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Cellular solids whose ligaments are made of two distinct materials are constructed for studying their auxeticity and negative thermal expansion via 2D models with the methodology of finite‐element numerical analysis. Three bimaterial cellular models with various radii of ligament curvature (Rc = 5, 8, 11 cm) are analyzed. It is found that when the ligaments comprise aluminum and titanium alloy with Rc = 5 cm, the cellular solid exhibits simultaneous negative effective Poisson's ratio (−0.418) and negative thermal expansion coefficient (−20.82 × 10−6 K−1). When the radius of ligament curvature increases, auxeticity is less pronounced. Positive and negative thermal expansion can be tuned solely by the coefficients of thermal expansion of ligaments' constituents. Furthermore, smaller radii of curvature give rise to larger negative thermal expansion. In addition, modulus mismatch in the bimaterial ligament can be used to tune overall properties. Our findings herein may serve as foundations for the future quantitative design of such cellular materials. In addition, effective Poisson's ratio and coefficient of thermal expansion can be positively or negatively enhanced due to the interplay between the positive and negative phases. Interactions between negative stiffness and larger curvatures may make the system less unstable. [ABSTRACT FROM AUTHOR]

Composite materials consisting of negative-stiffness inclusions in positive-stiffness matrix may exhibit anomalous effective coupled-field properties through the interactions of the positive and negative phases, giving rise to extremely large or small effective properties. In this work, effective viscoelastic properties of a continuum composite system under the effects of negative inclusion Young's modulus ratio λ E = E inc / E matrix are studied with the finite element method. Furthermore, effective coupled-field properties, such as thermal expansion coefficient, dielectric constants and piezeoelectric constants, are numerically calculated under the effects of negative inclusion bulk modulus ratio λ K = K inc / K matrix . Stability boundaries are determined by applying small dynamic perturbation to the systems through boundary surfaces, and the system is unstable if its field variables become divergent in time. For viscoelastic composite systems containing small volume fractions, less than V i = 1.5 % , the systems can be stable up to λ E ≈ - 0.3 in 0.3 s under 10 Hz driving frequency. For V i = 5.1 % case, its stability boundary is around λ E ≈ 0 . Larger inclusion volume fraction reduces allowable negative stiffness in the viscoelastic system. All anomalous peaks found in the coupled-field properties are in the unstable regime, except for the piezoelectric and thermal-expansion anomalies in the composite system with electrically insulated inclusions and large inclusion volume fraction V i = 26.81 % . Insulated inclusions may cause charge accumulation at the inclusion–matrix interface and boundary surface effects may serve as stabilizing agents to the composite system. Since it is known that negative-stiffness composite is unstable in the purely elastic system in statics, stability enhancement found here in the negative-stiffness systems with viscoelastic and coupled-field effects may be considered as multiphysics-induced stabilization. [ABSTRACT FROM AUTHOR]

Chiral materials may exhibit negative Poisson's ratio and deformation‐mode coupling phenomena. The finite element numerical method is adopted to analyze a class of 2D chiral and nonchiral materials and to show the effects of microstructural geometry on their effective elastic properties and coupling between tension/compression and bending. With the same area fraction (AF), nonchiral samples show larger effective moduli than chiral ones. The number of unit cells may reduce negativity in effective Poisson's ratio of the chiral samples due to nonuniform lateral deformation under uniaxial straining. Increasing AF in a hierarchical pattern in the chiral samples makes their Poisson's ratio more negative. Bending occurs in the chiral samples when they are under uniform, uniaxial, tensile, or compressive straining due to the coupling of deformation modes. The sensibility of tension–bending coupling may be controlled by the chiral microstructure. Optimization of the coupling sensitivity may help develop novel mechanical sensors. [ABSTRACT FROM AUTHOR]

Honeycombs or foams with reentrant microstructures exhibit effective negative Poisson's ratio. Although they are light weight due to inherently empty space, their overall stiffness and damping are somewhat limited. With judiciously chosen filler material to fill the voids in star‐shaped honeycomb, it is numerically demonstrated its auxeticity may be enhanced. By combining the filler and skeleton, the hierarchical composite materials are constructed. The magnitude of the enhancement depends on inner and outer filler's modulus mismatch, as well as the types of filling. Filler's auxeticity also largely enhances overall auxeticity of the outer‐ and all‐filled honeycomb. In addition, for outer‐filled honeycomb, its effective viscoelastic modulus and damping are significantly increased, while maintaining relatively light weight, due to local stress concentration. [ABSTRACT FROM AUTHOR]

