Shivakumar I. Ranganathan

Shaping the micromechanical behavior of multi-phase composites for bone tissue engineering

Mechanical stiffness is a fundamental parameter in the rational design of composites for bone tissue engineering in that it affects both the mechanical stability and the osteo-regeneration process at the fracture site. A mathematical model is presented for predicting the effective Youngs modulus (E) and shear modulus (G) of a multi-phase biocomposite as a function of the geometry, material properties and volume concentration of each individual phase. It is demonstrated that the shape of the reinforcing particles may dramatically affect the mechanical stiffness: E and G can be maximized by employing particles with large geometrical anisotropy, such as thin platelet-like or long fibrillar-like particles. For a porous poly(propylene fumarate) (60% porosity) scaffold reinforced with silicon particles (10% volume concentration) the Youngs (shear) modulus could be increased by more than 10 times by just using thin platelet-like as opposed to classical spherical particles, achieving an effective modulus E approximately 8 GPa (G approximately 3.5 GPa). The mathematical model proposed provides results in good agreement with several experimental test cases and could help in identifying the proper formulation of bone scaffolds, reducing the development time and guiding the experimental testing.

Scale-Dependent Homogenization of Inelastic Random Polycrystals

Rigorous scale-dependent bounds on the constitutive response of random polycrystalline aggregates are obtained by setting up two stochastic boundary value problems (Dirichlet and Neumann type) consistent with the Hill condition. This methodology enables one to estimate the size of the representative volume element (RVE), the cornerstone of the separation of scales in continuum mechanics. The method is illustrated on the single-phase and multiphase aggregates, and, generally, it turns out that the RVE is attained with about eight crystals in a 3D system. From a thermodynamic perspective, one can also estimate the scale dependencies of the dissipation potential in the velocity space and its complementary potential in the force space. The viscoplastic material, being a purely dissipative material, is ideally suited for this purpose.

Quantifying the Anisotropy in Biological Materials

Anisotropy is an essential attribute exhibited by most biological materials. We propose an appropriate measure (A) to quantify the extent of elastic anisotropy in such materials by recognizing the tensorial nature of the elastic properties. Furthermore, we derive a relationship between A with an empirically defined existing measure. Also, the above measure is used to quantify the extent of anisotropy in select biological materials that include bone, dentitional tissues and a variety of woods. Our results indicate that woods are an order of magnitude more anisotropic than hard tissues and apatites. Finally, based on the available data, it is found that the anisotropy in human femur increases by over 40 % when measured between 30 % and 70 % of the total femur length.

Invariants of mesoscale thermal conductivity and resistivity tensors in random checkerboards

Purpose – The purpose of this paper is to study the statistics of thermal conductivity and resistivity tensors in two-phase random checkerboard microstructures at finite mesoscales. Design/methodology/approach – Microstructures at finite scales are generated by randomly sampling an infinite checkerboard at 50 percent nominal fraction. Boundary conditions that stem from the Hill-Mandel homogenization condition are then applied as thermal loadings on these microstructures. Findings – It is observed that the thermal response of the sampled microstructures is in general anisotropic at finite mesoscales. Based on 1,728 boundary value problems, the statistics of the tensor invariants (trace and determinant) are obtained as a function of material contrast, mesoscale and applied boundary conditions. The histograms as well as the moments (mean, variance, skewness and kurtosis) of the invariants are computed and discussed. A simple analytical form for the variance of the trace of mesoscale conductivity tensor is pr...

Electrical properties of random checkerboards at finite scales

Under investigation is the scale dependent electrical conductivity (and resistivity) of two-phase random checkerboards at arbitrary volume fractions and phase contrasts. Using variational principles, rigorous mesoscale bounds are obtained on the electrical properties at finite scales by imposing a boundary condition that is either uniform electric potential or uniform current density. We demonstrate the convergence of these bounds to the effective properties with increasing length scales. This convergence gives rise to the notion of a scalar-valued scaling function that accounts for the statistical nature of the mesoscale responses. A semi-analytical closed form solution for the scaling function is obtained as a function of phase contrast, volume fraction and the mesoscale. Finally, a material scaling diagram is constructed with which the convergence to the effective properties can be assessed for any random checkerboard with arbitrary phase contrast and volume fraction.

