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In the paper at hand, a modelling approach for the simulation of the anisotropic long-term behaviour of wooden structures subjected to mechanical loading at constant moisture content for the use within the framework of the Finite Element Method is presented. Using a standard-solid body-model in serial combination with a B ingham -element allows for the differentiation between linear viscoelastic and non-linear viscoelastic–viscoplastic behaviour with respect to the applied stress level. Creep failure is considered by means of the concept of strain-energy density. Due to the cylindrical anisotropy of wood, the four material properties required for the description of the creep behaviour are determined depending on material direction and loading type (tension, compression, shear) by means of the re-calculation of experimental results. Finally the approach is applied to the re-calculation of two test-series in bending and to the analysis of a face staggered joint. The paper at hand is the first part of a more complex model and deals with the mechanical long-term behaviour of wood. In the second part, the hygro-mechanical coupling is covered with respect to the consideration of the influence of moisture content on mechanically induced creep and mechano-sorptive effects caused by simultaneous mechanical loading and moisture changes. [ABSTRACT FROM AUTHOR]

Contributions of 15 convex polyhedral particle shapes to the overall elastic properties of particle-reinforced composites are predicted using micromechanical homogenization and direct finite element analysis approaches. The micromechanical approach is based on the combination of the stiffness contribution tensor ( N -tensor) formalism with Mori–Tanaka and Maxwell homogenization schemes. The second approach involves FEA simulations performed on artificial periodic representative volume elements containing randomly oriented particles of the same shape. The results of the two approaches are in good agreement for volume fractions up to 30%. Applicability of the replacement relation interrelating N -tensors of the particles having the same shape but different elastic constants is investigated and a shape parameter correlated with the accuracy of the relation is proposed. It is concluded that combination of the N-tensor components of the 15 shapes presented for three values of matrix Poisson's ratios with the replacement relation allows extending the results of this paper to matrix/particle material combinations not discussed here. [ABSTRACT FROM AUTHOR]

An analytical formulation has been developed in this article for predicting the equivalent elastic properties of irregular honeycombs with spatially random variations in cell angles. Employing unit-cell based approaches, closed-form expressions of equivalent elastic properties of regular honeycombs are available. Closed-form expressions for equivalent elastic properties of irregular honeycombs are very scarce in available literature. In general, direct numerical simulation based methods are prevalent for this case. This paper proposes a novel analytical framework for predicting equivalent in-plane elastic moduli of irregular honeycombs using a representative unit cell element (RUCE) approach. Using this approach, closed-form expressions of equivalent in-plane elastic moduli (longitudinal and transverse Young’s modulus, shear modulus, Poisson’s ratios) have been derived. The expressions of longitudinal Young’s modulus, transverse Young’s modulus, and shear modulus are functions of both structural geometry and material properties of irregular honeycombs, while the Poisson’s ratios depend only on structural geometry of irregular honeycombs. The elastic moduli obtained for different degree of randomness following the proposed analytical approach are found to have close proximity to direct finite element simulation results. [ABSTRACT FROM AUTHOR]

Bio-inspired adhesion of micropatterned surfaces due to intermolecular interactions has attracted much research interest over the last decade. Experiments show that the best adhesion is achieved with compliant “mushroom”-shaped fibrils. This paper analyses numerically the effects of different mushroom shapes on adhesion to a rigid substrate. When a remote stress is applied on the free end of a fibril perfectly bonded to a rigid substrate, the resultant stress distribution along the fibril is found to change dramatically between the straight punch and mushroom fibrils. A singular stress field is present at the edge of the fibril where it contacts the substrate and, in this work, the amplitude of the singularity is evaluated for fibrils perfectly bonded to a flat substrate so that sliding cannot occur there. This exercise is carried out for fibril geometries involving combinations of different diameters and thicknesses of the mushroom cap. By assuming a pre-existing detachment length at the corner where the stress singularity lies, we predict the adhesive strength for various mushroom cap shapes. Our study shows that a smaller stalk diameter and a thinner mushroom cap lead to higher adhesive strengths. A limited number of results are also given for other shapes, including those having a fillet radius connecting the stalk to the cap. The results support the rational optimisation of synthetic micropatterned adhesives. [ABSTRACT FROM AUTHOR]