Microstructured plates, consisting of various conventional and re-entrant cells, are numerically constructed and analyzed for their effective elastic properties under in-plane deformation. The finite element numerical method is adopted. The calculated effective Poisson's ratios of the plates are found to be in the range between −1 and 1, in consistency with the theory of two-dimensional elasticity. Auxetic angles need to be greater than about 20° in order to obtain negative Poisson's ratio. Increasing the auxetic angles reduces the effective pure shear modulus. Elastically anisotropic characteristics of the homogenized plate are analyzed with the calculated effective Young's modulus, Poisson's ratio, and pure shear modulus. [ABSTRACT FROM AUTHOR]

The dynamic mechanical responses of the ferroelastic materials under uniaxial straining and temperature cycling are studied via the Landau-type phase field model in two dimensions. The model may exhibit a single-well (doublewell) energy profile when temperature is greater (less) than the critical temperature. Effective negative stiffness in the vicinity of the temperature-induced solid-solid phase transformation is numerically demonstrated through monotonic uniaxial straining on a single-domain ferroelastic under temperature cycling around the Curie temperature. Under sinusoidal uniaxial straining, the effective Young's modulus and damping, as indicated by the enclosed area of the stress-strain curve, may be largely increased due to the phase transition. Our calculated responses here are consistent with experimental data reported in the literature, as well as theoretical results based on the composite theory with inclusions assumed to have negative modulus. No negative stiffness values are directly assigned in our phase field model as the underlying physics of the order parameters, i.e., spontaneous strains, provides effective negative stiffness into the systems. [ABSTRACT FROM AUTHOR]

Composite materials containing negative-stiffness inclusions embedded in positive-stiffness matrix may exhibit unconventional (anomalous) effective coupled-field properties through interactions of the two phases. Effective coupled-field properties are calculated with the finite element methods under the quasi-static assumption. Stability boundaries are determined by applying 10 Hz sinusoidal loading on boundary surfaces, and the system is unstable if its energy becomes divergent for a chosen inclusion Young's modulus ratio ( λE) or bulk modulus ratio ( λK). Effective viscoelastic properties and their stability are studied for negative λE at 10 Hz, while the Poisson's ratio of the purely elastic inclusion is kept constant. For small inclusion volume fractions, their stability boundary is at λE ∼ -0.3, and extreme large effective damping and viscoelastic modulus are in the unstable regime. Furthermore, in the viscoelastic case, inclusion shapes have no effects on stability. As for the effective coupled-field properties, all anomalous peaks are in the unstable regime for negative λE or λK, except for an anomalous peak in effective thermal expansion coefficient with electrically insulated inclusions. Insulated inclusions may cause charge accumulation at the inclusion-matrix interface and boundary surface effects may serve as stabilizing agents to the composite system. [ABSTRACT FROM AUTHOR]

Metallic glasses, also known as amorphous metals, exhibit unique mechanical properties in terms of their strength and ductility. In this work, molecular dynamics simulation techniques were adopted to construct (Cu 50 Zr 50 ) 100− x Al x thin-film glasses, with x being the atomic percentage of aluminum, through simulated sputter deposition processes. The deposition simulations were conducted with a tight-binding interatomic potential, and argon working gas was modeled by the pair-wise Moliere potential. The calculated radial distribution functions of the films show more amorphous microstructures, consisting distorted icosahedral clusters. The as-deposited films were annealed at various temperature with the NPT ensemble, and aluminum clusters were found at temperature T > 800 K. The formation of the aluminum clusters may be due to the system being trapped into a local energy minimum. For their indentation properties at elevated temperatures, a right-angle conical carbon indenter tip was adopted with the NVT ensemble. No aluminum clusters were found with the NVT ensemble at high temperatures. In addition, the hardness and Young’s modulus show strong temperature dependence above the glass transition temperature. Pileup index, viscosity and elastic anisotropy exhibit anomalies around glass transition temperature. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the (Cu50Zr50)100-xAlx (X =0, 2, 4, 5, 6, 8, 10, 12, atomic percent) metallic-glass thin films on the titanium crystalline substrate were constructed by using molecular dynamics (MD) to simulate sputter deposition. The deposition simulations adopted a tight-binding potential with consideration of argon working gas from the pair-wise Moliere potential. The as-deposited films were amorphous and used as initial structures for nano-indentation simulations with a right-angle conical indenter tip to obtain their mechanical properties. All simulations were carried out at temperature 300 K to compare with experimental data. The radial distribution function of the film is calculated and compared with synchrotron experimental data. From the nanoindentation simulations, the hardness and Young's modulus of the films were calculated, as well as the pileup index under two different depth-to-thickness ratios. Our MD simulation results are consistent with experimental data. Furthermore, atomic strains were calculated to reveal deformation localization. In addition, elastic constants of the film and associated degrees of elastic anisotropy were studied to correlate structural anisotropy and to reveal structural relaxation. It is found that the deposited and MD-equilibrated films have notable anisotropic elastic constants, and their relaxation can be observed at the MD time scales. [Copyright &y& Elsevier]

