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This article presents a study on elastic anisotropy of Cu by indentations at different penetration depth ranges (sub-10 nm, several-10 nm, and several-100 nm), and the impact of elastic anisotropy on the stress in 3D stacked integrated circuits (3D ICs). The reduced modulus, ER, values determined at sub-10 nm indentations on Cu single crystals are very close to the unidirectional values. Similarly, cross-sectional sub-10 nm indentation tests on the Cu grains in a through-silicon via (TSV) show unidirectional ER values. In contrast, the Hill’s average values are observed at several-100 nm indentations. We propose that before lattice rotation happens within a volume beneath the indentation, elastic anisotropy can be strongly reflected in the ER value. When the experimentally measured Cu elastic anisotropy is used in a technology computer-aided design simulation of a Cu-filled TSV, significant impacts are observed on the stress field and the carrier mobility variation in an active Si region.
Here we quantify the time-dependent mechanical properties of a linear viscoelastoplastic material under contact loading. For contact load relaxation, we showed that the relaxation modulus can be measured independently of concurrent plasticity exhibited during the loading phase. For indentation creep, we showed that the rate of change of the contact creep compliance can be measured independently of any plastic deformation exhibited during loading through , where a(t) is the contact radius, h(t) is the displacement of the contact probe, and Pmax is the constant applied load during the creep phase. These analytical relations were compared with numerical simulations of conical indentation creep for a viscoelastoplastic material and validated against sharp indentation creep experiments conducted on polystyrene. The derived relations enable extraction of viscoelastic material characteristics, even if sharp probes confer concurrent plasticity, applicable for a general axisymmetric contact probe geometry and a general time-independent plasticity.
The conventional JKR theory was extended to the adhesive contact of a rigid sphere onto an elastic film perfectly bonded to a rigid substrate. An elasticity problem of axisymmetric indentation on an elastic film was revisited, in which the force–depth relations for both flat and spherical indentations were obtained in a simple form. With the obtained force–depth relations, the energy release rate at the debonding of a spherical tip from an elastic film was expressed in terms of pull-off force, elastic constants, and geometric parameters. The adhesion energy between a spherical tip and an elastic film can be measured as the critical energy release rate at the instability of debonding. This study suggests that when the critical radius of contact is larger than the thickness of an elastic film, the extended JKR theory should be used in place of the conventional JKR theory to correctly evaluate the adhesion energy between the spherical tip and the elastic film.
KMgF3:Eu nanocubes with a mean edge length of ∼12 nm were synthesized by a hydrothermal method. Result of x-ray diffraction reveals that the nanocubes are perovskite phase. Under ultraviolet excitation, the broad emission bands from trace oxygen and color centers in KMgF3 matrix were observed. In comparison with a bulk sample having the same chemical compositions, no characteristic emissions of Eu2+ were observed, which can be attributed to the overlappment of the emissions of Eu2+ and color centers in KMgF3:Eu nanocubes. In addition, the emissions of Eu3+ were also detected, and the intensity ratio of 5D0 → 7F2 to 5D0 → 7F1 changed with excitation wavelength, indicating that the material has multiple luminescence centers or emitting states.
What modifications could you make to a hip stem to minimize stress shielding of the surrounding bone while still using metals common to orthopedic implants?
An interesting property of human bones is the manner in which they efficiently build up bone density where the bones are under higher loading, and remove bone density where strength is not needed. This property can be seen in the increased bone strength of the dominant arm of tennis players as compared to the non-racquet-holding arm (Ashizawa et al., 1999). Because the dominant arm is constantly subjected to loading as a result of the impact between the ball and racquet, the bone in that arm has greater bone density than the non-dominant arm, which presumably sees only everyday loading.
This property of bones is of importance to designers of hip stems as it has been shown that patients who have hip implants with a high stiffness stem were experiencing noticeable bone loss. This phenomenon, known as stress shielding, was thought to be occurring because the hip implants themselves were taking up so much of the loading that the body removed from the now extraneous surrounding bone. This in turn led to implant problems, as the remaining bone was not strong enough to stabilize the hip stems, as shown in Figure 6.1. Because of this, researchers turned their attention to developing materials and implants that might provide the same strength and durability with decreased stiffness, forcing the bone to take up more of the load. By the end of this chapter, a method for determining the stresses in various configurations of materials and stem cross-sections, in order to reduce stress shielding, will be developed.
