Computational up-scaling of anisotropic swelling and mechanical behavior of hierarchical cellular materials

The hygro-mechanical behavior of a hierarchical cellular material, i.e. growth rings of softwood is investigated using a two-scale micro-mechanics model based on a computational homogenization technique. The lower scale considers the individual wood cells of varying geometry and dimensions. Honeycomb unit cells with periodic boundary conditions are utilized to calculate the mechanical properties and swelling coefficients of wood cells. Using the cellular scale results, the anisotropy in mechanical and swelling behavior of a growth ring in transverse directions is investigated. Predicted results are found to be comparable to experimental data. It is found that the orthotropic swelling properties of the cell wall in thin-walled earlywood cells produce anisotropic swelling behavior while, in thick latewood cells, this anisotropy vanishes. The proposed approach provides the ability to consider the complex microstructure when predicting the effective mechanical and swelling properties of softwood.     

双轴受压状态下的高延性纤维增强水泥基复合材料本构模型

基于Darwin和Pecknold考虑混凝土双轴力学行为的方法,建立一个同时考虑双轴受压状态下非线性力学行为和抗压强度变化的高延性纤维增强水泥基复合材料(ECC)二维正交各向异性本构模型。在因双轴加载而产生的正交各向异性的2个方向上引入等效单轴应变,建立非线性应力-等效单轴应变关系以考虑ECC的双轴非线性行为,并采用一条双轴强度包络线确定2个方向上的抗压强度。推导模型的显式数值算法,编写包含该算法的用户自定义材料子程序UMAT,并嵌于有限元计算程序ABAQUS v6.14中。通过对两组不同配合比的ECC试件在不同应力比下的双轴受压加载试验进行数值分析验证本模型的有效性。数值计算得到的主压应力方向上的应力-应变曲线及预测的抗压强度与试验结果吻合较好,表明该文提出的本构模型能够有效地预测ECC在双轴受压状态下的非线性力学行为和破坏强度。     

Shear coupling effects on stress and strain distributions in wood subjected to transverse compression

The mechanical behaviour of a wood board subjected to transverse compression is relevant to the performance of glulam beams and solid wood structures. The wood material can be described as polar orthotropic, due to the annual ring structure and to the differences in moduli in different directions in the radial–tangential plane. Strain measurements are performed on single wood boards using a whole-field digital speckle photography technique. Finite element analysis is performed and compared with experimental data. Good agreement in terms of strain fields and apparent moduli is observed between predictions and data. The experimental data show strong variations in local strain due to the polar orthotropic behaviour of wood in this plane, and the extremely low value for shear modulus G_rt as compared with the other moduli. This leads to shear coupling effects resulting in large local shear deformation and correspondingly low effective stiffness under transverse global loading.     

A MULTIAXIAL FATIGUE DAMAGE MODEL FOR ORTHOTROPIC MATERIALS UNDER PROPORTIONAL LOADING

A new multiaxial fatigue damage model for orthotropic materials is proposed based on the strain vector. Six material constants are included in the model. These material constants represent the dependence of fatigue resistance on material orientation, and they can be obtained by conducting strain-controlled uniaxial fatigue tests along the three principal orthotropic directions of an orthotropic material. The model can also be transformed in new coordinate systems to predict the fatigue lives of new material orientations. Biaxial low-cycle fatigue tests are conducted to verify the model. The prediction of the model agrees with the experimental results reasonably well.     

A continuum model for remodeling in living structures

A new remodeling theory accounting for mechanically driven collagen fiber reorientation in cardiovascular tissues is proposed. The constitutive equations for the living tissues are motivated by phenomenologically based microstructural considerations on the collagen fiber level. Homogenization from this molecular microscale to the macroscale of the cardiovascular tissue is performed via the concept of chain network models. In contrast to purely invariant-based macroscopic approaches, the present approach is thus governed by a limited set of physically motivated material parameters. Its particular feature is the underlying orthotropic unit cell which inherently incorporates transverse isotropy and standard isotropy as special cases. To account for mechanically induced remodeling, the unit cell dimensions are postulated to change gradually in response to mechanical loading. From an algorithmic point of view, rather than updating vector-valued microstructural directions, as in previously suggested models, we update the scalar-valued dimensions of this orthotropic unit cell with respect to the positive eigenvalues of a tensorial driving force. This update is straightforward, experiences no singularities and leads to a stable and robust remodeling algorithm. Embedded in a finite element framework, the algorithm is applied to simulate the uniaxial loading of a cylindrical tendon and the complex multiaxial loading situation in a model artery. After investigating different material and spatial stress and strain measures as potential driving forces, we conclude that the Cauchy stress, i.e., the true stress acting on the deformed configuration, seems to be a reasonable candidate to drive the remodeling process.     

