Bimodular Behavior Research Articles

Formulation of a nonlocal bimodular damage model based on mechanical properties parametrization

Material media representation by damage models presents difficulties in the parametrization process. The damage laws are generally written as functions of mathematical variables and, in many cases, without physical meaning. This lack of connection between the evolution of degradation and the material properties requires a diversity of tests to numerically reproduce results obtained experimentally, which makes such a process slow, costly, and subjective. Based on this context, a constitutive model capable of describing the material response with damage evolution laws defined in terms of material parameters obtained from experimental tests is proposed in this paper to overcome parametrization adversities. Such a model is focused on reproducing the bimodular behavior of quasi-brittle materials, such as concrete, which respond differently to tension and compression efforts. While these materials have a significant resistance under compression, they manifest cracks when subjected to tension, collapsing due to fracturing. The current model presents a nonlocal character as a regularization technique to avoid strain localization phenomena. The nonlocal equivalent strains are calculated according to the principal strains associated with uniaxial constitutive laws and physical parameters obtained experimentally. Finally, numerical simulations are conducted to validate and verify the constitutive model performance to represent the response of concrete structures.

Evaluation of Bi-modular Behavior of Rocks Subjected to Uniaxial Compression and Brazilian Tensile Testing

It is typical for rock material to be bi-modularity in terms of Young’s modulus and Poisson’s ratio. In other words, these values differ in compression ( $$E_{{\text{c}}} ,\upsilon_{c}$$ ) and in tension ( $$E_{{\text{t}}} {,}\upsilon_{{\text{t}}}$$ ). In this work, four kinds of rock materials (sandstone, marble, granite, basalt) were tested to study such bi-modularity behavior in uniaxial compression and in tension (Brazilian disc test). The compressive elastic constants were determined from uniaxial compression testing, while the tensile elastic constants were determined by an improved methodology using displacement measurement in both horizontal and vertical directions of points on the flat surface of a Brazilian disc. Digital image correlation (DIC) was used to monitor the strain and displacement field on the Brazilian disc surface. Validation of the reliability of the testing method is also carried out, and it is found that tensile cracks initiate at the disc center for all tested specimens. Then, the rationality of the determined tensile elastic constants is validated by comparison with the values obtained from the direct tensile tests. Finally, based on the experimental data, it is found that the values of $${{E_{{\text{t}}} } \mathord{\left/ {\vphantom {{E_{{\text{t}}} } {E_{{\text{c}}} }}} \right. \kern-\nulldelimiterspace} {E_{{\text{c}}} }}$$ and $${{\upsilon_{{\text{t}}} } \mathord{\left/ {\vphantom {{\upsilon_{{\text{t}}} } {\upsilon_{{\text{c}}} }}} \right. \kern-\nulldelimiterspace} {\upsilon_{{\text{c}}} }}$$ of each rock type are similar, except for marble. As the ratio of tensile to compressive strength increases, the value of $${{E_{{\text{t}}} } \mathord{\left/ {\vphantom {{E_{{\text{t}}} } {E_{{\text{c}}} }}} \right. \kern-\nulldelimiterspace} {E_{{\text{c}}} }}$$ also appears to increase slightly. Lastly, the mechanism of bi-modular behavior of rock is discussed.

Elasto-Plastic Finite Element Modeling of Short Carbon Fiber Reinforced 3D Printed Acrylonitrile Butadiene Styrene Composites

This research extends the existing classical lamination theory based finite element (FE) models to predict elasto-plastic and bimodular behavior of 3D printed composites with orthotropic material properties. Short carbon fiber reinforced acrylonitrile butadiene styrene was selected as the 3D printing material. Material characterization of a 3D printed unidirectional laminate was carried out using mechanical tests. A bimodular material model was implemented using explicit FE analysis to predict the tension and bending behavior of a 3D printed laminate. The results of the FE model predictions were experimentally validated. Hill’s yield function was effective at predicting the elasto-plastic stress–strain behavior of the laminate in tension. In bending, bimodular material behavior along with Hill’s yield function worked reasonably well in predicting the elasto-plastic bending of the laminate. The material model proposed can be used to predict the mechanical behavior of 3D printed parts with complex geometry under complex loading and boundary conditions.

