It is known that a local deformation mode affects the fracture behavior. First, a parameter that represents the deformation mode is defined for a fracture criterion that can consider the deformation mode in ordinary state-based peridynamics. This parameter is analogous to stress triaxiality in conventional continuum mechanics. The calculated values of the parameter agree well with the theoretical values

Anisotropic ductile fracture is of special importance for accurate modeling of failure in plastic forming of lightweight sheet metals. This research introduces a user-friendly approach to model loading direction effect on fracture limits of sheet metals. The approach is combined with a newly developed fracture criterion (DF2016) to illustrate anisotropic fracture in shear, uniaxial tension and plane

In engineering stretchable electronics, an intermediate layer between a thin stiff film and a substrate can enhance the adhesion of the film and modulate its buckling shape. Capturing buckling behaviour of the tri-layer film/intermediate layer/substrate structure is essential for designing stretchable electronics. In this paper, considering the shear stress between the film and intermediate layer and

Existing theoretical methods for solving the stress intensity factors (SIFs) of a cracked V-notch plane are products of highly sophisticated mathematical analyses and are therefore, challenging for engineers to study, derive, and reproduce. Based on our extension of the dimensional analysis, or the 'geometry parameter method', we investigated a V-notched edge of a semi-infinite plate with a crack at

A collocation mixed finite element method (MFEM) for direct and converse flexoelectricity in piezoelectric materials is developed for 2D problems. The size-effect phenomenon in micro/nano structures is considered by the strain- and electric intensity vector-gradient effects. C0 continuous finite element method is inadequate to treat flexoelectricity problems involving the size-effect. To this end,

In its original formulation by Forest & Sab (Math. Mech. Solids, 2017), stress gradient elastodynamics incorporate two inner-lengths to account for size effects in continuum theory. Here, an extended one-dimensional stress gradient model is developed by means of Lagrangian formalism, incorporating an additional inner-length and a fourth-order space derivative in the wave equation. Dispersive properties

In order to investigate the behavior of elastoplastic composites exhibiting both isotropic and nonlinear kinematic hardening, we extend the Double Incremental Variational (DIV) formulation of Lucchetta et al. [1], based on both the incremental variational principles introduced by Lahellec and Suquet [2] and the formulation proposed by Agoras et al. [3]. However, the Armstrong-Frederick model [4], which

The driving force on the line, zero height, fracture process zone (FPZ) is investigated in this paper. First, basic laws for crack propagation based on the configurational force approach are derived in the framework of traditional continuum mechanics. The driving force on steady line FPZ is a direct consequence of these derivations. Fracture parameters suitable for growing cracks in elastic–plastic

When subjected to cyclic loading, complete contacts with à la Coulomb friction may sometimes develop a favourable situation where slips cease after a few cycles, an occurrence commonly known as frictional shakedown. However, if the amplitude of the cyclic load is greater than a so-called shakedown limit, the system is unable to adapt and indefinitely persists in a dissipative state. In this paper,

Ferroelectric polymers have attracted increasing attention due to their distinguished dielectric and piezoelectric properties. Dielectric breakdown is one of the main failure behaviors for ferroelectric polymers. Understanding dielectric breakdown of ferroelectric polymers under mechanical and electrical loadings is crucial to their applications in energy storage and conversion devices with high-energy-density

The EVPSC-TDT model is first employed to investigate the yield behavior of a strongly basal textured Mg alloy plate under biaxial loading. The material parameters are calibrated according to experimental uniaxial tension and compression along the rolling and plate normal directions. The EVPSC-TDT model with the calibrated parameters is then employed to conduct various biaxial loadings under plane stress

We investigate localised bulging or necking in an incompressible, hyperelastic cylindrical tube under axial stretching and surface tension. Three cases are considered in which the tube is subjected to different constraints. In case 1 the inner and outer surfaces are traction-free and under surface tension, whilst in cases 2 and 3 the inner and outer surfaces (respectively) are fixed to prevent radial

A method is presented for approximating a curved surface by a developable rigid origami; a polyhedral shape which can be developed to a plane without deformation of its facets. Form generation starts from a triangulated surface, and an optimization problem is solved to obtain a polyhedron which satisfies the geometric conditions for developability. The degrees of freedom of a rigid origami mechanism

Predicting the structural performance of a joint requires mechanical characterization of the joint interface. Use of the cohesive-zone model (CZM) is an effective approach for implementing fractures, seams, and joints in the structures. The CZM requires a cohesive constitutive law, which, in the context of a welded joint, relates the traction at the interface to the separation displacement of the two

