Micromechanics, macromechanics and constitutive modeling of the elasto-viscoplastic deformation of rubber-toughened glassy polymers

Under certain conditions, such as sufficiently low temperatures, high loading rates and/or highly triaxial stress states, glassy polymers display an unfavorable characteristic—brittleness. A technique used for reducing the brittleness (increasing the fracture toughness) of these materials is rubber toughening. While there is significant qualitative understanding of the mechanical behavior of rubber-toughened polymers, quantitative modeling tools for the large-strain deformation of rubber-toughened glassy polymers are largely lacking.In this paper, we develop a suite of numerical tools to investigate the mechanical behavior of rubber-toughened glassy polymers, with emphasis on rubber-toughened polycarbonate. The rubber particles are modeled as voids in view of their deformation-induced cavitation early during deformation. A three-dimensional micromechanical model of the heterogeneous microstructure is developed to study the effects of initial rubber particle (void) volume fraction on the underlying elasto-viscoplastic deformation mechanisms in the material, and how these mechanisms influence the macroscopic response of the material. A continuum-level constitutive model is developed for the large-strain elasto-viscoplastic deformation of porous glassy polymers, and it is calibrated against micromechanical modeling results for porous polycarbonate. The constitutive model can be used to study various boundary value problems involving rubber-toughened (porous) glassy polymers. As an example, the case of an axisymmetric notched bar is simulated for the case of polycarbonate with varying levels of initial porosity. The quality of the constitutive model calibration is assessed using a multi-scale modeling approach.     

Plastic flow in oriented glassy polymers

A manufactured product often possesses residual texture which was either incidentally or deliberately acquired during its processing history. This is particularly true for the case of polymers, where the ability to easily preferentially preorient the material in specific directions is exploited in order to obtain a higher strength product. Specific examples include synthetic fibers, and biaxially-oriented films and containers. The response of the preoriented/textured product to normal service life loading conditions will differ considerably from that of a product composed of isotropic material. This paper addresses the issue of the effects of texture on the deformation behavior of glassy polymers. Here, the physically-based constitutive model of Boyce, Parks, and Argon describing the rate, temperature, and pressure dependent inelastic deformation of initially isotropic glassy polymers is used to model the effects of preorientation (i.e., initial texture), via the use of appropriate initial conditions on internal state variables. The model is then utilized in an analysis of the effects of texture on the yield of glassy polymers and the shear localization which normally follows yielding in oriented polymers. These results are compared with trends found in experiments as reported in the literature. The effectiveness of the proposed model for the present application is also compared with earlier models of yielding of anisotropic materials such as Hill's criterion.     

Geometric characterizations of centroids of simplices

We study the centroid of a simplex in space. Primary attention is paid to the relationships among the centroids of the different k-skeletons of a simplex in n-dimensional space. We prove that the 0-dimensional skeleton and the n-dimensional skeleton always have the same centroid. The centroids of the other skeleta are generically different (as we prove), but there are remarkable instances where they coincide in pairs. They never coincide in triples for regular pyramids.     

Variational Integrators for Interconnected Lagrange–Dirac Systems

Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interconnection of simpler subsystems. Lagrange–Dirac mechanical systems provide a broad category of mathematical models that are closed under interconnection, and in this paper, we develop a framework for the interconnection of discrete Lagrange–Dirac mechanical systems, with a view toward constructing geometric structure-preserving discretizations of interconnected systems. This work builds on previous work on the interconnection of continuous Lagrange–Dirac systems (Jacobs and Yoshimura in J Geom Mech 6(1):67–98, 2014) and discrete Dirac variational integrators (Leok and Ohsawa in Found Comput Math 11(5), 529–562, 2011). We test our results by simulating some of the continuous examples given in Jacobs and Yoshimura (2014).     