The paper presents a numerical implementation of the ZM model for shape memory alloys (Zaki and Moumni, 2007a) that fully accounts for nonproportional loading and its influence on martensite reorientation and phase transformation. Detailed derivation of the time-discrete implicit integration algorithm is provided, including an explicit closed-form expression for the continuous material jacobian. The algorithm is used for finite element simulations using Abaqus, in which the model is implemented by means of a user material subroutine. Extensive validation of the model is provided against multiple sets of experimental and numerical simulation data taken from the literature. [ABSTRACT FROM AUTHOR]

Abstract: The main purpose of this work is the computational simulation of the sensitivity coefficients of the homogenized tensor for a polymer filled with rubber particles with respect to the material parameters of the constituents. The Representative Volume Element (RVE) of this composite contains a single spherical particle, and the composite components are treated as homogeneous isotropic media, resulting in an isotropic effective homogenized material. The sensitivity analysis presented in this paper is performed via the provided semi-analytical technique using the commercial FEM code ABAQUS and the symbolic computation package MAPLE. The analytical method applied for comparison uses the additional algebraic formulas derived for the homogenized tensor for a medium filled with spherical inclusions, while the FEM-based technique employs the polynomial response functions recovered from the Weighted Least-Squares Method. The homogenization technique consists of equating the strain energies for the real composite and the artificial isotropic material characterized by the effective elasticity tensor. The homogenization problem is solved using ABAQUS by the application of uniform deformations on specific outer surfaces of the composite RVE and the use of tetrahedral finite elements C3D4. The energy approach will allow for the future application of more realistic constitutive models of rubber-filled polymers such as that of Mullins and for RVEs of larger size that contain an agglomeration of rubber particles. [Copyright &y& Elsevier]

Abstract: In this paper, a method to estimate fracture toughness, , from the first indenter-induced circumferential crack in a thin film is suggested. The method is based on the stresses in the film and finite element simulations are used to estimate these stresses. The film is taken to be linear elastic while plasticity is included in the substrate. Delamination is not taken into account in the method and the film is perfectly bonded to the substrate. The stress in the film is used to estimate the location where the circumferential crack will initiate from a defect in the film surface. The location is found to be at a distance away from the indenter which correlate with experiments. Also, the stress is used to calculate the stress intensity factor and the energy release rate for a plane strain crack. The energy release rate for the plane strain crack is then used to calculate the energy release for a crack channeling around the indenter forming the circumferential crack. By the energy release rate for the channeling crack fracture toughness is estimated independent of the initial defects in the film provided such defects exist. If the initial defects are smaller than a required minimum value, fracture toughness is overestimated by this method and this overestimation is calculated. Besides fracture toughness, the energy release rate for the channeling crack is used to estimate the depth of the plane strain crack which is found to be smaller than the film thickness. The method is used to estimate the fracture toughness, , for an alumina ( ) film using the critical indentation depth. In order to verify the result the estimated crack radius is compared to the actual radius of the circumferential crack in the alumina. The differences between the two radius is found to be within a few percent. [Copyright &y& Elsevier]

Abstract: This paper investigates the deformation and failure mechanisms of wood at the ultrastructural scale. At this level, wood is composed of a periodic alternation of amorphous and crystalline cellulose fractions, embedded in a soft hemicellulose-lignin matrix. The mechanical response of wood is calculated under tensile loading conditions by means of the computational homogenisation of a representative volume element (RVE) of material. Three potential mechanisms of failure are suggested: axial straining of the crystalline fraction of cellulose, accumulation of plastic strain in the amorphous portion of cellulose and tensile rupture in the hemicellulose-lignin matrix due to cellulose fibres separation. In order to validate the present multi-scale framework, we compare our numerical predictions for the reorientation of cellulose fibres with experimental data, finding a good agreement for a wide range of strains. Furthermore, we assess successfully our numerical predictions for ultimate strains at the instant of failure when compared to experimental values. Numerical simulations show that our model is able to provide new clues into the understanding of how trees and plants optimise their microstructure in order to develop larger strains without apparent damage. A remarkable prediction by our model suggests that the extensibility of the material is maximised for initial microfibril angles (MFA) between 50° and 55°, a range of values found typically in branches of trees, in which the extensibility is an essential requirement. These findings are likely to shed more light into the dissipative mechanisms of wood and natural materials, which are still not well-understood at present. [Copyright &y& Elsevier]