Two simple and fully analytical models are presented for a SMA bar or wire of circular cross section subjected to fully-reversed cyclic torsional loading, by taking into consideration the reorientation of the martensitic variants occurring during unloading and reverse loading. The process is assumed to take place at constant temperature between the start temperatures of the martensitic and austenitic

Phononic crystals and elastic metamaterials have recently received significant attention due to their potential for unconventional wave control. Despite this interest, one outstanding issue is that their band diagram is typically fixed once the structure is designed. To overcome this limitation, periodic structures with adaptive elastic properties have recently been proposed for Bragg- and local resonance-driven

Polymer matrix exhibit linear viscoelasticity during processing of composites. The viscoelastic homogenization problem in the time-domain play a vital role in the virtual process simulations. In this paper, full-field simulations using finite element (FE) are carried out for different regular periodic microstructures of unidirectional (UD) fiber reinforced polymer (FRP) (i.e., short, and long fiber)

Subsequent yield surfaces of ductile solids, pre-strained in shear and/or tension, exhibit various characteristic features that depend on the proof strain used to detect yield. These features include kinematic hardening when the proof strain denoting yield is low, isotropic hardening when it is high, formation of a ‘nose’ in the loading direction and flattening of the rear part of the yield surface

A novel two-dimensional (2D) mechanical metamaterial with highly programmable mechanical response under compressive load is presented in this paper by introducing hierarchical rotating structures, in which flexible structures are used to replace the rigid part in conventional rotating rigid structures. Multi-step deformation pathways and negative Poisson’s ratio were observed in in situ compression

Temperature is an important factor affecting the physical and chemical properties of materials, especially when the temperature changes significantly, such as in the process of heat conduction. The corresponding changes of material properties greatly complicate the distribution of temperature and thermal stress, and make it much more difficult to accurately solve the thermal-elastic field. Using the

Homogenization theory is increasingly applied to coupled phenomena, i.e. when different physical processes have to be modeled in order to correctly describe a system. The reason is that this methodology provides the means to propose a consistent morphological description of the system irrespective of the different phenomena involved, which is deemed to be physically sound. Here, we perform numerical

This paper determines the elastic fields in a positive half-space embedded with a spherical inhomogeneity under the context of Steigmann–Ogden surface/interface mechanical model. The half-space is loaded by an equal-biaxial far-field tension applied at infinity. While bulk domains are treated as linearly isotropic elastic solids, both the half-space plane boundary and the matrix/inhomogeneity interface

In this work, a mathematical model is developed based on Griffith’s crack theory while incorporating couple stress and surface elasticity in order to examine the performance and operability of cracked vibrating beam micro/nanogyroscopes. A size dependent crack severity factor is used to represent increased local flexibility due to surface crack. The gyroscope size is decreased from micro- to nano-scale

High density polyethylene (HDPE) is increasingly used in infrastructure applications with a design service lifetime of several decades. In many cases, the HDPE member is exposed to a corrosive environment, such as in pipes carrying potable water, where the dissolved bleach selectively attacks the loosely packed amorphous phase of the polymer. The failure mechanism of HDPE transitions from a ductile

A multi-scale method based on a combination of the boundary element method (BEM) and peridynamics (PD) was developed to model crack propagation problems in two-dimensional (2D) elastic bodies. The special feature of this method is that it can take full advantage of both the BEM and PD to achieve a higher level of computational efficiency. Based on the scale of the structure and the crack location,

This paper provides estimates for the stress, strain-rate and spin field statistics in viscoplastic polycrystals. They are obtained by combining the fully optimized second-order (FOSO) homogenization method with the self-consistent estimate for linear polycrystalline aggregates. The FOSO linearization method allows the consistent estimation of the field statistics in nonlinear composites and polycrystals

In this study, we developed a micromechanics scheme to predict the upper and lower bounds on the creep strain and stress relaxation induced by interface diffusion in metal-matrix particulate composites. The normal stress acting on the matrix-inclusion interface, which is the driving force for interface diffusion, is estimated by using the Hashin-Shtrikman bounds and mean-field micromechanics theory

The present work addresses two key issues relating to the study of rate effects in adhesively bonded joints. Firstly, the accurate determination of the crack tip strain rate and secondly the accurate determination of cohesive zone length. The rate-dependent fracture behaviour of adhesive joints bonded with either a toughened epoxy or a ductile polyurethane adhesive was investigated under mode I loading

