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In this study composite and sandwich beams with homogeneous core and homogeneous or Functional Graded Materials (FGM) faces under three point bending have been confronted. The purpose of this paper is to study numerically sandwich beams with homogeneous core and homogeneous or FGM faces under three point bending and to compare the results for the stress and displacement fields with those resulted of coating – substrate and homogeneous beams. Considering a crack in the lower face sheet to study the influence of the material gradation on the stress intensity factors.

At first a static finite element analysis is performed throughout the composite and sandwich beams, which is taking into account the graded character or not of the faces. For this reason five plane models are considered in order to have a comparable study for the stress and displacement fields of composite beams, which are subjected to three point bending. Second a crack in the lower face is considered parallel to the axis of gradation. When subjected to three point bending, this crack will propagate slowly perpendicular to the lower face.

Computed distributions of the stress fields across the core material and near the interfaces are given for different materials gradation of the faces; and possible crack-initiation positions have been identified. Stress intensity factors are calculated using finite element method, and assuming linear fracture mechanics and plane strain conditions.

The originality of the proposed analysis is to investigate for the first time numerically the influence of the FGMs or homogeneous faces in the core material of sandwich beams under three point bending relative to the coating – substrate and to the homogeneous beams. Second to study the influence of a crack in the lower graded face sheet on the overall behavior of the composite beam and to investigate the influence of the material gradation on the values of stress intensity factors.

The purpose of this paper is to analyse the eigenforms and eigenfrequencies of stator core stack by experimental and numerical investigation. The influence of material parameters on the structural vibrations is carried out in order to describe the laminated structure of stator core stack with a homogeneous material model.

The finite element method is applied for a numerical modal analysis. Therefore, a homogeneous transversally isotropic material model is introduced and the influence of each material parameter on the dynamical behavior is investigated. These material parameters are stepwise adjusted to the results from the experimental modal analysis. The investigation includes results from different stator core stacks.

The influence of material on the modal parameters is shown. Furthermore, material parameters are carried out for stator core stacks, which describe the measured dynamical behaviour.

The presented investigations show a useable material model and corresponding parameters to the description of the laminated structure of stator core stacks.

The tensile test is one of the fundamental experiments used to evaluate material properties. Simulating a tensile test can be a replacement of experiments to determine mechanical parameters of a continuous material. The paper aims to discuss these issues.

This research uses a new approach to model a tensile test of a high-carbon steel on the basis of discrete element method (DEM). In this research, the tensile test specimen was created by using a DEM packing theory. The particle-particle bond model was used to establish the internal forces of the tensile test specimen. The particle-particle bond model was first tested by performing two-particle tensile test, then was adopted to simulate tensile tests of the high-carbon steel by using 3,678 particles.

This research has successfully revealed the relationships between the DEM parameters and mechanical parameters by modelling a tensile test. The parametric study demonstrates that the particle physical radius, particle contact radius and bond disc radius can significantly influence ultimate stress and Young’s modulus of the specimen, whereas they slightly impact elongation at fracture. Increasing the normal and shear stiffness, the critical normal and shear stiffness can enable the increase of ultimate stress, however, up to maximum values.

To improve the particle-particle bond model to simulate a tensile test for high-carbon steel, the damping factors for compensating energy loss from transition of particle motions and failure of bonds are required.

This work reinforces the knowledge of applying DEM to model continuous materials.

This research illustrates a new approach to model a tensile test of a high-carbon steel on the basis of DEM.

The purpose of this paper is to investigate and explain the unexpected current flow patterns and twisting equipotential surfaces observed in strongly anisotropic materials.

Potential distributions and current flow paths in highly anisotropic composite materials were studied via numerical simulation and experimentally. Simplified composite panels with two plyes were analysed using a finite‐element model; the predictions were then confirmed experimentally.

The unexpected twisting equipotential surfaces and current flow patterns were found to be consistent with minimising of Joule heat release in the material. Numerical modelling suggests that the twisted profiles of the potential are highly sensitive to the anisotropic electrical conductivity.

This paper discusses the reverse current flows witnessed in a two‐layer anisotropic system. Such behaviour has never been predicted or observed experimentally before. The reported results will be of interest to anyone who is considering using anisotropic materials such as carbon fibre composites which might experience applied potential difference, such as lightning strikes.

The purpose of this paper is to use the discrete element method (DEM) to model the fracture behaviour of brittle materials in 2D.

The material consists of a set of particles in contact with a close‐packed structure. It allows the derivation of an expression for the stress intensity factor as a function of the contact forces near the crack tip. A classical failure criterion, based on the material's toughness, is then adopted for the analysis of crack propagation, represented by the contact loss between particles.

