Borys Drach

Fraction-exponential representation of the viscoelastic properties of dentin

We propose the fraction-exponential description of the viscoelastic properties of dentin. Creep tests are performed on specimens cut from the molar coronal part. Four parameters determining instantaneous and long term Youngs moduli as well as the relaxation time are extracted from the experimental data. The same procedure is repeated using the experimental measurements of Jantarat et al (2002) for the specimens cut from the root part of incisor. Physical meaning of the parameters and the difference between them for different sets of specimens are discussed.

Modeling of Cure-Induced Residual Stresses in 3D Woven Composites of Different Reinforcement Architectures

This paper presents finite element modeling effort to predict possible microcracking of the matrix in 3D woven composites during curing. Three different reinforcement architectures are considered: a ply-to-ply weave, a one-by-one and a two-by-two orthogonal through-thickness reinforcement. To realistically reproduce the as-woven geometry of the fabric, the data from the Digital Fabric Mechanics Analyzer software is used as input for finite element modeling. The curing processed is modeled in a simplified way as a uniform drop in temperature from the resin curing to room temperature. The simulations show that the amount of residual stress is strongly influenced by the presence of through-thickness reinforcement.

A Novel Small-Specimen Planar Biaxial Testing System With Full In-Plane Deformation Control

Simulations of soft tissues require accurate and robust constitutive models, whose form is derived from carefully designed experimental studies. For such investigations of membranes or thin specimens, planar biaxial systems have been used extensively. Yet, all such systems remain limited in their ability to: (1) fully prescribe in-plane deformation gradient tensor F2D, (2) ensure homogeneity of the applied deformation, and (3) be able to accommodate sufficiently small specimens to ensure a reasonable degree of material homogeneity. To address these issues, we have developed a novel planar biaxial testing device that overcomes these difficulties and is capable of full control of the in-plane deformation gradient tensor F2D and of testing specimens as small as ∼4 mm × ∼4 mm. Individual actuation of the specimen attachment points, combined with a robust real-time feedback control, enabled the device to enforce any arbitrary F2D with a high degree of accuracy and homogeneity. Results from extensive device validation trials and example tissues illustrated the ability of the device to perform as designed and gather data needed for developing and validating constitutive models. Examples included the murine aortic tissues, allowing for investigators to take advantage of the genetic manipulation of murine disease models. These capabilities highlight the potential of the device to serve as a platform for informing and verifying the results of inverse models and for conducting robust, controlled investigation into the biomechanics of very local behaviors of soft tissues and membrane biomaterials.

Micromechanical Modeling of Heterogeneous Materials with Irregularly Shaped Pores

An approach to predict the overall mechanical properties of materials containing pores of irregular shapes is described. Micromechanical modeling is performed by evaluating cavity compliance contribution tensors of individual pores [1] which are then used as an input for well-developed homogenization models. The cavity compliance contribution tensor can be found either analytically or numerically depending on the pore geometry and the level of anisotropy of the surrounding material. The results of numerical analysis can be used to compare the ability of differently shaped pores to initiate fracture.

Viscoelasticity and plasticity mechanisms of human dentin

Theoretical models of viscoelastic behavior and plastic deformation mechanisms of human dentin are considered. Using the linear viscoelasticity theory in which creep and relaxation kernels have the form of fraction-exponential functions, numerical values of instantaneous and long-time Young’s moduli and other characteristics of dentin viscoelasticity under uniaxial compression are found. As dentin plastic deformation mechanisms, mutual collagen fiber sliding in the region of contact of their side surfaces, separation of these fibers from each other, and irreversible tension of some collagen fibers, are proposed. It is shown that the second mechanism activation requires a smaller stress than that for activating others. The models of plastic zones at the mode I crack tip, which correspond to these mechanisms, are studied. It is shown that the plastic zone size can increase from a few hundreds of nanometers to hundreds of micrometers with increasing applied stress.

Effect of micromechanical parameters of composites with wavy fibers on their effective response under large deformations

Abstract The large deformation response of composites reinforced by continuous wavy fibers is investigated using three-dimensional Finite Element Analysis. The focus is placed on in-phase fibers with circular cross-sections following sinusoidal paths. The effects of the following micromechanical parameters are analyzed – relative fiber radius, fiber crimp ratio, fiber arrangement and matrix material compressibility. In addition, the responses predicted by three-dimensional and two-dimensional plane strain models are compared. The considered composite is modeled as a fully periodic wavy unit cell subjected to periodic boundary conditions and three load cases – elongations in the x1 (longitudinal) and x2 (transverse) directions, and simple shear in the x1–x2 plane. Both constituents of the composite, the fibers and the matrix, are modeled using an isotropic hyperelastic material formulation. The results are presented as plots of macroscopic Cauchy stress components versus applied stretch (or strain in the case of the shear loading) and of fiber undulation versus applied stretch for the longitudinal elongation.

Prediction of Damage Initiation and Simulation of Damage Propagation in 3D Woven Composites During Processing

Some configurations of 3D woven composites are known to be susceptible to processing induced damage in the form of microcracks that develop in the polymer matrix during curing. The microcracking is believed to originate from high residual stresses that develop due to a significant mismatch in the coefficients of thermal expansion between the constituent materials. In this paper, we investigate the applicability of several commonly used stress-based failure criteria for glassy polymers – the von Mises, the Bauwens (Drucker-Prager), the parabolic stress, and the dilatational strain energy density. We study the microcracking phenomenon on the example of the one-to-one orthogonal configuration of the epoxy matrix/carbon fiber 3D woven composites. This configuration is characterized by the high level of the throughthickness reinforcement which appears to exacerbate the matrix damage. The investigation is based on a high-fidelity mesoscale finite element model of an orthogonally reinforced 3D woven composite. We simulate the material’s response to the uniform temperature drop from the curing to room temperature and compare the results of the simulation with the X-ray computed microtomography. We conclude that the curing induced matrix failure is well predicted by the parabolic stress criterion with a proper choice of the material constants. Initiation and propagation of this failure are simulated via sequential deactivation of the elements exceeding the allowable equivalent stress.

Comparison of Full Field and Single Inclusion Approaches to Homogenization of Composites with Non-Ellipsoidal Pores

This paper compares two approaches to predict the overall mechanical properties of solids with irregularly shaped pores. The first approach involves direct finite element simulations of representative volume elements containing arrangements of irregularly shaped pores subjected to periodic boundary conditions. The second approach utilizes numerical results for individual defect shapes in a micromechanical scheme. Several realizations of parallel and randomly oriented distributions of defects are considered. It is determined that the Mori-Tanaka micromechanical scheme provides good correlation with the full field finite element simulations.