The von Mises yield criterion and its associated flow rule are adopted to provide the exact analytic solution for the elastic-plastic stress and strain distributions within the discs with temperature-dependent properties subject to thermal loading by a uniform temperature field and subsequent unloading. This article examines the effect of temperature-dependent properties on the size of the plastic zone. Qualitative features of the solution are emphasized. The primary objective of the article is to provide a benchmark problem having the exact analytic solution for justifying the possibility to neglect or the necessity to account for temperature-dependency of thermomechanical properties in analysis of elastic-plastic discs under plane stress conditions. [ABSTRACT FROM AUTHOR]

The stability of viscoelastic composites with negative stiffness (NS) inclusions and their associated extreme mechanical properties are studied with time-domain finite element analysis and composite theory. In the finite element analysis, the stability of the plane-strain, two-phase NS composite is evaluated by monitoring the stress divergence under uniaxial straining. In addition, 2D and 3D two-phase NS composites are studied by using composite theories and the elastic-viscoelastic correspondence principle. Effective stiffness and damping anomalies are observed, and the stability of the composites is evaluated. In the low frequency regime, stability conditions for purely elastic systems are suitable to estimate the stability of the viscoelastic composites. This is verified with the finite element analysis. For the 2D problem, the finite element analysis and composite theory agree well with each other in terms of the overall properties and stability. For the 3D problem, only the results obtained from the composite theory are presented. Our analysis shows that the extreme mechanical properties for both of the 2D and 3D cases are located near the strong ellipticity boundary. When the matrix modulus is suitably chosen to satisfy all stability conditions, the effective stiffness softening anomaly (i.e., damping enhancement) may be in the stability range. The effective stiffness enhancement locates in the non-elliptic range of the negative inclusion bulk modulus parameter space. [ABSTRACT FROM AUTHOR]

Plastic anisotropy significantly influences the behavior of structures subjected to various loading conditions. The extremum principles in the theory of rigid plastic solids are convenient and reliable tools for plastic design. The present paper combines the upper bound theorem and Hill's quadratic yield criterion for orthotropic materials to evaluate the plastic collapse load of a highly undermatched welded tensile panel with a crack in the weld. The base material is supposed to be rigid. The shape of the crack is quite arbitrary. The orientation of the principal axes of anisotropy varies through the thickness of the weld. The upper bound solution is based on an exact solution for a layer of an anisotropic material. This feature of the upper bound solution is advantageous for increasing its accuracy. A numerical treatment is only necessary to find the solution for the uncracked specimen. This specimen has two axes of symmetry, which simplifies the solution. Simple analytic formulae transform this solution into a solution for the cracked specimens with one axis of symmetry and no symmetry. It is shown that the through-thickness distribution of anisotropic properties significantly affects the limit load. [ABSTRACT FROM AUTHOR]

Abstract: The recent development of using negative stiffness inclusions to achieve extreme overall stiffness and mechanical damping of composite materials reveals a new avenue for constructing high performance materials. One of the negative stiffness sources can be obtained from phase transforming materials in the vicinity of their phase transition, as suggested by the Landau theory. To understand the underlying mechanism from a microscopic viewpoint, we theoretically analyze a 2D, nested triangular lattice cell with pre-chosen elements containing negative stiffness to demonstrate anomalies in overall stiffness and damping. Combining with current knowledge from continuum models, based on the composite theory, such as the Voigt, Reuss, and Hashin–Shtrikman model, we further explore the stability of the system with Lyapunov''s indirect stability theorem. The evolution of the microstructure in terms of the discrete system is discussed. A potential application of the results presented here is to develop special thin films with unusual in-plane mechanical properties. [Copyright &y& Elsevier]

Analytical investigations on the contact problems between two homogeneous and isotropic soft bodies were performed to simulate the contact of human buttocks and seat cushions. The cushion materials'' Poisson''s ratio were allowed to be negative. The human buttocks were modeled as an ideal sphere with radius 15 cm, and assumed to have a low Young''s modulus and a Poisson''s ratio close to 0.5. These parameters were held constant during our analysis. Peak contact pressure was reduced by adjusting the contour curvature of cushions according to Hertz theory, as expected. Moreover, analysis by both the Hertz model and a finite thickness 3D elasticity model showed that using negative Poisson''s ratio cushions could further reduce the pressure. Negative Poisson''s ratio cushions may be beneficial in the prevention of pressure sores or ulcers in the sick and in reduction of pressure-induced discomfort in seated people. [Copyright &y& Elsevier]

