cellulose nanocrystal (CNC) nanopaper, chitin nanopaper, carbon nanotube (CNT) nanopaper, and graphene nanopaper. Finally, we present the ideas, status quo, and future trends in mechanical modeling of cellulose nanopaper, including atomistic- and microscale-level numerical modeling, and theoretical modeling. This review serves as a modest spur intended to induce scientists to present their valuable contributions and especially to design more advanced cellulose nanopapers and promote the development of their mechanics.

Composite laminate has extensive usage in the aerospace and automotive industries. Thus delamination, one of its most prevalent and challenging failure modes, has attracted substantial research efforts, and lead to the rapid development of both simulation and experiment method. Although reviews exist about simulation and experiment methods, there are not many that cover the development in the last five years. This paper is targeted to fill that gap. We covered a broad range of topic in delamination, from the basic delamination onset and propagation theories to complex loading scenarios, like impact and fatigue loading. From a simulation point of view, virtual crack closure technique (VCCT) and cohesive zone model (CZM), the two most famous methods of delamination modeling, are compared and elaborated. Their implementation techniques are described, and their merits and drawbacks are discussed. We also covered the failure mode of combined delamination and matrix cracking, which is prevalent in impact loading scenarios. Simulation techniques, along with the failure mechanisms, are presented. From experiment point of view, the discussed topics range from delamination fracture toughness (DFT) tests under static, dynamic, or cyclic loading conditions, to impact tests that aim to obtain the impact resistance and residual strength after impact. Moreover, a collection of recent experiment data is provided.

Mechanics at the nanoscale is radically different from mechanics at the macroscale. Atomistic simulations have revealed this important fact, and experiments are being performed to support it. Specifically, in situ testing is being performed by researchers using different approaches with different material systems to interrogate the material at the nanoscale and prove or disprove many of the proposed models. This paper attempts to provide a fairly comprehensive review of the in situ testing that is being performed at the nanoscale, together with a brief description of the models that in situ testing are being used to verify. This review paper intends to primarily provide a broad snapshot of in situ testing of different nanocarbon-based polymeric nanocomposite materials.

A wide variety of crystalline nanowires (NWs) with outstanding mechanical properties have recently emerged. Measuring their mechanical properties and understanding their deformation mechanisms are of important relevance to many of their device applications. On the other hand, such crystalline NWs can provide an unprecedented platform for probing mechanics at the nanoscale. While challenging, the field of experimental mechanics of crystalline nanowires has emerged and seen exciting progress in the past decade. This review summarizes recent advances in this field, focusing on major experimental methods using atomic force microscope (AFM) and electron microscopes and key results on mechanics of crystalline nanowires learned from such experimental studies. Advances in several selected topics are discussed including elasticity, fracture, plasticity, and anelasticity. Finally, this review surveys some applications of crystalline nanowires such as flexible and stretchable electronics, nanocomposites, nanoelectromechanical systems (NEMS), energy harvesting and storage, and strain engineering, where mechanics plays a key role.

Advanced design methodologies enable lighter and more reliable composite structures or components. However, efforts to include fatigue delamination in the simulation of composites have not yet been consolidated. Besides that, there is a lack of a proper categorization of the published methods in terms of their predictive capabilities and the principles they are based on. This paper reviews the available experimental observations, the phenomenological models, and the computational simulation methods for the three phases of delamination (initiation, onset, and propagation). It compiles a synthesis of the current state-of-the-art while identifying the unsolved problems and the areas where research is missing. It is concluded that there is a lack of knowledge, or there are unsolved problems, in all categories in the field, but particularly in the category of computational methods, which in turn prevents its inclusion in the structural design process. Suggested areas where short-term and midterm research should be focused to overcome the current situation are identified.

Tooth fracture is a major concern in the field of restorative dentistry. However, knowledge of the causes for tooth fracture has developed from contributions that are largely based within the field of mechanics. The present manuscript presents a technical review of advances in understanding the fracture of teeth and the fatigue and fracture behavior of their hard tissues (i.e., dentin and enamel). The importance of evaluating the fracture resistance of these materials, and the role of applied mechanics in developing this knowledge will be reviewed. In addition, the complex microstructures of tooth tissues, their roles in resisting tooth fracture, and the importance of hydration and aging on the fracture resistance of tooth tissues will be discussed. Studies in this area are essential for increasing the success of current treatments in dentistry, as well as in facilitating the development of novel bio-inspired restorative materials for the future.