Experimental characterization of orthotropic technical textiles under uniaxial and biaxial loading

The paper deals with the development of an experimental protocol for the mechanical characterization of plain weave technical textiles. The textiles are modelled as orthotropic materials with known directions of material symmetry, and a “linear-by-step” approximation is introduced to account for the nonlinearity exhibited by the stress–strain behaviour. Material coefficients are determined by fitting uniaxial stress–strain curves along the warp, weft and 45° directions. The full-field evaluation of the strain distribution on the specimen surface, carried out by an optical approach, allows to assess the absence of edge effects and to quantify the shear strains introduced by off-axis loading.The protocol is applied to the characterization of a monofilament polyester textile and the model identified upon uniaxial data is validated by comparing analytical simulations with experimental data obtained under biaxial stress conditions. Finally the reliability of failure criteria based upon both uniaxial and biaxial data is investigated.     

Applicability of classical isotropic fracture mechanics specimens to wood crack propagation studies

Different specimen types (double cantilever beam: DCB, compact tension: CT, single edge notched in tension: SENT) have been numerically studied (with special finite elements) for ten wood species and for cracks situated in a material plane of symmetry (the crack is denoted xy with x the direction of the normal to the crack plane and y the direction of propagation). Single-edge notched speciments used in RL, TL directions appear to be insensitive to the orthotropic properties of the material. So, calibration known for isotropic materials can be used in stress intensity factor calculations. In transverse directions (LT, LR), such specimens could be used with a double height. Small differences, but depending on the species tested, have also been obtained in TR and RT directions. Calibration of CT specimens of an isotropic material cannot be used even in TL and RL directions. A calibration acceptable for all the studied species is proposed. A different calibration is also given in the TR direction. It is suggested, however, not to use specimens in the RT direction without a calibration specific for the wood species tested. DCB specimens could be used in RL, TL and TR directions with a calibration which is a function of elastic moduli. This calibration is obtained from analytical calculations. In other directions, these specimens do not offer any experimental interest.     

A 3D moisture-stress FEM analysis for time dependent problems in timber structures

This paper presents a 3D moisture-stress numerical analysis for timber structures under variable humidity and load conditions. An orthotropic viscoelastic-mechanosorptive material model is specialized on the basis of previous models. Both the constitutive model and the equations needed to describe the moisture flow across the structure are implemented into user subroutines of the Abaqus finite element code and a coupled moisture-stress analysis is performed for several types of mechanical loads and moisture changes. The presented computational approach is validated by analyzing some wood tests described in the literature and comparing the computational results with the reported experimental data.     

Numerical modelling of ductile damage evolution in tensile and bending tests of timber structures

The characteristic values for strength and stiffness of all sorts of timber products are based on the assumption of a linear relation between stress and strain prior to failure and consequently verification of the load-bearing capacity of individual members in a construction is also based on a similar linear relation. Such an approach is very conservative and ill suited for performance-based design, which requires a full analysis of the structure with the possibility of moment and/or stress redistribution within parts of the structure. The development of material models that encompass the complex behaviour of wood is therefore necessary. The present work presents a model formulated within the frameworks of plasticity and continuum damage mechanics (CDM). It applies the classical flow theory of plasticity to formulate ductile failure of wood in compression and damage mechanics for the brittle failure modes. It takes into account the orthotropic elastic behaviour, the plastic anisotropic isotropic hardening, the isotropic ductile damage, and the large plastic deformations. The model was used to predict the initiation and growth of ductile damage in tensile and bending tests on different timbers types. Good agreement was found between the predictions of the model and the experimental results.     

Étude des paramètres de fabrication d'un béton de bois à matrice argileuse

The subject of the present study is to highlight the use of clay waste resulting from the operations of aggregate quarries through developing lightened clayey concretes. The lightening is achieved by adding wood aggregates, which are waste materials from woodworking activities. The authors account for the influence of components on the mechanical characteristics of hardened concretes and on the behaviour of the material just after mixing. They propose a formulation allowing the development a dry material with a volumic weight equal to 800 kg/m³ and a compressive strength, at hydrous stability, equal to 2.5 MPa offering the possibility tof being poured easily. Attempts at treating wood aggregates have proved the necessity for a systematic study to take into account the specificity of clay.     