An efficient analytical/numerical method has been developed and programmed to predict the distribution of residual stresses and springback in plane strain pure bending of functionally graded sheets at large strain, followed by unloading. The solution is facilitated by using a Lagrangian coordinate system. The study is concentrated on a power law through thickness distribution of material properties. However, the general method can be used in conjunction with any other through thickness distributions assuming that plastic yielding initiates at one of the surfaces of the sheet. Effects of material properties on the distribution of residual stresses are investigated. [ABSTRACT FROM AUTHOR]

Two‐dimensional (2D) elastic materials consisting of microstructure may exhibit positive or negative effective Poisson's ratio in the range between −1 and +1. Wang et al. (article no. 1700024) adopt the finite element numerical method, and systematically analyse the 2D medium with conventional or re‐entrant cell‐shape defined by the auxetic angle (θ). When θ = −45°, the microstructural cell has the diamond shape, and the corresponding effective Poisson's ratio is close to +1. As θ increases to positive values, the microstructure gradually changes to re‐entrant shapes. Not all re‐entrant cell shapes give rise to negative Poisson's ratio. To obtain negative Poisson's ratio, the auxetic angle needs to be greater than about 20°. Increasing auxetic angles reduce the effective pure shear modulus monotonically, while the effective Young's modulus shows a slight hump around θ = 25°. Full anisotropic elastic constants of the 2D medium are calculated, and its partial auxetic characteristics is revealed. [ABSTRACT FROM AUTHOR]

High damping and high stiffness (HDHS) viscoelastic materials, which exhibit desired energy‐dissipating capability and structural integrity, may be achieved by using negative‐stiffness inclusions, such as ferroelastic particles, in composite materials. However, stability has long been questioned for such composites to be realistic. Wang and Ko (pp. 2070–2079) examine a two‐dimensional, two‐phase, negative‐stiffness viscoelastic composite under partial displacement loading by time–domain analysis with the finite element method. It was found that force responses may be stable or unstable, depending on the amount of negative stiffness. A small amount of negative stiffness in the viscoelastic composites may not deteriorate their stability, but is insufficient to trigger HDHS. Through examining the existing stability criteria of three‐dimensional composites, the softening anomaly in the overall viscoelastic stiffness may be in the stability range, indicating stable damping enhancement. However, simultaneously enhancing damping and stiffness violates ellipticity requirements, hence the system is unstable/metastable. The cover image shows stress distributions around the inclusion of the two‐dimensional composite in the background and stiffness/damping anomalies, as well as divergent force responses, deviating from expected sinusoidal responses. [ABSTRACT FROM AUTHOR]

The upper bound theorem is used in conjunction with Hill's quadratic yield criterion for determining the force required to upset a solid cylinder. The kinematically admissible velocity field accounts for the singular behavior of the real velocity field in the vicinity of the friction surface if the maximum friction law is adopted. The regime of sticking is also taken into consideration. The effect of this regime on the upper bound limit load is revealed. In particular, the kinematically admissible velocity field that includes the regime of sticking may result in a lower upper bound than that with no sticking. The boundary value problem is classified by a great number of geometric and material parameters. Therefore, a systematic parametric analysis of the effect of these parameters on the compression force is practically impossible. An advantage of the solution found is that it provides a quick estimate of this force for any given set of parameters. [ABSTRACT FROM AUTHOR]

Elastoplastic analysis of a composite cylinder, consisting of an isotropic elastic inclusion surrounded by orthotropic matrix, is conducted via numerical parametric studies for examining its residual stress under thermal cycles. The matrix is assumed to be elastically and plastically orthotropic, and all of its material properties are temperature-dependent (TD). The Hill's anisotropic plasticity material model is adopted. The interface between the inclusion and matrix is perfectly bonded, and the outer boundary of the cylinder is fully constrained. A quasi-static, uniform temperature field is applied to the cylinder, which is analyzed under the plane-strain assumption. The mechanical responses of the composite cylinder are strongly affected by the material symmetry and temperature-dependent material properties. When the temperature-independent material properties are assumed, larger internal stresses at the loading phase are predicted. Furthermore, considering only yield stress being temperature dependent may be insufficient since other TD material parameters may also affect the stress distributions. In addition, plastic orthotropy inducing preferential yielding along certain directions leads to complex residual stress distributions when material properties are temperature-dependent. [ABSTRACT FROM AUTHOR]