The remarkable increases in computational speed and memory size that have occurred over the past three decades have impacted virtually every area of scientific inquiry. With regard to the measurement community, the digital age has revolutionized the way in which data are acquired, stored, and analyzed to extract the maximum amount of information. For the purposes of this discussion, the focus will be on computer vision–based, noncontacting measurement methods, specifically those commonly known as 2D image correlation, 3D image correlation, and digital volume correlation (also known as volumetric image correlation), and their increasingly significant role in the broad field of solid mechanics. The review closes with a visionary perspective regarding the integration of measurements and models and the impact it may have on the design process.

The design of structures with a nonuniform stress field is of great industrial interest. The ability of the size effect law and critical distance theories to predict the nominal strength of notched and open hole specimens is analyzed in the present paper. The results obtained with these methods are compared with the solution of the problem computed, taking into account the material cohesive law. A conclusion of this paper is that the role of the critical fracture energy in determining the structural strength is negligible, except in large cracked structures. For unnotched structures of any size and for small cracked structures, the key parameter is the initial part of the softening cohesive law. This allows us to define design charts that relate the structural strength to a specimen size normalized with respect to a material characteristic length.

One of the fundamental aspects in cohesive zone modeling is the definition of the traction-separation relationship across fracture surfaces, which approximates the nonlinear fracture process. Cohesive traction-separation relationships may be classified as either nonpotential-based models or potential-based models. Potential-based models are of special interest in the present review article. Several potential-based models display limitations, especially for mixed-mode problems, because of the boundary conditions associated with cohesive fracture. In addition, this paper shows that most effective displacement-based models can be formulated under a single framework. These models lead to positive stiffness under certain separation paths, contrary to general cohesive fracture phenomena wherein the increase of separation generally results in the decrease of failure resistance across the fracture surface (i.e., negative stiffness). To this end, the constitutive relationship of mixed-mode cohesive fracture should be selected with great caution.

The prevalent feature that characterizes masonry structures and makes them dissimilar from modern reinforced concrete and steel structures is quite definitely their inability to resist tensile stresses. Therefore, it is natural that the material model that is intended to be an “analog” of real masonry cannot resist tensile stress but possibly behaves elastically under pure compression, opening a perspective on the adoption of the no-tension (NT) material constitutive assumption. Founded on the NT theory, the basic direction and aim of the present work is to propose a unified treatment of masonry structures presenting an overall and comprehensive up-to-date insight in the analysis of masonry constructions while providing basic and advanced concepts and tools already available or original. The note is intended to lead to several notable results including, just to mention some of the outcomes, that the St. Venant’s postulate does not hold in NT solids, no energy is dissipated by fracture, special accommodations for discontinuous loads are needed, and the relevant developments are provided, among other significant outcomes such as the identification of operative procedures for engineering solutions of structural problems. In the first part of the paper, the basics for the foundation of a NT material theory are illustrated, and the relevant principles for structural analysis, mainly identified in the classic energy theorems and suitably adapted to the material at hand, are formulated. In (apparently) simple cases, closed-form solutions can be obtained, or, at least, the solution process can be prepared after a preliminary screening of the equilibrium scenario. The application to two-dimensional no-tension elasticity is then illustrated in the last section, with reference to two sample cases. The first example proves that the solution in a NT panel acted on by vertical loads on the top is clearly identified in terms of stress, but if discontinuities are present in the load pattern, these reflect in some strong singularities in the deformation field that requires to deepen the problem. The second example is concerned with a NT-elastic half-plane, and a technique to find approximate solutions is outlined and carried on in detail. In Part II of the note, it is demonstrated that discontinuous or lumped load patterns can be looked at as frontier cases: They are not in contrast, but in some sense they are not natural to NT solids. Still in Part II, it is shown how the equilibrium problem can be managed both through the strain and the stress approach.

The present note follows the previous one, part I, where theoretical tools for analyzing structures made by no-tension (NT) material are presented in extensive form. Some significant results are presented in this part II of the note, ranging from the highlight of problems related to the treatment of singularities possibly occurring in the modeling of loads that burden on NT structures, and the development of tools for their treatment, to the specialization of general problems to planar and spatial structures, with the related ad hoc conceived analytical set up, original numerical tools, and noncommercial software. The implementation of the problems, deriving from the set up of the constrained optimization presented in part I of the note, is developed together with a number of applications, also providing, in some cases, the comparison of numerical, experimental, and/or field evidence referred to masonry structures, which finally validates the applicability of the adopted approach for the analysis of masonry constructions.