A simple model describing the non-linear biaxial tensile behaviour of PVC-coated polyester fabrics for use in finite element analysis

A simple model based on experimental observations of the yarn-parallel biaxial extension of PVC-coated polyester fabric cruciform specimens is proposed. In situ loading conditions are considered. The material behaviour is assumed to be plane stress orthotropic for a particular load ratio, while the elastic properties can vary with the load ratio in order to represent the complex interaction between warp and fill yarns. A linear relationship is experimentally found between elastic moduli and normalized load ratios for a wide range of PVC-coated polyester (Type I to Type IV). Two new parameters corresponding to the moduli variations are introduced to complement the existing plane stress orthotropic model. Theoretical results show that only five biaxial tests are required to accurately describe the material response with the proposed material model. Finally, the model was integrated in a commercial finite element software. It is shown that the proposed material model significantly increases the accuracy of the finite element predictions compared to the standard orthotropic linear material model with almost identical computation times.     

ELASTO-PLASTIC INTERFACE MODEL FOR 3D-FRICTIONAL ORTHOTROPIC CONTACT PROBLEMS

The present study deals with the solution of the fully three-dimensional contact/friction problem taking into account microstructural characteristics of the surfaces. An incremental non-associated hardening friction law model analogous to the classical theory of plasticity is used. Two different non-linear friction functions in the orthogonal directions are used to account for the orthotropic properties of the contacting bodies. A frontal solver processing unsymmetric matrices is adopted. Two numerical examples have been selected to show applicability of the method proposed. © 1997 by John Wiley & Sons, Ltd.     

Verification of a non-local stress criterion for mixed mode fracture in wood

An extension of a non-local stress fracture criterion to orthotropic materials based on the damage model of an elastic solid containing growing microcracks was presented in this paper. By taking this approach, a new fracture condition expressed in terms of the mixed mode stress intensity factors for orthotropic materials was proposed and its applicability to predict of a crack initiation and propagation in wood was validated. Predicted values of the stress intensity factors at failure were compared to experimental observations carried out on wood specimens for cracks arbitrarily oriented with respect to the orthotropy axes. Special considerations were applied to the comparison of the non-local stress fracture criterion with some classical fracture criteria for orthotropic materials.     

A Comparison Between the EN 383 and ASTM D5764 Test Methods for Dowel‐Bearing Strength Assessment of Wood: Experimental and Numerical Investigations

Abstract: The purpose of this paper is to provide a comparison between embedding tests covered by the EN383 and ASTM D5764 standards, highlighting some difficulties regarding the application of the referred standards. These embedding tests are essential to evaluate the embedding strength of wood, which is required for the assessment of joints strength. The proposed comparison is based either on experimental data and numerical simulations through the finite element (FE) method. Tests were performed on maritime pine wood (Pinus pinaster Ait. species) according to the longitudinal and radial directions, allowing the comparison of the embedding strength and elastic foundation modulus. Three dimensional FE models of the tests were built using contact elements technology and assuming the steel dowel and wood as linear elastic isotropic and orthotropic materials, respectively. The contact modelling is a challenging topic for which this paper also proposes some guidance. The test configuration proposed in the EN383 standard for assessment of the embedment strength in compression is more susceptible to the dowel bending than the half‐hole test configuration proposed in the ASTM D5764 standard. The numerical simulation of the EN383 embedding test raises some additional difficulties regarding the dowel boundary conditions.     

A continuum shell finite element model for impact simulation of woven fabrics

A new computational approach is developed to predict the impact behaviour of fabric panels based on the detailed response of the smallest repeating unit (unit cell) in the fabric. The unit cell is constructed and calibrated using measured geometrical (weave architecture, crimp, voids, etc.) and mechanical properties of the fabric. A pre-processor is developed to create a 3D finite element mesh of the unit cell using the measured fabric cross-sectional micro-images. To render an efficient method for simulation of multi-layer packs, these unit cells are replaced with orthotropic shell elements that have similar macroscopic (smeared) mechanical properties as the unit cell. The aim is to capture the essence of the response of a unit cell in a single representative shell element, which would replace the more complicated and numerically costly 3D solid model of the yarns in a crossover. The 3D finite element analysis of the unit cell is used to provide a baseline mechanical response for calibrating the constitutive model in the equivalent shell representation. This shell element takes advantage of a simple physics-based analytical relationship to predict the behaviour of the fabric's warp and weft yarns under general applied displacements in these directions. The analytical model is implemented in the commercial explicit finite element code, LS-DYNA, as a user material routine (UMAT) for shell elements. Layers of fabric constructed from these specialized elements are stacked together to create fabric targets that are then analysed under projectile impact. This approach provides an efficient numerical model for the dynamic analysis of multi-layer fabric structures while taking into account several geometrical and material attributes of the yarns and the fabric.     