How would you create a bone graft for the supporting structure of a dental implant if the patient has periodontal disease accompanied by bone loss in the jaw and also suffers from osteoporosis (porous bone)?
The above inquiry presents a realistic challenge that one might face in the field of dentistry. A dental implant must be integrated into the underlying bone in order to have the necessary structural support needed for function. A patient who has periodontal disease accompanied by bone loss in the jaw and who also suffers from osteoporosis (porous bone) is unlikely to have bone tissue that can be used as a structural graft. Traditionally bone grafts are obtained from elsewhere in the patient's body such as ribs, pelvis, or skull. If the patient has had severe trauma or other disease such as osteoporosis, there may be insufficient quantity or quality of bone available. In such cases, viable alternatives such as coral may be necessary. The case study presented at the end of this chapter examines coral as a bone substitute.
Historical perspective and overview
Structural materials, such as plaster of Paris (loosely categorized as a resorbable ceramic), were first employed as a bone substitute in the late 1800s (Pelter, 1959). Even today this material is used as a structural support for fractured bones. Plaster of Paris, which is made of calcium sulphate hemihydrate (CaSO4·H2O), is also used in radiotherapy to make immobilization casts for patients and in dentistry for modeling of oral tissues. Only within the last 50 years have medical ceramics been incorporated into load-bearing applications. The use of ceramics in structural applications has been restricted due to their inherent susceptibility to fracture and sensitivity to flaws (Kingery, 1976). For this reason, ceramics have had limited use in medical implants in which any tensile stresses were expected. Modern manufacturing methods, including sintering and high-pressure compaction, have enabled these materials to be produced with fewer defects and better mechanical properties. As a result of such technological development, ceramics are now utilized in a variety of applications including heart valves (More and Silver, 1990), bone substitutes (Bajpai, 1990), dental implants (Hulbert et al., 1987), femoral heads (Oonishi, 1992), middle ear ossicles (Grote, 1987), and bone screws (Zimmermann et al., 1991). Additionally, ceramics can be utilized in inert, active, and resorbable forms.
What methods can be used to keep soft tissue replacements fixed in the body?
A key challenge of developing soft tissue replacements is selecting a method for keeping them in place. Whether the implant is highly load-bearing (such as an artificial ligament) or only minimally (as in artificial cheekbones), implant migration is a serious issue. Because soft tissue replacements are typically made of compliant materials, implant fixation is particularly difficult. Tools such as screws or wires, commonly used in orthopedic implants, will only serve to damage these more delicate materials. Some typical methods for soft tissue replacements include suturing and encouraging tissue ingrowth into porous meshes. Are there ways to incorporate adhesives or less compliant materials for improved fixation?
Historical perspective and overview
Previous chapters in the clinical section of this textbook have described devices used to replace hard tissues (such as bone or teeth) and blood-interfacing implants (including vascular grafts and stents). Hard tissue replacements have their special challenges: for example, the need for a hip implant to be strong enough to withstand loading but have a low stiffness so as to reduce stress shielding. Blood-interfacing devices are required to provide structural support while preventing adhesion of platelets and without damaging blood cells. A third category of implant is soft tissue replacements. These can be further subdivided into mechanical supports (demanding a specific stiffness or strength as in sutures and synthetic ligaments), space fillers (primarily cosmetic implants, but also including artificial skin, which require compliance match and conformability), and highly specialized ophthalmic implants, which have further specifications related to their optical properties.
Mechanics of Biomaterials: Fundamental Principles for Implant Design provides the requisite engineering principles needed for the design of load-bearing medical implants with the intention of successfully employing synthetic materials to restore structural function in biological systems. This textbook makes available a collection of relevant case studies in the areas of orthopedics, cardiology, dentistry, and soft tissue reconstruction and elucidates the functional requirements of medical implants in the context of the specific restorative nature of the device. Each chapter opens with an exploratory question related to the chapter content in order to facilitate inquiry-based learning. Subsequently, a general overview, learning objectives, worked examples, clinical case studies, and problems for consideration are provided for each topic.
The organization of the book is designed to be self-contained, such that a student can be trained to competently engineer and design with biomaterials using the book as a standalone text, while practicing engineers or clinicians working with medical devices may use its content frequently in their careers as a guide and reference. The book comprises three basic sections: (i) overview of the materials science of biological materials and their engineered replacements; (ii) mechanical behavior of materials and structural properties requisite for implants; and (iii) clinical aspects of medical device design.