Design maps for scaffold constructs in bone regeneration

In this article, we propose a methodology for the rational design of scaffold constructs in bone-tissue engineering. The construct under investigation is a sandwich structure with an Intramedullary rod (IM), a Biological Sponge (BS) and an External sleeve (ES). The IM rod provides axial resistance, BS facilitates the growth of new bone and ES provides stability to the construct by resisting torsion and bending. We demonstrate that only select combinations of stiffness between IM and ES facilitate the growth of new bone. Perren’s interfragmentary strain theory is employed to clearly identify regions favoring bone growth from those favoring the formation of cartilage. Finally, design maps are constructed that clearly identify the combinations facilitating timely bone growth.

Buckling of slender columns with functionally graded microstructures

ABSTRACT The buckling of slender columns with functionally graded microstructures is studied. In such columns, the flexural modulus is varied in a controlled manner along the column length. The objective is to identify microstructures that maximize (and minimize) the critical buckling load when compared to a reference homogeneous column. Several microstructures are examined and a constraint is imposed so that the volume averaged flexural modulus remains the same in all columns. The buckling load is determined using both the linear perturbation analysis as well as the Rayleigh–Ritz method. A relationship between the material distribution and the corresponding mode shape is established.

Geometrical Anisotropy in Biphase Particle Reinforced Composites

Particle shape plays a crucial role in the design of novel reinforced composites. We introduce the notion of a geometrical anisotropy index A to characterize the particle shape and establish its relationship with the effective elastic constants of biphase composite materials. Our analysis identifies three distinct regions of A: (i) By using ovoidal particles with small A, the effective stiffness scales linearly with A for a given volume fraction α; (ii) for intermediate values of A, the use of prolate particles yield better elastic properties; and (iii) for large A, the use of oblate particles result in higher effective stiffness. Interestingly, the transition from (ii) to (iii) occurs at a critical anisotropy A cr and is independent of α.

Optimization of piping expansion loops using ASME B31.3

Piping is the main transportation method for fluids from one location to another within an industrial plant. Design and routing of piping is heavily influenced by the stresses generated due to thermal effects and high pressure of the operating fluid. In particular, pressurized fluids create critical loads on the supports and elbows of the pipe which increases the overall stresses in the piping. Moreover, long pipes operating under high temperature gradients tend to expand significantly. Therefore, designers and engineers usually provide an expansion loop in order to relieve the pipe from the critical stresses. However, expansion loops require extra space, supports, elbows, bends, additional steel structure that could adversely affect the operating cost. It is therefore necessary to optimize the geometry, the number of expansion loops, and the supports. Reducing the number of loops in one single system or reducing the length of the loop itself is always favored as long as stresses are within safe limits. Usually, the commercial software (PipeData) is used in the industry to get the dimensions of the expansion loop. However, this software is mostly based on empirical models that rely on past experience rather than engineering fundamentals. Accordingly, this paper conducts an optimization analysis concerning the expansion loop dimensions and the number of supports without compromising on the safety of piping. The design approach is conducted as per the guidelines of ASME B31.3 (Process Piping) code and uses the commercial software (CAESAR II) for stress calculations. A full comparison for the expansion loop dimension is conducted between the empirical approach and the optimization analysis using ASME B31.3 for one of the existing oilfield projects. Results indicate that optimization reduces the dimensions and the number of expansion loops as well as the total number of supports. This results in significant savings in the piping cost without any compromise on the safety.

3D printed liner for treatment of periprosthetic joint infections

In the United States, long standing deep infections of joint arthroplasty, such as total knee and total hip replacements, are treated with two-stage exchange. This requires the removal of the prior implant, placement of an antibiotic eluting spacer block made of polymethylmethacrylate (PMMA), followed by re-implantation of a new implant after treatment with intravenous antibiotics for six to eight weeks. Unfortunately, the use of PMMA as a spacer material has limitations in terms of mechanical and drug-eluting properties. PMMA is brittle and elutes most of the antibiotics within the first few days. Furthermore, the polymerization reaction for PMMA is highly exothermic, thereby limiting the use to heat-stable antibiotics. We hypothesize that the use of a 3D printed polymeric liner made of polylactic acid (PLA) would overcome the limitations of PMMA because it is a stronger and a less brittle material than PMMA. Furthermore, the liner can also act as a controlled drug delivery vehicle by using built in reservoirs and a network of micro-channels as well as by incorporating antibiotics directly into the polymer during manufacturing stage. Finally, the liner can be 3D printed according to the anatomy of the patient and thereby has the potential to transform the manner in which periprosthetic joint infections are currently treated.