An analytical solution for the morphological evolution of a hole in the interconnect embedded in matrix

An orthotropic model for the morphological evolution of a hole in representative interconnection lines embedded in a matrix with different line aspect (volume) ratio, under mechanical loadings, is established. The thermodynamics potential of the morphological evolution of a hole in the orthotropic model is given based on energy principle. Thus, the path and the bifurcation condition of the morphological evolution of the hole in the orthotropic model are described, which gives some insight into the reliability of the representative interconnect embedded in a matrix under mechanical loading.     

On the anisotropic elastic properties of woods

In 2003 Nature Materials article, Keckes et al. presented deformation properties of a variety of woods in relation to deformation of their individual wood cells. Their point is “The remarkable mechanical properties of biological materials reside in their complex hierarchical structure…”. This holds for mineral-based biological materials such as bone as well as for wood. Indeed, one of us (J.L.K.) introduced the concept that to explain the material properties of cortical bone, it was necessary to treat it as a complex material/structural hierarchical composite. Calculations to determine anisotropic properties of bone measured using ultrasonic wave propagation techniques, were extended to similar measurements on both soft and hard woods. These anisotropic properties calculations have been extended to include data based on mechanical measurements of orthotropic elastic constants of both soft and hard woods for comparison with both earlier ultrasonic measurements and mechanical testing on other woods. This work illustrates the fact that understanding and modeling the properties of wood is a complex task as the symmetry changes with scale. For example, lignin is isotropic, hemicellulose and cellulose are transversely isotropic, while the cells and microstructure have orthotropic symmetry.

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Application of an orthotropy rescaling method to edge cracks and kinked cracks in orthotropic two-dimensional solids

Oblique edge cracks and kinked cracks in orthotropic materials with inclined principal material directions under inplane loadings are investigated. The Stroh formalism is modified by introducing new complex functions, which recovers a classical solution for a degenerate orthotropic material with multiple characteristic roots. An orthotropy rescaling technique is presented based on the modified Stroh formalism. Stress intensity factors for edge cracks as well as kinked cracks are obtained in terms of solutions for a material with cubic symmetry by applying the orthotropy rescaling method. Explicit expressions of the stress intensity factors for a degenerate orthotropic material are obtained in terms of solutions for an isotropic material. The effects of orthotropic parameter, material orientation, and crack angle on the stress intensity factors for the degenerate orthotropic material are discussed. The stress intensity factors for cubic symmetry materials are calculated from finite element analyses, which can be used to evaluate the stress intensity factors for orthotropic materials. The energy release rate for the kinked crack in an orthotropic material is also obtained.     

Mode II fracture testing method for highly orthotropic materials like wood

In this paper a mode II fracture testing method has been developed for wood from analytical, experimental and numerical investigations. Analytical results obtained by other researchers showed that the specimen geometry and loading type used for the proposed mode II testing method results in only mode II stress intensity and no mode I stress intensity at the crack tip. Experiments have been carried out to determine mode II fracture toughness K _IIC and fracture energy G _IIF from the test data collected from both spruce (pice abies) and poplar (populus nigra) specimens. It was found that there existed a very good relation between fracture toughness K_IIC and fracture energy G _IIF when the influence of orthotropic stiffness E _II ^* in mode II was taken into account. It verified that for this mode II testing method the formula of LEFM can be employed for calculating mode II fracture toughness even for highly orthotropic materials like wood. In the numerical studies for the tested spruce specimen, the crack propagation process, stress and strain fields in front of crack tips and the stress distributions along the ligament have been investigated in detail. It can be seen that the simulated crack propagating process along the ligament is a typical shear cracking pattern and the development of cracks along the ligament is due to shear stress concentrations at the crack tips of the specimen. It has been shown that this mode II fracture testing method is suitable for measuring mode II fracture toughness K _IIC for highly orthotropic materials like wood.