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The purpose of this paper is to perform an analytical study of non-linear elastic delamination fracture in the multilayered functionally graded split cantilever beam (SCB) configuration. The SCB studied may have an arbitrary number of vertical layers. The material in each layer is functionally graded along the layer thickness. Also, the material properties may be different in each layer. The analytical solution derived was applied for parametric investigations in order to evaluate the effects of material properties and delamination crack location on the non-linear fracture behaviour.

The delamination fracture was studied in terms of the strain energy release rate. The SCB mechanical response was described by using a power-law stress-strain relation. A non-linear analytical solution for the strain energy release rate was derived by considering the SCB complementary strain energy. In order to verify the solution, an additional analysis of the strain energy release rate was developed by considering the complementary strain energy in the beam cross-sections ahead and behind the crack front.

The effects of material gradient, crack location along the beam width and non-linear material behaviour on the delamination fracture were evaluated. The analytical solution derived is useful for parametric studies of non-linear fracture in multilayered functionally graded beams.

Delamination fracture in the multilayered functionally graded SCB configuration was analysed with considering the non-linear material behaviour.

The purpose of this paper is to identify the energy absorption characteristics of arch micro-strut (ARCH) lattice structure (different from traditional straight micro-strut lattice structure) under high-speed impact, and promote the development of special-shaped micro-strut lattice structure.

The study serves to study the anti-impact and energy absorption characteristics of ARCH lattice structure under different strain rates and different unit layers of lattice structure. In this paper, quasi-static compression and Hopkinson compression bar experiments are used for comparative analysis.

The results show that the ARCH lattice structure has obvious strain rate effect. When the strain rate is low, the number of layers of lattice structure has a great influence on the mechanical properties. With the increase of strain rate, the influence of the number of layers on the mechanical properties gradually weakens. So the ARCH lattice structure with fewer layers (less than five layers) should be selected as the impact energy absorbing materials at lower impact rate, while at higher impact rate, the number of layers can be selected according to the actual requirements of components or devices space size.

This study shows that Arch lattice structure has excellent energy absorption performance, and provides a theoretical reference for the application of ARCH lattice structure in energy-absorbing materials. ARCH lattice structure is expected to be applied to a variety of energy absorption and anti-impact components or devices, such as aircraft black box fall buffer components, impact resistant layer of bulletproof and landing buffer device.

The paper aims to build a finite element simulation model for pilling of polyester hairiness on the fabric to study the effects of hairiness performance on pilling and reveal pilling mechanisms.

The finite element simulation model of pilling of polyester hairiness was established by ABAQUS. Polyester hairiness was treated as elastic thin rod, which was divided by two-node linear three-dimensional truss element. The effects of hairiness elastic modulus, hairiness friction coefficient and hairiness diameter on frictional dissipation energy, strain energy and kinetic energy produced by pilling have been studied. The analysis solution values were compared with the finite element simulation results, which was used to verify finite element simulation.

The paper provides new insights about how to reveal pilling mechanisms of polyester hairiness with different performance. Comparing finite element simulation results with analysis solutions shows that the fitness is greater than 0.96, which verifies finite element simulation. Larger hairiness elastic modulus gives rise to higher friction dissipation energy and strain energy of hairiness but lower kinetic energy. Increasing friction coefficient enhances friction dissipation and strain energy of hairiness. However, kinetic energy decreases with the increase of friction coefficient. Hairiness diameter also has an important effect on hairiness entanglement and pilling. Increasing hairiness diameter can decrease friction dissipation energy but enhance strain energy and kinetic energy.

Finite element simulation was verified by analysis solutions. The solutions include friction dissipation energy, strain energy and kinetic energy, which cannot measured b experiment. Therefore, researchers are encouraged to simulate pilling to obtain pilling grades, which be compared with experiment results.

Pilling of polyester hairiness was simulated by ABAQUS. This method makes pilling process visualization, and pilling mechanisms was revealed from non-linear dynamics.

The purpose of this paper is to develop an analysis of longitudinal fracture behaviour of a functionally graded non-linear-elastic circular shaft loaded in torsion. It is assumed that the material is functionally graded in both radial and longitudinal directions of the shaft (i.e. the material is bi-directional functionally graded).

The Ramberg–Osgood stress-strain relation is used to describe the non-linear mechanical behaviour of the functionally graded material. The fracture is studied in terms of the strain energy release rate by analysing the balance of the energy. The strain energy release rate is obtained also by differentiating of the complementary strain energy with respect to the crack area for verification.

Parametric studies are carried out in order to evaluate the influence of material gradients in radial and longitudinal directions, the crack location in radial direction and the crack length on the fracture behaviour of the shaft. It is found that by using appropriate gradients in radial and longitudinal directions, one can tailor the variations of material properties in order to improve the fracture performance of the non-linear-elastic circular shafts to the externally applied torsion moments.

A longitudinal cylindrical crack in a bi-directional functionally graded non-linear-elastic circular shaft loaded in torsion is analysed by using the Ramberg–Osgood stress-strain relation.