Novel applications of shape memory alloys (SMAs) in various fields of medicine and engineering necessitate theoretical models that can capture non-inherent material behaviors such as the two-way shape memory effect (TWSME). Most often, this requires the use of completely different sets of models or parameters to distinguish the “virgin” material exhibiting the fundamental behaviors like superelasticity

Several phenomenological models have been proposed in the last decades to understand and describe the phenomenology of elastic hysteresis observed in dynamic experiments, i.e. the combination of nonlinear phenomena, usually referred to as “fast” and “slow” dynamics, including harmonic generation, resonance frequency shift, time variation of elastic properties when large conditioning strain is applied

This study presents an incremental variational formulation (IVF) for the thermo-mechanical problem of resin products subjected to curing, for which a dual dissipation potential (DDP) for the cure state is originally derived in conjunction with that for viscoelasticity. Following the thermodynamically consistent formulation for the time evolution equation of the degree of cure (DOC) of a thermosetting

In the problem of the synthesis of metamaterials, the pantographic architecture revealed remarkable potentialities. Indeed it allowed for the synthesis of second gradient 2D (nonlinear) continua: i.e. 2D shells whose deformation energy depends also on the second derivatives of displacements in the tangent directions to the reference configuration. Moreover, pantographic architecture seems to be able

The electrocaloric (EC) effect in dielectrics has shown great potential in the next-generation solid-state refrigeration; however, most dielectrics cannot satisfy the requirement for refrigeration at various temperatures. How to control large EC response to various temperatures is a critical problem for practical cooling applications. In this work, based on entropy analysis, a nonlinear thermodynamic

Taking into account damping effects, the propagation-distance dependence of the amplitude of nonlinear guided waves arising from an internal resonance was investigated. In the analysis of Lamb-wave propagation, we introduced nonlinear quadratic effects derived from both geometric and material nonlinearities, referred to as classical nonlinearities, and damping effects by expressing the Lamé constants

Titanium alloys exhibit complex microstructures containing heterogeneities at different lengthscales. Although the size of primary α grains is typically in the micrometer range, processing of α/β titanium alloys can introduce millimeter long clusters of α particles with the same or nearly the same crystallographic orientation. These microtextured regions (MTRs), also called macrozones, are known to

Accurate asymptotic solutions are presented for axisymmetric deformation of thin layers constrained by either two rigid plates or two rigid spheres. Those solutions are developed using Saint-Venant’s principle and the layer thinness as the only assumptions. The solutions are valid in the entire range of Poisson’s ratios, and allow one to distinguish among compressible, nearly incompressible, and incompressible

In the present paper, theoretical foundations of redundancy in spatially continuous, elastostatic, and linear representations of structures are derived. Adopting an operator-theoretical perspective, the redundancy operator is introduced, inspired by the concept of redundancy matrices, previously described for spatially discrete representations of structures. Studying symmetry, trace, rank, and spectral

A two-order asymptotic solution for sharp V-notch tip mechanics field in elasto-viscoplastic solids with power-law form under mode I loading is developed. The stress exponents and angular distributions for various notch angles and viscoplastic exponents for the second terms are reported. The stress exponent of the first order is singular and is non-singular except for low creep exponent with small

This paper presents the formulation of a finite element enclosing a specific internal mechanical equilibrium in order to model cable-based structures in dynamics conditions. It is based on the concept of macro finite element which allows embedding complex mechanical systems solved inside the element boundaries. A significant advantage is to allow an easy implementation within classical commercial codes

Failure of Thermal barrier coatings (TBCs) caused by interface oxidation directly determines the ultimate durability of TBCs. The interfacial delamination and brittle fracture will co-occur during the interface oxidation of the TBCs. To study the interaction between the two failure modes, we develop a thermodynamically-consistent coupling framework combining the phase-field model of the brittle fracture

The novel theoretical models for the temperature dependence of the contact mechanical properties of the particulate composites in Hertzian contact are proposed in this paper, based on an assumption of the temperature-independent constant energy storage capacity for a specific brittle particulate composite, associating with the material yielding, and the theory of Hertzian contact. The yield stress

Shape Memory Alloys (SMAs) are widely used in endodontics as instruments for root canal preparation namely endodontic rotary files. Despite their high performances, compared to stainless steel instruments, it is still possible to enhance their cutting efficiency by acting on their shape and material properties. As an example, increasing the exhibited reversible martensitic transformation strain makes

The configuration of a crack with respect to the multi-material fiber reinforced composite joint determines the order of singularity of the stress solutions reproduced around the crack-tip. These solutions for different configurations of crack are obtained for carbon nano-tube (CNT) reinforced CFRP composite using an innovative finite element asymptotic analysis. Micro-cracks aligned with CNTs covered