The first section of this book begins with a synopsis of medical devices and the fundamental issues pertaining to biocompatibility, sterilization, and design of medical implants. Engineered biomaterials including metals, ceramics, polymers, and composites are examined. The first segment of the book concludeswith a description of structural tissues. In these chapters, the mechanical properties of common synthetic and natural materials are discussed within the context of their structure-property relationships.
How are the material properties of cartilage and polymer bearing materials affected by the rate and duration of applied loading? How then does one design with biomaterials, accounting for time-dependent material properties?
The majority of important biomaterials, polymers, and tissues, for example, express some of the most complicated mechanical behaviors. When subjected to a constant load these materials will relax and continue to deform potentially indefinitely in a process called creep, making their use in structures problematic. Further, their response to high-frequency loading may differ dramatically from that observed under quasi-static conditions, directly impacting their performance in service. For instance, imagine the dynamic loading experienced by natural cartilage or a total knee replacement during downhill skiing, and how this rapid and severe loading could differ from the carefully controlled quasi-static testing typically performed in a laboratory. Comprehensive and effective modeling techniques are needed to properly account for time-dependent material properties in viscoelastic materials.
Overview
Viscoelastic materials, displaying both solid-like and fluid-like characteristics, are common in biomedical applications, from polymeric structures and coatings, to load-bearing connective tissues. The behavior of these materials cannot be described using only linear elasticity or plasticity theory, as is typical for many engineering materials. Rather, they are best described as having time-dependent material properties, such as an effective elastic modulus that is a function of the duration of applied loading. This time-dependence is usually associated with a characteristic time scale, called the relaxation time, and for time scales much greater or less than the relaxation time the material may not appear viscoelastic at all. Mathematical models of varying complexity can capture this behavior well, many times with only two or three material constants. Energy dissipation from the fluid-like part of the response can be separated from solid-like energy storage using a complex modulus, where they are represented by an imaginary and real part (respectively) of a complex material property (discussed below). In some cases, the material behavior is not simple enough to be represented by linear superposable functions, and nonlinear methods are especially suitable, for example when the unloading response does not match the loading response of the material.
You are designing a total knee replacement – a high-load device for which wear is a major concern. What would your ideal materials be for a low-wear device? Are there other concerns at play here, and how do they affect your material selection?
The inquiry posed above gives an idea of the issues that must be balanced in medical device design. A total knee replacement will see contact stresses of 40 MPa (Bartel et al., 1986) and will undergo 1 million fatigue cycles per year. We have already discussed the dangers of stress shielding which can occur when using high stiffness materials. Selecting a material that can meet these demands and still maintain low amounts of wear is a challenge that must be tackled by a team of engineers and scientists.
Overview
When thinking about designing devices that will have contact with any other materials, it is necessary to consider issues of friction, lubrication, and wear, also known as the field of tribology. These are particularly critical in load-bearing medical device applications such as total joint replacements, where the generation of wear debris is a known issue that begins a cycle of immune response and the eventual need for device replacement. Frictionless contact would be ideal, but does not exist in the real world. It has also been shown that low-friction contact can still lead to appreciable wear (Stachiowak and Batchelor, 2005). In orthodontic implants such as braces, a smooth surface to the arch wires is very important – frictional forces are known to reduce the amount of force applied to the teeth by 50% or more (Bourauel et al., 1998 ). The characterization of the interface between two surfaces, including the composition of the articulating materials, the surface finishes, and the lubricant (if any) will play a large role in determining the friction and wear behavior.
All metals, with the exception of high noble metals, are susceptible to corrosion. This problem is exacerbated in the body, where implants must function in aqueous environments under complex loading and often utilize designs that contain inherent stress concentrations and material discontinuities. How would you design a modular hip system composed of metal components that minimizes the likelihood for fretting and crevice corrosion?
The inquiry posed above represents a realistic challenge that one might face in the field of orthopedic biomaterials. At a minimum one would want to minimize the galvanic potential of the alloys involved in the implant design. Fretting is the loss of material owing to the rubbing or contact of components; to minimize this type of surface degradation it is necessary to utilize designs that optimize component tolerances for device fixation. Crevice corrosion occurs in metal components that contain fissures, notches, or other geometries that facilitate local changes in the environment. This type of corrosion is further enabled in the presence of elevated stresses or stress concentrations within the component. To minimize fretting and crevice corrosion in a modular hip it is necessary to diminish geometric gaps at junctions such as the Morse Taper (where the stem and acetabular head join) and to keep the stem and neck at reasonable lengths in order to reduce bending stresses at the stem-neck juncture. The case study presented at the end of this chapter addresses this issue.