This paper presents the generalized theory of the most important energy principles in structural analysis. All derive from two basic complementary theorems denoted as the principles of virtual displacements and virtual forces. Both exact and approximate methods are discussed and particular attention is paid to the derivation of upper and lower limits. The theory is not restricted to linearly elastic bodies but includes ab initio the effect of non‐linear stress‐strain laws and thermal strains. Finally the basic principles are illustrated on a number of simple examples in preparation for the more complex ones to appear in Parts II and III.

The localized strain softening behaviour of concrete has been modelled by two approaches: (i) the stiffness degrading model based on the total stress‐strain constitutive relationship, and (ii) the tangent softening model based on the incremental stress‐strain relationship. The models are implemented using a new softening initiation criterion proposed for application in multi‐dimensional finite element analysis. Parametric analyses on plain concrete beams, tested experimentally by other researchers, have been carried out to investigate the required numerical efforts, the mesh objectivity, and the energy dissipation characteristics of the structures. The stiffness degrading model is very stable even when applied with relatively coarse finite element meshes. However, the computational demand of this model is relatively high. The combination of a total stress‐strain constitutive relationship to compute the element responses, and an incremental relationship to formulate the stiffness matrix, appears to be computationally efficient and stable, provided that adequately refined finite element mesh is used to model the structure.

Engineering components/structures with geometric discontinuities normally bear complex and variable loads, which lead to a multiaxial and random/variable amplitude stress/strain state. Hence, this study aims how to effectively evaluate the multiaxial random/variable amplitude fatigue life.

Recent studies on critical plane method under multiaxial random/variable amplitude loading are reviewed, and the computational framework is clearly presented in this paper.

Some basic concepts and latest achievements in multiaxial random/variable amplitude fatigue analysis are introduced. This review summarizes the research status of four main aspects of multiaxial fatigue under random/variable amplitude loadings, namely multiaxial fatigue criterion, method for critical plane determination, cycle counting method and damage accumulation criterion. Particularly, the latest achievements of multiaxial random/variable amplitude fatigue using critical plane methods are classified and highlighted.

This review attempts to provide references for further research on multiaxial random/variable amplitude fatigue and to promote the development of multiaxial fatigue from experimental research to practical engineering application.

Presents an alternative lower bound to the elastic buckling collapse of thin shells of revolution, in comparison with results from geometrically non‐linear elastic analysis. The numerical finite element method is based on axisymmetric rotational shell elements whose strain‐displacement relations are described by Koiter’s small finite deflection theory, with displacements expanded circumferentially using a Fourier series. First, compares the reduced stiffness linear analysis, based on the buckling equation without incremental linear in‐plane energy components corresponding to the lowest eigenmode (for a particular cylindrical shell under external pressure), with the results obtained by Batista and Croll. Second, the non‐linear astatic (quasi‐static) elastic analysis to clamped spherical caps under uniform external pressure is carried out in order to compare the results from a reduced stiffness analysis from viewpoints of not only buckling loads, but also total potential energy. Argues that the astatic buckling loads may relate to reductions due to a specific imperfection effect on elastic buckling collapses.

This paper aims to analyze the elastic-plastic delamination fracture behaviour of multilayered functionally graded four-point bending beam configuration.

The mechanical response of beam is described by a power-law stress-strain relation. The fracture is studied analytically in terms of the strain energy release rate by considering the beam complimentary strain energy. The beam can have an arbitrary number of layers. Besides, each layer may have different thickness and material properties. Also, in each layer, the material is functionally graded along the beam width. A delamination crack is located arbitrary between layers. Thus, the crack arms have different thickness.

The analysis developed is used to elucidate the effects of crack location, material gradient and non-linear behaviour of material on the delamination fracture. It is found that the material non-linearity leads to increase in the strain energy release rate. Therefore, the non-linear behaviour of material should be taken into account in fracture mechanics-based safety design of structural members and components made of multilayered functionally graded materials. The analysis revealed that the strain energy release rate can be effectively regulated by using appropriate material gradients in the design stage of multilayered functionally graded constructions.

Delamination fracture behaviour of multilayered functionally graded four-point bending beam configuration is studied in terms of the strain energy release rate by taking into account the material non-linearity.

Continuum‐atomistic modeling denotes a mixed approach combining the usual framework of continuum mechanics with atomistic features like e.g. interaction potentials. Thereby, the kinematics are typically characterized by the so called Cauchy‐Born rule representing atomic distance vectors in the spatial configuration as an affine mapping of the atomic distance vectors in the material configuration in terms of the local deformation gradient. The application of the Cauchy‐Born rule requires sufficiently homogeneous deformations of the underlying crystal. The model is no more valid if the deformation becomes inhomogeneous. By virtue of the Cauchy‐Born hypothesis, a localization criterion has been derived in terms of the loss of infinitesimal rank‐1 convexity of the strain energy density. According to this criterion, a numerical yield condition has been computed for two different interatomic energy functions. Therewith, the range of the Cauchy‐Born rule validity has been defined, since the strain energy density remains quasiconvex only within the computed yield surface. To provide a possibility to continue the simulation of material response after the loss of quasiconvexity, a relaxation procedure proposed by Tadmor et al. [1] leading necessarily to the development of microstructures has been used. Alternatively to the above mentioned criterion, a stability criterion has been applied to detect the critical deformation. For the study in the postcritical region, the path‐change procedure proposed by Wagner and Wriggers [2] has been adapted for the continuum‐atomistics and modified.