Multiscale Materials and Design Optimization Lab

This lab aims to create and optimize the microstructure of multifunctional materials using computational and experimental means. The objective is to optimally design materials and structures that meet certain functional requirements. Following are some of the research projects pursued in our lab:

The long term goal of this laboratory is to integrate computer aided engineering tools together with 3D printing technologies to build useful real world applications. Graduate and undergraduate students in our lab get trained in using CAD/CAM/CAE tools as well as in conducting hands on experimental tests. Our lab is located in the South Jersey Technology Park and collaborates with medical professionals at Cooper University Hospital and researchers at U.S. Army Armament Research, Development and Engineering Center (ARDEC). Some of the past research projects are summarized below:

1.      Multiscale mechanics of heterogeneous materials

The framework of stochastic mechanics is employed to obtain scale-dependent bounds on the response of heterogeneous media (random composites, polycrystals). In doing so, one infers the approach to the Representative Volume Element (RVE), the corner-stone of the separation of scales in continuum mechanics. The RVE is approached by setting up and solving stochastic Dirichlet and Neumann boundary value problems consistent with the Hill(-Mandel) macrohomogeneity condition. Further, the concept of a scaling function is introduced to establish unifying scaling laws. It turns out that the scaling function depends on a mesoscale (scale of observation relative to grain size) and an appropriate metric quantifying the single crystal anisotropy. Based on the scaling function, a material selection diagram is constructed that clearly separates the microscale from the macroscale [Figs. 1(a), 1(b)]. Using such a diagram, one can determine the size of RVE for a whole range of polycrystals made of various crystal classes. Application problems include the scaling of the fourth-rank elasticity and the second-rank thermal/electrical conductivity tensors. The trends in approaching the RVE for planar conductivity, linear/non-linear (thermo)elasticity, plasticity, and Darcy permeability is also established.   

       (a)                                                                                                         (b)

FIG. 1: (a) Homogenization methodology; (b) Material scaling diagram

The impact of this research lies in the fact that one can establish scaling laws that seamlessly integrate the microscale to the macroscale. Such a methodology can be used to understand and predict the properties of a variety of materials. In turn, this will enable the design of novel microstructures with target properties (enhanced strength, stiffness, conductivity and buckling resistance). Such microstructures can then be engineered to build low cost applications that are light in weight and safer.

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2.      Smart Biomaterials and Biomechanics

a)      Smart Biomaterials:

The focus of this project is on the design and development of a novel BioNanoScaffold (biologically active composite) for Post-Traumatic OsteoRegeneration. The objective is to design a `smart fracture putty' to help repair serious bone injuries [see Fig. 2(a)]. The fracture putty is a complex biomaterial made up of individual components with characteristic dimensions that span across a variety of length scales (nano to macroscales). The putty has both mechanical and biological functions to fulfill and is essentially made up of a biodegradable polymeric matrix with stiffer reinforcements, pores and other functional materials [see Fig. 2(b)]. The putty is designed to take up the normal mechanical loads acting on the bone and is administered with stem cells and growth factors to facilitate the growth of new bone. Eventually, as the healthy bone grows, the putty starts degrading until the wound is completely healed. From a mechanistic perspective, the successful design of the putty requires a careful control of key design parameters such as: i) volume fraction of particles; ii) particle orientation distribution; iii) the shape; and iv) the size of particles. We have also developed mathematical models and design maps [see Fig. 2(c)] to predict bone growth and the degradation of the polymeric scaffold.

 (a)                                                                                    (b)                                                                         (c)

FIG. 2: (a) A scaffold is implanted or injected into the fracture site; (b) Schematic of a possible design for the scaffold construct; (c) Admissible design region favoring bone growth

b)     Biomechanics:

Motorcyclists are road-users with a higher risk than the car occupants. In crash safety research, there is a significant increase in the use of computer simulations over the past two decades. This is due to the advances in computer hardware/software and due to the development of reliable models describing the human body in a crash situations. Mathematical models offer a very economical and versatile method for the analysis of the crash scenarios and substantially bring down the need for experimental studies. One of the most important task in such studies is to position the MATD model close to the experimentally measured co-ordinates. A computer program was developed to generate the necessary geometrical transformations to achieve this objective [see Figs. 3(a), 3(b)].