The DEM approach is compared to two tensile cases (mode I); both presenting a monotonous convergence towards classical solutions for more precise discretization.

The paper proposes a DEM approach in fracture mechanics of isotropic brittle materials entirely compatible with continuous classical theory. Hence the toughness value is directly introduced as a parameter of the material without any previous calibration of the DEM.

Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from pathological mesh‐dependence when strain‐softening models are employed in failure analyses. In this contribution the governing field equations are regularized by adding rotational degrees‐of‐freedom to the conventional translational degrees‐of‐freedom. This so‐called elasto‐plastic Cosserat continuum model, for which an efficient and accurate integration algorithm and a consistent tangent operator are also derived in this contribution, warrants convergence of the load—deflection curve to a unique solution upon mesh refinement and a finite width of the localization zone. This is demonstrated for an infinitely long shear layer and a biaxial test of a strain‐softening elasto‐plastic von Mises material.

The purpose of this paper is to develop a method to model entire structures on a large scale, at the same time taking into account localized non-linear phenomena of the discrete microstructure of cohesive-frictional materials.

Finite element (FEM) based continuum methods are generally considered appropriate as long as solutions are smooth. However, when discontinuities like cracks and fragmentation appear and evolve, application of models that take into account (evolving) microstructures may be advantageous. One popular model to simulate behavior of cohesive-frictional materials is the discrete element method (DEM). However, even if the microscale is close to the macroscale, DEMs are computationally expensive and can only be applied to relatively small specimen sizes and time intervals. Hence, a method is desirable that combines efficiency of FEM with accuracy of DEM by adaptively switching from the continuous to the discrete model where necessary.

An existing method which allows smooth transition between discrete and continuous models is the quasicontinuum method, developed in the field of atomistic simulations. It is taken as a starting point and its concepts are extended to applications in structural mechanics in this paper. The kinematics in the method presented herein is obtained from FEM whereas DEM yields the constitutive behavior. With respect to the constitutive law, three levels of resolution – continuous, intermediate and discrete – are introduced.

The overall concept combines model adaptation with adaptive mesh refinement with the aim to obtain a most efficient and accurate solution.

To provide an efficient and robust constitutive equations for concrete ion application to high rate dynamics.

Develops an explicit‐implicit integration scheme for a concrete model. This robust integration scheme ensures computational efficiency. Comparison between simulations of impact of equivalent aircraft engine projectiles and the tests carried out in Sandia laboratory also demonstrate its efficiency.

Shows that modeling transient high rate dynamic behavior of concrete is very important to take into account for design concrete structures in the cases of dynamic loading conditions, such as an impact on the structure.

Proposes an original integration scheme for a coupled rate dependent damage plasticity model. Also provides a detailed consideration of the numerical stability of this kind of scheme for rate‐dependent damage model.

Blast‐induced traumatic brain injury (TBI) is a signature injury of the current military conflicts. Among the different types of TBI, diffuse axonal injury (DAI) plays an important role since it can lead to devastating effects in the inflicted military personnel. To better understand the potential causes associated with DAI, this paper aims to investigate a transient non‐linear dynamics finite element simulation of the response of the brain white matter to shock loading.

Brain white matter is considered to be a heterogeneous material consisting of fiber‐like axons and a structure‐less extracellular matrix (ECM). The brain white matter microstructure in the investigated corpus callosum region of the brain is idealized using a regular hexagonal arrangement of aligned equal‐size axons. Deviatoric stress response of the axon and the ECM is modeled using a linear isotropic viscoelastic formulation while the hydrostatic stress response is modeled using a shock‐type equation of state. To account for the stochastic character of the brain white matter microstructure and shock loading, a parametric study is carried out involving a factorial variation of the key microstructural and waveform parameters.

The results obtained show that the extent of axon undulations and the strength of axon/ECM bonding profoundly affect the spatial distribution and magnitude of the axonal axial normal and shear stresses (the stresses which can cause diffuse axonal injury).

The present approach enables a more accurate determination of the mechanical behavior of brain white matter when subjected to a shock.

An inhomogeneous element method of solving the strain and stress distribution of a cone‐like synthetic rope termination, which is designed and manufactured to enhance the strength of end connection of the rope, is described. The 8‐node quadrilateral isoparametric axisymmetric element was used. Different material constants were specified at different Gauss sampling points, so as to simulate the non‐homogeneity of the termination. The results indicate that maximum axial stress value in strand is much larger than the element average stress value. This element proved to be useful in calculating stresses and strains in reinforcing fibre strand embedded in resin matrix. The results obtained give some insight into the non‐uniformity of the stress distribution and will be meaningful to the designer of the rope end termination.