Since the previous paper was written ( Banks-Sills, 1991, “Application of the Finite Element Method to Linear Elastic Fracture Mechanics,” Appl. Mech. Rev., 44, pp. 447–461 ), much progress has been made in applying the finite element method to linear elastic fracture mechanics. In this paper, the problem of calculating stress intensity factors in two- and three-dimensional mixed mode problems will be considered for isotropic and anisotropic materials. The square-root singular stresses in the neighborhood of the crack tip will be modeled by quarter-point, square and collapsed, triangular elements for two-dimensional problems, respectively, and by brick and collapsed, prismatic elements in three dimensions. The stress intensity factors are obtained by means of the interaction energy or M -integral. Displacement extrapolation is employed as a check on the results. In addition, the problem of interface cracks between homogeneous, isotropic, and anisotropic materials is presented. The purpose of this paper is to present an accurate and efficient method for calculating stress intensity factors for mixed mode deformation. The equations presented here should aid workers in this field to carry out similar analyses, as well as to check their calculations with respect to the examples described.

Hopkinson bar experimental techniques have been extensively employed to investigate the mechanical response and fracture behavior of engineering materials under high rate loading. Among these applications, the study of the dynamic fracture behavior of materials at stress-wave loading conditions (corresponding stress-intensity factor rate ∼ 10 6 MPa m / s ) has been an active research area in recent years. Various Hopkinson bar loading configurations and corresponding experimental methods have been proposed to date for measuring dynamic fracture toughness and investigating fracture mechanisms of engineering materials. In this paper, advances in Hopkinson bar loaded dynamic fracture techniques over the past 30 years, focused on dynamic fracture toughness measurement, are presented. Various aspects of Hopkinson bar fracture testing are reviewed, including (a) the analysis of advantages and disadvantages of loading systems and sample configurations; (b) a discussion of operating principles for determining dynamic load and sample displacement in different loading configurations; (c) a comparison of various methods used for determining dynamic fracture parameters (load, displacement, fracture time, and fracture toughness), such as theoretical formula, optical gauges, and strain gauges; and (d) an update of modeling and simulation of loading configurations. Fundamental issues associated with stress-wave loading, such as stress-wave propagation along the elastic bars and in the sample, stress-state equilibrium validation, incident pulse-shaping effect, and the “loss-of-contact” phenomenon are also addressed in this review.

This article reviews three aspects of large strain elasticity. First, various conjugate stress tensors to strain tensors are reviewed. Many researchers have studied the theory of large strain elasticity. Many stress tensors including the Cauchy stress tensor, the first and the second Piola–Kirchhoff stress tensor, and the Jaumann stress tensor have been proposed to describe the stress state at a point. Recently, the first author of this article proposed a concept of “base forces” to reveal the essence of stress state. By the concept of base forces, the description of the stress state becomes clearer than other stress tensors. We attempt to take base forces as a basic point of view to deal with a review in which different descriptions of stress state are discussed and compared. The governing equations and boundary conditions expressed by the base forces are given. Second, this article reviews the solution of some singularity problems for large strain elasticity, i.e., problems of stress singularity at a crack or a notch tip, at the point of application of a concentrated force and at the vertex of contact in rubberlike materials. Methods of getting the singularity index of stress by using base forces are introduced and compared to earlier work. Complementary energy principles for large strain elasticity have eluded researchers for nearly 100 years . A review of some important advances in this is also given, and a new complementary energy principle related to base forces is introduced.

This article presents an overview of recent progress on magnetomechanical deformation and fracture of functional ferromagnetic materials. Following a brief introduction of the classical magnetoelasticity and the magnetomechanical behavior of traditional ferromagnetics, recent development on the deformation and fracture of soft ferromagnetic materials and the mechanics of ferromagnetic composites is critically reviewed. Also included are the authors’ own works both on experimental testing and theoretical modeling of soft ferromagnetics, ferromagnetic composites, and shape memory ferromagnetic alloys. This review article cited 162 references.