Vibrational and electronic spectra of 9,10-dihydrobenzo(a)pyren-7(8H)-one and 7,8,9,10-tetrahydrobenzo(a)pyrene: an experimental and computational study

The molecular geometries, vibrational and UV-vis spectra of 9,10-dihydrobenzo(a)pyrene-7(8H)-one (9,10-H(2)BaP) and 7,8,9,10-tetrahydrobenzo(a)pyrene (7,8,9,10-H(4)BaP) were investigated using density functional theory (DFT-B3LYP), with the triple-ζ 6-311+G(d,p) and Dunning's cc-pVTZ basis sets. From the comparison of infrared experimental and calculated infrared, and Raman data comprehensive assignments are made. The calculated infrared frequencies below 1800 cm(-1) are in good agreement with experimental data, with an average deviation of <4 cm(-1). Using the B3LYP/6-311+G(d,p)//TD-B3LYP/6-311G(d,p) level of theory, transition energies, and oscillator strengths of the 30 lowest electronic absorption bands are assigned to π-π* transitions, with good qualitative agreement between experimental and simulated absorption data. In addition, the HOMO-LUMO gaps and their chemical hardness were analyzed.     

Brittle-coating-patterns evaluation

Usual interpretation of brittle-coating patterns may be erroneous in cases when two large compressive stresses are present. This note deals with a study of the mechanism of the coating cracking under those conditions. An example illustrating the situation is given.     

Folding model analysis of 10, 11B, 12C + 27Al, 39K and 40Ca

Elastic scattering angular distributions for ^{10, 11}B + ⁴⁰Ca at E_lab = 46.6 and 51.5 MeV and¹²C+³⁹K at E_lab = 54 and 63 MeV have been measured and compared with Woods-Saxon and double-folding optical models. The oscillatory structure observed previously for ¹²C + ⁴⁰Ca disappears when the projectile is changed to ^10,11B or the target is changed to ³⁹K. The angular distributions are adequately reproduced by a double-folding analysis, which employs the nucleon-nucleon potential of Bertsch et al., with a range of real normalizations N_R = 1.0–1.38. This same range of real normalizations was also able to describe previously measured ^10,11B, ¹²C + ²⁷A1 data. The double-folding analysis of ¹²C + ⁴⁰Ca scattering indicates that this system behaves differently from neighboring systems.     

A ROLE FOR STEROLS IN THE PORPHYRIN MEDIATED PHOTOSENSITIZATION OF YEAST

The yeast Saccharomyces cerevisiae was used as a model system to determine the role of sterols in the porphyrin mediated photosensitization of yeast. A sterol auxotroph, RD5-R, was grown on sterols with different levels of unsaturation and assayed for photosensitivity in the presence of either protoporphyrin IX or hematoporphyrin (both at 100 micrograms/ml). Cells grown on the completely saturated sterol (stanol), cholestanol, were substantially more resistant to the photosensizing effects of the porphyrin. We hypothesize that this resistance arises from the inability of the porphyrin to mediate the oxidation of the membrane sterol. Our results indicate that photodegradation of the native yeast sterol, ergosterol, can account for substantial losses of cell viability.     

The ordered dispersal of point defects over cubic lattices: Application to fluorite-related structures

Superlattices, formed by ordering one kind of defect among the sites of a cubic lattice, may be generated by the repetition of an octahedral unit which has a defect at its center and six more defects at its vertices. The superlattices are severely restricted in number by requiring the vertices of the unit to be equidistant from the center at a radius, R, and mutually separated by at least the same distance, R. Such a restriction applies to cation superlattices in pyrochlores, type-C sesquioxides, and UY₆O₁₂, and to the formal anion vacancies which relate UY₆O₁₂ to fluorite. At each value of R, several superlattices may be possible, involving different fractions, 1/n, of the cubic sites, and these are catalogued for R values less than (14)^1/2a_A (where a_A is the cell edge of the cubic lattice). Parallel defect-rich rows may occur for the highest values of 1/n at a given R, but in most cases the restriction disperses defects efficiently, i.e., tends to satisfy repulsions between defects, as is demonstrated by computed electrostatic potentials. The stability of such ordered dispersals of defects (relative to their randomized alternatives) decreases as n increases, except where an increment in n involves an increase in R. Variations in the stability of superlattice phases in PrO_x may be of this type. Site potentials in the superlattices are related empirically to n^1/3 using reduced variables involving R. High symmetry is not essential to the efficient dispersal of point defects.