Mechanical behavior of walnut (Juglans regia L.) and cherry (Prunus avium L.) wood in tension and compression in all anatomical directions. Revisiting the tensile/compressive stiffness ratios of wood

Abstract The mechanical properties of walnut (Juglans regia L.) and cherry (Prunus avium L.) woods, as frequent raw materials in cultural heritage objects, have been investigated as a function of the anatomical directions and the moisture content (MC). The strength data are decreasing with increasing MC, whereas the tensile strength in the longitudinal direction is higher by factors of 1.5–2 compared to the compression strength. Moreover, the inequality of tensile and compressive stiffness is discussed, which is a matter of debate since a long time. This so-called bimodular behavior is difficult to describe in a generalized mode due to the high data variability if tension and compression properties are analyzed on different samples. If tensile and compressive stiffness tests are performed on the same samples of walnut and cherry wood, the ratio between these properties is significantly higher than 1.

A computational micromechanics approach to evaluate elastic properties of composites with fiber-matrix interface damage

Computational micro-mechanics is employed in this work to evaluate effects of fiber-matrix interface damage on the elastic properties of polymer matrix composites with continuous glass fibers. It is assumed that damage affects local zones along the fiber and a sector on the perimeter around the fiber. Elastic modulii are evaluated using Finite Element analysis, for a range of values in damage parameters considered. The occurrence of bi-modular behavior, with differences in Young’s modulus under tension and compression, has been represented by contact without friction. Based on extensive parametric results, a Least Squares Method is employed to derive analytical expressions for each material property as a function of damage parameters. In most cases the elastic modulus has a nonlinear relation with the damage parameter in the length of the fiber, with the exception of the transverse elastic modulus under tension. The analytical expressions are used to couple micro and macro scales in an off-line scheme, without the need to perform in-time micro-scale computations.

Buckling behavior of curved composite beams with different elastic response in tension and compression

A geometrically nonlinear finite element model of a composite curved beam is presented, accounting for moderately large rotations of the cross-sections, moderately large shear strains, small axial strains, and different elastic response of the material in tension and compression (bimodular behavior). A path following procedure in displacement control is employed to compute the stability points and the post-buckling response of the given model. Several comparisons are established with different numerical approaches available in the literature, showing the accuracy of the proposed finite element scheme in the unimodular case. Some original results on the in-plane and out-of-plane buckling of bimodular arches highlight that the post-buckling response of such structures is strongly influenced by the ratios between tensile and compressive moduli.

Moisture-dependent orthotropic tension-compression asymmetry of wood

Abstract The influence of moisture content (MC) on the tension-compression (Te-Co) asymmetry of beech wood has been examined. The elastic and strength parameters, including Te and Co Young’s moduli, Poisson’s ratios, and ultimate and yield stress values, were determined and compared in terms of different MCs for all orthotropic directions. The results reveal a distinctive Te-Co strength asymmetry with a moisture dependency that is visualized clearly by the Te to Co yield stress ratio. The Te-Co asymmetry is further shown by the inequality of the elastic properties, known as the “bimodular behavior”. The latter is proven for the Young’s moduli values in the radial and tangential directions and for individual Poisson’s ratios. Although the bimodularity of the Young’s moduli is significant at low MC levels, there is no evidence of moisture dependency on the Te-Co asymmetry of the Poisson’s ratios.

Fibrous Materials as Soft Matter

This paper proposes a new type of soft matter, namely fibrous materials. The common characteristics of soft matter that are shared by fibrous materials, such as the multiphase composition, porous and highly deformable structures, and the non-negligible contributions of entropy to the material behavior are illustrated. More importantly, some unique problems, complex and interesting, yet more or less unrealized, or ignored in dealing with fibrous materials are highlighted. The study includes the packing geometry of fibers, macro—micro behavioral inconsistencies, friction and self-locking mechanisms, bi-modular behavior, and allometric or scaling problems. The fabric wrinkling or crumpling problem and its peculiar fracture behavior and failure criteria are discussed. This paper also elucidates the significance of treating fibrous materials as soft matter and the great potential of such study to materials in general and to biomaterials in particular.

