Bone Stress-Strain Curves in Compression and Tension | Biomechanics K305

Viscoelasticity describes materials whose mechanical properties depend on time, not just stress or strain magnitude. The rate of force application critically affects response: rapid loading creates greater internal resistance, while slow loading makes materials appear softer. Fracture points shift with loading rate. The viscous component follows stress proportional to strain rate (stress = μ × strain rate), modeled by a dashpot. The elastic component follows Hooke's Law (stress proportional to strain), represented by a linear stress-strain graph with Young's modulus. Three mathematical models describe viscoelastic behavior: Maxwell (series spring-dashpot), Kelvin-Voigt (parallel spring-dashpot), and Standard Linear Solid (combined arrangement). Creep is time-dependent deformation under constant stress; relaxation is stress decrease under constant strain.

Bone exhibits viscoelastic behavior, meaning its mechanical response depends not only on the magnitude of applied stress or strain but also on the rate at which they are applied; specifically, faster application of strain results in higher stress development and lower deformation compared to slower application, and this behavior can be modeled using the Kelvin viscoelastic model where the response depends on whether the loading time is comparable to or much smaller/larger than the material's characteristic time constant.

Bone exhibits viscoelastic properties, meaning its mechanical response depends on loading rate. Bone withstands greater forces under fast loading compared to slow loading, enabling adaptation to rapid physical activities like running and jumping. This strain rate sensitivity drives bone remodeling - fast loading stimulates bone growth while slow or no loading leads to decreased bone mineral density. This principle underlies the importance of weight-bearing exercise for bone health.

Bone mechanical properties are highly sensitive to strain rate. Human cortical bone shows approximately 1.6% strain at failure at low strain rates (0.001/s), but ductility decreases significantly at higher rates (up to 1500/s), with elastic modulus and strength increasing. This time-dependent response occurs because bone contains water molecules (~98%) and collagen (polymer), unlike ceramics which show less time-dependent behavior. Soft tissues (cardiovascular, tendons, ligaments) have elastic moduli approximately 3 orders of magnitude lower than bone (<2 MPa vs. ~20-27 GPa), with maximum strains of 40-50% before failure, characteristic of polymer-based materials.

This lecture explains the mechanical properties of bone and connective tissues, covering stress (force divided by surface area), strain (deformation relative to original length), and stiffness (stress-to-strain ratio). Bone is strongest against compression, followed by tension, and weakest against shear forces. Tissues exhibit viscoelasticity, meaning their stiffness and strength depend on loading rate—faster loading increases stiffness and strength while slower loading reduces them. Bone fatigue occurs from repeated loading without adequate recovery time. Articular cartilage, composed of water, collagen, and proteoglycans, provides shock absorption and reduces friction through a sponge-like mechanism that relies on loading for nutrient exchange. Tendons transmit forces from muscle to bone and are stronger than ligaments, which provide joint stability. Both tendons and ligaments have a toe region (uncrimping), linear elastic region, yield point, and failure point, with tendons more likely to fail at insertion points rather than mid-substance.

Interface fixation choices between conventional (friction-based preload) and locking (fixed-angle devices) create fundamentally different biomechanical behaviors. Conventional fixation relies on individual screw pullout strength, while locking fixation requires simultaneous failure of all elements. Blood supply preservation through minimally invasive approaches and low-contact designs supports healing, with periosteal blood flow patterns changing throughout life and after trauma. Effective fracture fixation requires defining intention (primary vs secondary healing), achieving method (anatomical reduction, rigid vs relative fixation), and maintaining stability until healing. Working length—the unsupported construct segment—is critical for stability, measured between support points at the diaphyseal diameter. Increasing rigidity involves maximizing nail diameter (fourth power effect), using thicker constructs, adding screws, selecting stiffer materials, and achieving optimal reduction. Titanium's lower modulus (closer to bone) enables load-sharing constructs preventing stress shielding, while stainless steel provides stiffer load-bearing options. Anatomical considerations dictate plate selection—for the forearm, neutralization plates supplement lag screws providing necessary bending and torsional stability that compression alone cannot achieve.

Multiple surgical techniques achieve interfragmentary compression for primary healing. Lag screws use either technique (drilling near holes perpendicular to fracture line, then threaded far holes with countersinking) or design (partially threaded screws gliding through fracture gap). Dynamic compression plates use eccentrically drilled holes that slide screw heads toward center, compressing purchased bone. Tension band technique converts extensor mechanism tension to articular compression. Buttress plating redirects expected stress patterns into compression. Each method provides compression but requires additional neutralization plates for resisting bending and shear forces in unstable fractures.

Fracture fixation devices are classified into two main categories based on their biomechanical effects on bone healing: devices that favor secondary consolidation (such as Kirschner wires, external fixators, and intramedullary nails) which promote callus formation through controlled micromovements and mechanical stress, and devices that favor primary consolidation (such as compression plates) which provide rigid fixation and minimize movement at the fracture site.

Plates function as load-bearing devices most effective on the tension side of fractures. Concave plates apply compression across both cortices when screws are inserted. Working distance—the distance between screws near the fracture—affects implant stiffness; closer screws increase rigidity. Titanium's biomechanical properties most closely match cortical bone due to similar Young's modulus values. Healing principles distinguish absolute stability (strain <2%) promoting primary bone healing from relative stability (strain 2-10%) allowing secondary healing with callus formation. Strain exceeding 10% leads to fibrous union or non-union. Five major plate types serve different fracture patterns: compression, neutralization, bridging, buttress, and locking plates.