 (a)                                                                                    (b)

FIG. 3: (a) Side view of the initial and final positions of the dummy; (b) Front view of the initial and final positions of the dummy

Another area of interest in biomechanics is the dynamics of thin elastic rods and helices such as the DNA. We have developed a finite element model to include the effects of rotary inertia in isotropic circular rods. In developing this model, the angular velocities are first expressed in terms of the time derivatives of the Frenet frame. This definition is then used to determine the contributions of rotary inertia. A salient feature of this model is that only six variables representing the absolute position vectors are used as nodal coordinates. Galerkin’s weighted residual approach is used to complete the discretization.

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3.      Material and Geometrical Anisotropy

Etymologically, the word anisotropy is a combination of `an' (not), `isos' (equal) and `tropos' (turn) implying `not equal turn'. In the context of this research, anisotropy implies geometric and material properties are direction dependent. As a simple example, an ellipse (ellipsoid) can be thought of being anisotropic whereas a circle (sphere) could be considered isotropic when viewed from the center. There are several situations in which there is an inherent need to use a measure that quantifies the extent of anisotropy (material and geometric). Basing on sound mathematical principles, we came up with a definition of an anisotropy index that was universally applicable. The impact of this research lies in its simplicity, yet a very fundamental and useful definition that is applicable to a variety of fields.

a)      Material anisotropy--application to elastic crystals:

Practically all elastic single crystals are anisotropic, which calls for an appropriate universal measure to quantify the extent of anisotropy. A review of the existing anisotropy measures in the literature leads to a conclusion that they lack universality in the sense that they are non-unique and ignore contributions from the bulk part of the elastic stiffness (or compliance) tensor. Proceeding from extremal principles of elasticity, a new universal anisotropy index is introduced that overcomes the above limitations. Furthermore, special relationships between the proposed anisotropy index and the existing anisotropy measures for special cases are established. A new elastic anisotropy diagram is constructed for over 100 different crystals (from cubic through triclinic), demonstrating that the proposed anisotropy measure is applicable to all types of elastic single crystals, and thus fills an important void in the existing literature.

b)     Material anisotropy--application to biological materials:

Anisotropy is an essential attribute exhibited by most biological materials. Based on the recent work on anisotropy of a wide range of crystals and polycrystals, we propose an appropriate measure (A) to quantify the extent of elastic anisotropy in biomaterials by accounting the tensorial nature (both stiffness-based and compliance-based) of their elastic properties. Next, we derive a relationship between A and an empirically defined existing measure. Also, the preceding measure is used to quantify the extent of anisotropy in select biological materials that include bone, dentitional tissues, and a variety of woods. 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.

c)      Geometrical anisotropy:

Particle shape plays a crucial role in the design of novel reinforced composites. The notion of a geometrical anisotropy index `A' is introduced to characterize the particle shape and its relationship with the effective elastic constants of biphase composite materials is established. The 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 a; 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 `Acr' and is independent of a.

Both forms of anisotropy (material and geometric) have applications in a wide range of disciplines that include geophysics, biological materials [see Fig. 4(a)], diffusion tensor imaging, phase transformations, dislocation dynamics, condensed matter physics and composite materials. For instance, using stiffer ellipsoidal fillers as reinforcement in a softer matrix generates a composite material with properties superior than a similar composite reinforced with spherical fillers [see Figs. 4(b), 4(c)]. Further, material anisotropy plays a very important role in seismology with applications to petroleum exploration/production and in the understanding of lower mantle composition and behavior [see Fig. 4(d)].




FIG. 4: (a) Anisotropy of trees; (b) Contours of geometrical anisotropy; (c) Contours of elastic properties; (d) Lowermost mantle anisotropy [see Walker & Wookey, Computers and Geosciences (2012)]

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