Transverse stiffness properties of unidirectional fiber composites containing debonded fibers

First-principles micromechanics modeling for the determination of transverse stiffness properties of a unidirectional fiber composite with fiber–matrix interfacial debonding is presented. The composite has a packing arrangement of a periodic square array of fibers, but contains randomly distributed debonded fibers. The finite element method is employed for the exact treatment of local microscopic stress and strain fields in a representative volume element of the composite material, and of the nonlinear problem of separation and contact of fiber and matrix at debonded interface. The randomness of the distribution of debonded fibers is dealt with by means of the Monte Carlo method, and the composite stiffness properties are found as ensemble average properties over a large number of representative volume elements. Bimodular behavior of the composite under transverse loading, i.e., different stiffnesses in tension and compression, is accurately captured.

Transient analysis of delaminated smart composite structures by incorporating theFermi–Dirac distribution function

The transient response of delaminated smart composite laminates is studied using animproved layerwise laminate theory. The theory is capable of capturing interlaminarshear stresses that are critical to delamination. The Fermi–Dirac distributionfunction is combined with an improved layerwise laminate theory to model a smoothtransition in the displacement and the strain fields of the delaminated interfacesduring ‘breathing’ of delaminated layers. Stress free boundary conditions areenforced at all free surfaces. Continuity in displacement field and transverse shearstresses is enforced at each ply level. In modeling piezoelectric composite plates, acoupled piezoelectric–mechanical formulation is used in the development of theconstitutive equations. Numerical analysis is conducted to investigate the effectof nonlinearity in the transient vibration of bimodular behavior caused by thecontact impact of delaminated interfaces. Composite plates with surface-bonded orembedded sensors, subject to external loads, are also investigated to study theeffects on transient responses due to various sizes and locations of delamination.

층간 분리가 있는 지능 복합재 적층판의 동적특성에 대한 연구

The dynamic characteristics of delaminated smart composite laminates are studied using animproved layerwise laminate theory. The theory is capable of capturing interlaminar shear stresses that are critical to delamination. The presence of discrete delamination is modeled through the use of Heaviside unit step functions. Stress free boundary conditions are enforced at all free surfaces. Continuity in displacement field and transverse shear stresses are enforced at each ply level. In modeling piezoelectric composite plates, a coupled piezoelectric-mechanical formulation is used in the development of the constitutive equations. Numerical analysis is conducted to investigate the effect of nonlinearity in the transient vibration of bimodular behavior caused by the contact impact of delaminated interfaces. Composite plates with delamination, subject to external loads and voltage history from surface bonded sensors, are investigated and the results are compared with corresponding experimental results and plates without delamination.

Effect of delamination on transient history of smart composite plates

The transient analysis of delaminated composite and smart composite plates is studied using a newly developed improved layerwise laminate theory, extended to include large deformation and the interlaminar contact during ‘breathing’ phenomena in the delaminated zone. The theory is capable of capturing interlaminar shear stresses that are critical to delamination. The presence of multiple, discrete delaminations is modeled through the use of Heaviside step functions. Stress free boundary conditions are enforced at all free surfaces and continuity in displacement field and transverse shear stresses are enforced at each ply level. In modeling piezoelectric composite plates, a coupled piezoelectric-mechanical formulation is used in the development of the constitutive equations. Numerical analysis is conducted to investigate the effect of nonlinearity in the transient vibration, attributable to large displacements and rotations and to the coupled effect of the large deformation and bimodular behavior caused by the contact impact of delaminated interfaces. Composite plates with delaminations, subject to external loads and voltage history from surface bonded sensors, are investigated and the results are compared with corresponding linear transient history, experimental results and plates without delamination.

Elastic-quasi-dynamic Solution of the Mallory Tube Test

Abstract A novel numerical approach to model the bending of a straight Mallory tube into a desired configuration is described. The effect of the bimodular behavior of synthetic reinforcement cord on the bending process is reported. The reinforcement used encompasses the most widely used fibers such as polyester, nylon, and rayon. The principal strain magnitudes at the reinforcement layer are computed under pure bending. The internal inflation pressure and the angular velocity at which the tube is rotated do not have a noticeable effect on the strain magnitudes. However, the axial length of the tube, the location of the reinforcing layers inside the thickness of the tube, and the orientation of this layer have shown remarkable influence on the strain distribution. Finally, the strain magnitudes from the numerical solution are compared with the strain magnitude measured from actual photographs of the tube during testing. The calculated strain magnitudes and the measured ones were found to be in good agreement.