Abstract: This paper presents a comparison with experimental data of the resistance of stiffened panels to penetration damage. It also carried out comparisons between numerical simulations and experiments investigating the grounding of ships. The finite element method and FEA software are used to predict penetration damage and this modelling simulation is then extended to investigate damage to a ship’s double bottom structure in different grounding scenarios. The progressive failure of the double bottom is investigated in terms of plastic deformation and also the evolution of damage including material rupture. Three different levels of complexity were used in modelling the double bottom structure concerning the inner and outer shell plating; longitudinal stiffeners in the shell plating, and structures with stiffening in longitudinal floors. The analysis was carried out in the ABAQUS explicit code. The results presented include the crushing force as a function of time, an investigation of the energies involved in the plastic deformation and rupture of the double bottom structure, and comparisons with experimental data where available. [Copyright &y& Elsevier]

Abstract: In this paper we revisit a strain-adaptive bone remodelling problem, assuming that the rate of the apparent density at a particular location is described as a local objective function and depending on a particular stimulus at that location. Normally, continuum mathematical descriptions of adaptive bone remodelling can lead to discontinuous solutions on the global apparent density distribution. To improve this numerical solution, in this work, as the main novelty, we include the diffusion of the bone remodelling into the model. The variational problem is written as a coupled system of a nonlinear variational equation for the displacement field and a parabolic elliptic variational inequality for the apparent density. An existence and uniqueness result is stated. Then, a fully discrete problem is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. A priori error estimates are proved from which, under adequate additional regularity conditions, the linear convergence of the algorithm is deduced. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximation and the behaviour of the solution. [Copyright &y& Elsevier]

Abstract: Systems consisting of a hard layer resting on an elastic graded soft substrate are frequently encountered both in nature and industry. In this paper, we study the surface wrinkling problem of such a composite system subjected to in-plane compression. The Young’s modulus of the elastic substrate is assumed to vary along its depth direction. In particular, we investigate two typical variations in the modulus, described by a power function and an exponential function, respectively. Analytical solutions which permit to determine the critical compressive strain for the onset of wrinkling and the wrinkling wavelength are derived. A series of finite element simulations are performed to validate the theoretical solutions and demonstrate the prominent features of the postbuckling evolution of the system. The results may not only find applications in thin-film metrology and surface patterning but also provide insight into the wrinkling phenomena of various living tissues. [Copyright &y& Elsevier]

Abstract: In this paper, we established a strain-gradient damage model based on microcrack analysis for brittle materials. In order to construct a damage-evolution law including the strain-gradient effect, we proposed a resistance curve for microcrack growth before damage localization. By introducing this resistance curve into the strain-gradient constitutive law established in the first part of this work (), we obtained an energy potential that is capable to describe the evolution of damage during the loading. This damage model was furthermore implemented into a finite element code. By using this numerical tool, we carried out detailed numerical simulations on different specimens in order to assess the fracture process in brittle materials. The numerical results were compared with previous experimental results. From these studies, we can conclude that the strain gradient plays an important role in predicting fractures due to singular or non-singular stress concentrations and in assessing the size effect observed in experimental studies. Moreover, the self-regularization characteristic of the present damage model makes the numerical simulations insensitive to finite-element meshing. We believe that it can be utilized in fracture predictions for brittle or quasi-brittle materials in engineering applications. [Copyright &y& Elsevier]