Historical perspective and overview
Metals have been utilized in medical implants for several hundred years; in fact gold has been used as dental material from as early as 500 BC and noble metals have been employed in structural dentistry for use in fillings, crowns, bridges, and dentures since the 15th century (Williams, 1990). Noble alloys contain varying percentages of gold, palladium, silver, or platinum. High noble metals are metal systems that contain more than 60% noble metals (gold, palladium, or platinum) with at least 40% of the metal being composed of gold. It is known that gold was used in the 16th century to repair cleft palates; gold, bronze, and iron evolved as suture wires over the 17th–18th centuries; and steel plates were commonly employed as internal fixation devices by the early 19th century (Aramany, 1971; Williams et al., 1973). By the mid-1920s, stainless steels were introduced as implant materials and a decade later cobalt-chromium alloys were utilized in the body to provide enhanced corrosion resistance (Park and Bronzino, 2003). Titanium found its use as a surgical material shortly thereafter (Leventhal, 1951). Much of what motivated the development of metals as implant materials was the need for both strength and corrosion resistance in load-bearing devices.
Mechanics of Biomaterials: Fundamental Principles for Implant Design provides the requisite engineering principles needed for the design of load-bearing medical implants with the intention of successfully employing natural or synthetic materials to restore structural function in biological systems. One challenge in the medical device field is the multifactorial nature of the design process. Numerous elements affect device performance, including clinical variables, structural requirements, implant design, materials selection, manufacturing, and sterilization processes. The crucial requirement of any medical device is that it is biocompatible; the implant must restore function without adverse reaction or chronic inflammatory response in the body. In this respect, choice of materials used in the implant is key to the device integrity.
Moreover, the structural requirements of the implant are determined through an assessment of the expected physiological stresses that vary depending upon the patient's anatomy, weight, and physical activity. Analyses of these stresses are key in making certain that the selected material offers the appropriate mechanical properties such as requisite elastic modulus and yield stress, as well as resistance to creep, fracture, fatigue, and wear. This book addresses the complexities that are encountered in physiological loading such as three-dimensional stress states; the complex interplay of dynamic loading, contact mechanics, viscoelastic deformation, and rupture; as well as the combined effects of environmental degradation of the materials owing to biological attack, aqueous environment, and sterilization method employed.
How does the arrangement of collagen fibers in tendons assist in their function?
The question above represents a fundamental philosophy of this textbook. All materials, natural tissues included, have mechanical properties that reflect the chemical makeup and physical architecture of their microstructures. Tendons are assemblies of bundled collagen fibers arranged on a long axis that connect muscle to bone. Because tendons regularly experience axial tensile stresses with only very rare instances of other types of loading, this alignment optimizes the strength conferred by the collagen fibers by keeping them oriented in the direction of the greatest stress.
Historical perspective and overview
The earliest written records of anatomical study date back to 500 BCE, when Alcmaeon of Crotona asserted that the brain is the organ that governs intelligence. Later experiments by Claudius Galen (129–299 CE) were conducted on monkeys because human dissection was forbidden at that time. His theories on medicine (many of them incorrect, such as the concept that blood vessels were filled with grasping fibers that were responsible for blood flow) remained the basis of medical education for the next 1,400 years. Andreas Vesalius (1514–1564) made the next well-known advance in the understanding of human anatomy. Vesalius sought to recreate several of Galen's findings using human cadavers (by that time, human dissection was more accepted) and ultimately disproved many of them. In 1543, Vesalius published his results in De humani corporis fabrica (Mow and Huiskes, 2005; O’Malley, 1964), where, among other things, he concluded that it was the heart that caused blood to flow through arteries and veins. More recent developments in the study of natural tissues can be attributed to advances in histological techniques (microscopy), biochemical techniques (sample preparation and storage), and understanding of molecular biology (Piesco, 2002). While growth in these fields has led to a dramatic increase in our understanding of natural tissues, there remain aspects of many tissues that are still not fully understood, particularly regarding the relationship between their microstructure and overall physiological performance.