The paper addresses the theoretical framework and the numerical procedure developed to carry out the sectional analysis preliminary to the use of a recently formulated isotropic and homogeneous beam model consistently derived from the Saint Venant solid one. Specifically, in order to ensure the equivalence of the new beam model with the 3D solid one, both in terms of elastic energy and displacements

The aim of this contribution is to improve the behavior and failure prediction accuracy for magnesium alloy sheet forming simulation by using advanced fully coupled Continuum Damage Mechanics (CDM) model. Starting from known fully coupled constitutive equations at large inelastic (plastic or viscoplastic) strains, three aspects are enhanced on the CDM model developed by Saanouni (2012). The first one

We investigate the thermal-electric-elastic fields around two circular holes in a thermoelectric material. Solutions describing electric, thermal and elastic fields are obtained via complex variable and numerical methods. Our results show that the presence of the holes has the same effect on the effective electric and thermal conductivities but no effect whatsoever on the effective Seebeck coefficient

Strong, lightweight structures are increasingly in demand for various engineering applications. Here we present a method to produce a lightweight lattice composite tube with hexagonal unit cells using a high production rate, textile-based method. A weft knitting process was employed for the first time to produce lattice preforms made of a common high-performance E-glass yarn. The lattice preforms were

The degree of statical indeterminacy as a fundamental property in structural mechanics is today mainly known as a property of a complete system without any information about its spatial distribution. The redundancy matrix provides information about the distribution of statical indeterminacy in the system and by this gives an additional valuable insight into the load-bearing behaviour. The derivation

Metastructures based on kirigami (the Japanese art of paper folding and cutting) have great potential for applications in stretchable electronics, bioprobes, and controllable optical and thermal devices. However, a theoretical framework for understanding the physics of their buckling behavior and to facilitate the search for ultrahigh stretchability has yet to be developed. Here, we present such a

This study utilises a third-order expansion of the strain energy density function and finite strain elastic theory to derive an analytical solution for an isolated, spherical void subjected to axisymmetric loading conditions. The solution has been validated with previously published results for incompressible materials and hydrostatic loading. Using this new solution and a homogenisation methodology

Delamination is one of the main mechanisms involved in the fatigue damage evolution in multidirectional laminates made of unidirectional plies. Typically, delamination is induced by off-axis cracks, the tips of which terminate at the interface with the adjacent layers. One of the consequences of the presence of delamination is the degradation of the apparent laminate stiffness. In this work, an analytical

Mechanical responses of cold pilgered Zircaloy-4 (Zr-4) tubes are measured under different uniaxial (tension/compression) loading directions. Tensile tests were carried out along three directions: rolling direction (RD), transverse direction (TD) and 45° to the rolling direction (45RD) at quasi static strain rate. Compression test was also performed in the RD. Texture was characterized at intermediate

The analysis of multiple necking phenomenon during dynamic stretching of a metallic plate is investigated. For that purpose, a new 1D linear stability analysis is proposed to capture the perturbation evolution. The multidimensional aspect of the stress field within the neck region is taken into account with a Bridgman correction factor. The novelty of the 1D approach is to let the time evolution of

The instability behavior of a compressive bilayer on a soft substrate is of significance for epidermal electronics adhered to human skin. Conventionally, two different wrinkling modes dependent of the modulus of intermediate layer were proposed to evolve from flat feature. Here, we uncover a new periodic pattern of secondary wrinkling feature with further compression in the case of a moderate-modulus

This paper deals with the fatigue of shape memory alloys considering both experimental and theoretical approaches. Initially, experimental tests are performed considering NiTi pseudoelastic wires subjected to different load conditions. Functional and structural fatigue are investigated considering situations related to phase transformations and plastic behavior. Afterward, experimental macroscopic

In Part I of this paper, a quasi-static experimental path-following method was developed that uses tangent quantities in a feedback controller, based on Newton’s method. The ability to compute an experimental tangent stiffness opens the door to more advanced path-following techniques. Here, we extend the experimental path-following method to: (i) pinpointing of critical points (limit and branching

This study presents a variationally consistent formulation of the thermo-mechanically coupled problem with non-associative viscoplasticity for glassy amorphous polymers. First, the decomposition of the equivalent plastic strain is carried out to derive the variational consistent evolution law of the shear yield strength with reference to the analogous approach taken for formulating the Armstrong-Frederick