Abstract: Metal matrix composites (MMCs) comprising nano/microcrystalline matrices and reinforcements exhibit impressive mechanical behaviors derived by exploiting the size effects due to development of geometrically necessary dislocations. In such nanostructured MMCs intricate interactions between the grain size dg and inclusion size di may exist in their overall response, but are difficult to isolate in experiments and are also not accounted for in the size-dependent homogenized models. In this paper, we computationally investigate the grain size–inclusion size interaction in model MMCs architectures wherein the grains and inclusions are explicitly resolved. A mechanism-based slip-gradient crystal plasticity formulation () is implemented in a finite element framework to model polycrystalline mass as an aggregate of randomly oriented single crystals that host elastic inclusions. The slip gradients that develop across grain boundaries and at inclusion–grain interfaces during deformation result in length-scale dependent responses that depend on both dg and di , for a fixed inclusion volume fraction f. For a given di and f, the overall hardening exhibits a nonlinear dependence on grain size for dg ⩽ di indicating that interaction effects become important at those length-scales. Systematic computational simulations on bare polycrystalline and MMC architectures are performed in order to isolate the contributions due to grain size, inclusion size and the interaction thereof. Based on these results, an analytical model developed for the interaction hardening exhibits a Hall–Petch type dependence on these microstructural sizes that can be incorporated into homogenized approaches. [Copyright &y& Elsevier]

Abstract: Laminated paperboard is often used as a packaging material for products such as toys, tea and frozenfoods. To make the paperboard packages appealing for consumers, the fold lines must be both neat and undamaged. The quality of the folds depends on two converting processes: the manufacture of fold lines (creasing) and the subsequent folding. A good crease contains some delamination, initiated during creasing, to reduce the bending stiffness and to prevent the board from breaking during folding. However, for boards of high grammage breaking of the top layer is nevertheless a frequent problem. The mechanisms that operate in the creasing zone during creasing and folding, and that may thus result in breaking of the top layer, are studied in this contribution on the basis of idealized small-scale creasing and folding experiments. However, since experimental observations are only limited means to study the paperboard’s behavior, a mechanical model is proposed to obtain more detailed insight. Although the material and delamination descriptions used in the mechanical model are both relatively straightforward, comparisons between the model and the experimental data show that the model predicts the paperboard’s response well. The mechanical model shows – in combination with experimental strain fields – that multiple delaminations are initiated in the shear regions. Moreover, only the mechanical model reveals the mechanism that is responsible for the failure of the top layer if a crease is too shallow. Finally, the model also demonstrates that not only delamination but also plastic behavior must occur during creasing if breaking of the top layer is to be avoided. [Copyright &y& Elsevier]

Abstract: This paper deals with a finite element algorithm for the creep crack growth process in a viscoelastic medium. The main developments focus on the coupling between the M-integral and an incremental formulation for the viscoelastic behavior. In this context, mixed mode configurations are simulated for orthotropic symmetries. An algorithm uncoupling viscoelastic incremental formulation and the fracture procedure is resolved with finite element software. The global approach is validated in terms of the evolution of energy release rate versus time and the advance of cracks. Numerical simulations are based on a Constant Tension Shear model. The insensitivity of the M-integral to the integration domain is shown from creep crack growth simulations for mixed mode configurations. [Copyright &y& Elsevier]

Abstract: This paper employs static atomistic simulations to investigate the effect of a void on the nanoindentation of Cu (111). The simulations minimize the potential energy of the complete system via finite element formulation to identify the equilibrium configuration of any deformed state. The size and depth of the void are treated as two variable parameters. The numerical results reveal that the void disappears when the indentation depth is sufficiently large. A stress concentration is observed at the internal surface of the void in all simulations cases. The results indicate that the presence of a void has a significant influence on the nanohardness extracted from the nanoindentation tests. [Copyright &y& Elsevier]

Abstract: This paper provides a theoretical and numerical framework to investigate the interactions between domain walls and arrays of dislocations in ferroelectric single crystals. A phase-field approach is implemented in a non-linear finite element method to determine equilibrium solutions for the coupled electromechanical interactions between a domain wall and a dislocation array. The numerical simulations demonstrate the effect of the relative size and orientation of dislocations on 180° and 90° domain wall configurations. In addition, results for the pinning strength of dislocations in the case that domain walls move due the application of external electric field and shear stress are computed. The presented numerical results are compared with the findings reported for charged defects and it is shown that non-charged defects, such as dislocations, can also interact strongly with domain walls, and therefore affect the ferroelectric material behavior. [Copyright &y& Elsevier]