Fracture fixation using plates and screws requires understanding two key healing mechanisms: absolute stability (zero motion for direct bone remodeling) and relative stability (controlled micro-motion for callus formation), with surgeons selecting appropriate plate types (compression, neutralization, butress, bridging, or locking plates) and screw types (cortical, cancellous, lag, or locking screws) based on fracture characteristics, bone quality, and desired biological response, while respecting working length principles and avoiding over-instrumentation to protect blood supply and promote reliable bone healing.

Wolff's Law states that bone will remodel itself in accordance with habitual chronic stress and loading patterns. This principle explains why bones adapt to mechanical demands over time. For example, tennis players show differences in bone density between their dominant and non-dominant arms due to repeated loading patterns. This law applies to both cortical bone (outer hard portion) and trabecular bone (inner spongy portion).

Wolff's Law, formulated by German anatomist Julius Wolff in 1870, states that bone adapts to the loads it bears; when functional forces change in direction or magnitude, the bone remodels its internal structure and external form to become stronger in areas of increased stress and less dense in areas of decreased use, following the principle that trabecular bone arrangement follows the pathways of maximal pressure and tension.

Wolff's Law states that bone responds to mechanical loading by remodeling itself to accommodate the stress placed upon it. When bone is loaded, it stimulates new bone formation; conversely, when bone is not loaded, it resorbs and weakens. This principle explains why astronauts experience rapid bone loss in zero-gravity conditions.

Wolff's Law states that bone adapts to the mechanical loads placed upon it. The internal structure of bone (trabecular architecture) changes based on the direction and magnitude of forces. When forces are distributed incorrectly, the bone remodels to accommodate the new stress patterns, which can lead to deformities over time.

Bone is living tissue filled with blood vessels, nerves, collagen, minerals, marrow, and active cells that build, break down, sense, repair, and reshape it throughout life. The hardness of bone comes largely from minerals, especially calcium phosphate arranged as hydroxyapatite, which gives bone stiffness and strength under compression. Bone also contains collagen, a flexible structural protein that helps it resist bending and cracking. Three cell types are especially important: osteoblasts (bone-building cells), osteoclasts (bone-absorbing cells), and osteocytes (mature bone cells embedded within the matrix). Bone remodeling happens even without obvious injury—tiny areas of older bone are broken down and replaced, and microscopic damage from ordinary movement is repaired. Wolff's Law describes the principle that bone adapts to the loads placed upon it: stronger or repeated loading can encourage stronger bone architecture while reduced loading can contribute to bone loss.

Stress shielding is a phenomenon where orthopedic implants that are too rigid prevent the underlying bone from receiving mechanical loading, causing the bone to weaken and reabsorb over time, which can lead to implant loosening and failure; modern implant design aims to balance sufficient durability with natural flexibility to maintain bone health.

Human bone is a dynamic structure that exists only as long as it feels mechanical stress. In orthopedics, this biological law long remained the main obstacle for durable prosthetics. Ordinary titanium alloys and stainless steel have excessive stiffness, five to seven times greater than living tissue. When such a stiff pin is implanted in the femur, stress shielding occurs. The metal, being a significantly stronger framework, takes all axial load, depriving the bone of natural work. The biological system, following the principle of resource economy, interprets the absence of load as a signal for demolition. Bone tissue around the implant begins to resorb and atrophy.

Mechanical properties are critical for biomaterials, particularly stiffness (resistance to deformation). The stiffness of a biomaterial should match the target tissue to prevent stress shielding. For example, titanium (stiffness ~85 GPa) is much stiffer than bone (~30 GPa). When a stiff implant is placed in bone, it bears most of the load, preventing natural bone from receiving mechanical stimulation. Without this stimulation, bone resorbs and weakens (stress shielding effect). This is why astronauts experience bone loss in microgravity - their bones lack mechanical loading. In vascular applications, Dacron grafts are much stiffer than natural blood vessels, causing abnormal stress on vessel walls and potential long-term complications. The golden rule in biomaterials is to match stiffness to target tissue for proper load distribution.

Biomaterials must have appropriate mechanical properties, not necessarily the highest possible. The stress shielding phenomenon occurs when an implant and bone form a combined system under load. Because metals have much higher elastic modulus than bone, the implant bears most stress while the bone experiences reduced stress, causing bone to lose mass (osteoporosis) and weakening the bone-implant interface. Cortical bone has an elastic modulus of approximately 30 GPa, while stainless steel is about 240 GPa (8 times higher), and cobalt-chromium alloys are about 10 times higher. Titanium and titanium alloys (100-110 GPa) are closer to bone, making them better choices for load-bearing implants. Metallic biomaterials are valued for excellent mechanical properties (strength, ductility, elastic modulus) allowing them to withstand high loads, but most corrode when exposed to body fluids, releasing ions that trigger immune responses. Stainless steel (iron-carbon-chromium alloy) is widely used due to low cost but has high rigidity (240 GPa, 8x cortical bone) and moderate corrosion resistance, typically used for applications under 10 years. Cobalt-chromium alloys (65% cobalt, 30% chromium) have superior mechanical properties and excellent corrosion resistance but are expensive.

Stress shielding occurs when an implant is too stiff compared to the surrounding bone, causing the bone to bear less load. This reduced loading can lead to bone resorption and weakening over time. The design of implants must balance stiffness to provide adequate support while allowing sufficient stress transfer to maintain bone health.