Joining of different materials is a situation frequently observed in mechanical engineering and in materials science. Due to the difference in the elastic properties of the constituent materials, the junction points can be the origin of stress singularities and a possible source of damage. Hence, a full appreciation of these critical situations is of fundamental importance both from the mathematical and the engineering standpoints. In this paper, an overview of interface mechanical problems leading to stress singularities is proposed to show their relevance in engineering. The mathematical methods for the asymptotic analysis of stress singularities in multimaterial junctions and wedges composed of isotropic linear-elastic materials are reviewed and compared, with special attention to in-plane and out-of-plane loadings. This analysis mathematically demonstrates in a historical retrospective the equivalence of the eigenfunction expansion method, of the complex function representation, and of the Mellin transform technique for the determination of the order of the stress singularity in such problems. The analogies between linear elasticity and the Stokes flow of dissimilar immiscible fluids, the steady-state heat transfer across different materials, and the St. Venant torsion of composite bars are also discussed. Finally, advanced issues for the stress singularities due to joining of angularly nonhomogeneous elastic wedges are presented. This review article contains 147 references.

The content of this review consists of recent developments covering an advanced treatment of multiple crack problems in plane elasticity. Several elementary solutions are highlighted, which are the fundamentals for the formulation of the integral equations. The elementary solutions include those initiated by point sources or by a distributed traction along the crack face. Two kinds of singular integral equations, three kinds of Fredholm integral equations, and one kind of hypersingular integral equation are suggested for the multiple crack problems in plane elasticity. Regularization procedures are also investigated. For the solution of the integral equations, the relevant quadrature rules are addressed. A variety of methods for solving the multiple crack problems is introduced. Applications for the solution of the multiple crack problems are also addressed. The concept of the modified complex potential (MCP) is emphasized, which will extend the solution range, for example, from the multiple crack problem in an infinite plate to that in a circular plate. Many multiple crack problems are addressed. Those problems include: (i) multiple semi-infinite crack problem, (ii) multiple crack problem with a general loading, (iii) multiple crack problem for the bonded half-planes, (iv) multiple crack problem for a finite region, (v) multiple crack problem for a circular region, (vi) multiple crack problem in antiplane elasticity, (vii) T-stress in the multiple crack problem, and (viii) periodic crack problem and many others. This review article cites 187 references.

Three-dimensional (3D) constitutive equations of piezoelectric (PZ) plates and shells are considered for inverse linear and electrostrictive (quadratic) piezoeffects. Prestressed multilayer PZ shells reinforced with metal including the case of uneven thickness polarization are studied. Asymptotic and variational methods to solve the governing differential equations of PZ shells are considered. Concentrations of electrical and mechanical fields near structure imperfections and external local loading are investigated. The electrothermoviscoelastic heating of PZ shells is considered at harmonic excitation. From numerical analysis and the experimental data of energy dissipation and the temperature behavior of PZ shell the conditions of optimal transformation of electric energy into mechanical deformations are defined. Thus, the geometrical parameters and working frequencies are determined with due account of dielectric relaxation processes. The following nonlinear phenomena are studied: acoustoelectronic wave amplification; electron injection into metalized polar dielectric; resonance growth by 5–20 times of internal electrical field strength in the PZ shells and plates; and autothermostabilization of ferroelectric resonators. For a better understanding of R.D. Mindlin’s gradient theory of polarization in view of electron processes in thin metal-dielectric-metal structures, use was made of solid state physics interpretations as well as experimental data. High concentration of mechanical stresses and temperature and electrical fields near structure defects (first of all, near boundary between various materials) defines the main properties of polar dielectrics. An unknown domain of electrode rough surface influence was estimated, and as result an uneven polarization distribution was found. A theory of nonlinear autowave systems with energy dissipation was used in a physical model of the electrothermal fracture of dielectrics (contacting with metal electrodes), and as a result a nondestructive testing method to study the microstructure defect formation has been suggested.

The present paper is a review of research carried out on scaling laws and multiscaling approach in the mechanics of heterogeneous and disordered materials in the last two decades, especially at the Politecnio di Torino. The subject encompasses theoretical, numerical and experimental aspects. The research followed two main directions. The first one concerns the implementation and the development of the cohesive crack model, which has been shown to be able to simulate experiments on concrete like materials and structures. It is referred to as the dimensional analysis approach, since it succeeds in capturing the ductile-to-brittle transition by increasing the structural size owing to the different physical dimensions of two material parameters: the tensile strength and the fracture energy. The second research direction aims at capturing the size-scale effects of quasibrittle materials, which show fractal patterns in the failure process. This approach is referred to as the renormalization group (or fractal) approach and leads to a scale-invariant fractal cohesive crack model. This model is able to predict the size effects even in tests where the classical approach fails, e.g., the direct tension test. Within this framework and introducing the fractional calculus, it is shown how the Principle of Virtual Work can be rewritten in its fractional form, thus obtaining a scaling law not only for the tensile strength and the fracture energy, but also for the critical strain.