This paper addresses an axisymmetric quasi-static contact problem on both thermal and mechanical interactions of a circular punch and a nonhomogeneous elastic half-space whose mechanical and thermophysical properties are assumed to be arbitrary functions of the depth coordinate. To solve the formulated boundary value problem, the technique of Hankel’s integral transformation is used. Using the bilateral asymptotic method, an approximate analytical–numerical solution is constructed for the heat flux, boundary displacements of the half-space, and contact stress under the punch. Numerical implementation is performed for different dependences of the material properties on the depth of the half-space. [ABSTRACT FROM AUTHOR]

Abstract: Buckling strengths, in terms of compressive strain, of single-, double- and triple-walled carbon nanotubes (CNTs) are investigated to study the effects of slenderness ratio () via the molecular dynamics (MD) simulations with the Tersoff potential. Under constant ratio of slenderness, the CNTs with small behave like a continuum shell object. For large ''s, multi-walled CNTs exhibit the characteristics of the Euler columns. In addition, smaller nanotubes possess higher buckling-resistance. The buckling strength of multi-walled nanotubes is controlled by the size of their outermost shell. [Copyright &y& Elsevier]

Slopes with carbonaceous mudstone (CM) are widely distributed in the southwest of China and have experienced numerous geological disasters in special climate, especially in rainfall conditions. Therefore, novel materials to stabilize CM slopes have attracted increasing interests. However, developing ultra-stable and cost-effective additives for CM slopes is still a great challenge. Herein, a hydrophobic polymeric material (polyvinylidene fluoride, PVDF) is investigated as an additive to enhance the mechanical strength and long-time stability of CM slopes. The PVDF is uniformly dispersed in CM matrix via interfacial interaction. The contact angle of the PVDF-modified carbonaceous mudstone (PVDF-MCM) can reach as high as 103.95°, indicating an excellent hydrophobicity. The unconfined compressive strength (UCS) and tensile strength (TS) of PVDF-MCM have been intensively enhanced to 4.07 MPa and 1.96 MPa, respectively, compared with ~0 MPa of pristine CM. Moreover, the UCS and TS of PVDF-MCM remain at 3.24 MPa and 1.03 MPa even after curing for 28 days in high humidity conditions. Our findings show that the PVDF can improve the hydrophobicity of CM significantly, which leads to super mechanical stability of PVDF-MCM. The excellent performance makes PVDF a promising additive for the development of ultra-stable, long-lifetime and cost-effective carbonaceous mudstone slopes. [ABSTRACT FROM AUTHOR]

High-entropy alloy (HEA) offers great flexibility in materials design with 3–5 principal elements and a range of unique advantages such as good microstructure stability, mechanical strength over a broad range of temperatures and corrosion resistance, etc. Welding of high entropy alloy, as a key joining method, is an important emerging area with significant potential impact to future application-oriented research and technological developments in HEAs. The selection of feasible welding processes with optimized parameters is essential to enhance the applications of HEAs. However, the structure of the welded joints varies with material systems, welding methods and parameters. A systemic understanding of the structures and properties of the weldment is directly relevant to the application of HEAs as well as managing the effect of welding on situations such as corrosion that are known to be a service life limiting factor of welded structures in conditions such as marine environments. In this paper, key recent work on welding of HEAs is reviewed in detail focusing on the research of main HEA systems when applying different welding techniques. The experimental details including sample preparation, sample size (thickness) and welding conditions reflecting energy input are summarized and key issues are highlighted. The microstructures and properties of different welding zones, in particular the fusion zone (FZ) and the heat affected zones (HAZ), formed with different welding methods are compared and presented in details and the structure-property relationships are discussed. The work shows that the weldability of HEAs varies with the HEA composition groups and the welding method employed. Arc and laser welding of AlCoCrFeNi HEAs results in lower hardness in the FZ and HAZ and reduced overall strength. Friction stir welding results in higher hardness in the FZ and achieves comparable/higher strength of the welded joints in tensile tests. The welded HEAs are capable of maintaining a reasonable proportion of the ductility. The key structure changes including element distribution, the volume fraction of face centered cubic (FCC) and body centered cubic (BCC) phase as well as reported changes in the lattice constants are summarized and analyzed. Detailed mechanisms governing the mechanical properties including the grain size-property/hardness relationship in the form of Hall–Petch (H–P) effect for both bulk and welded structure of HEAs are compared. Finally, future challenges and main areas to research are highlighted. [ABSTRACT FROM AUTHOR]