VISCOELASTICITY
Creep | Stress Relaxation | Hysteresis | Rate-Dependent
Viscoelastic Models
Critical Must-Knows
- Viscoelasticity = Time-dependent mechanical behavior combining viscous and elastic properties
- Creep = Progressive deformation under constant load
- Stress relaxation = Force decreases at constant deformation
- Hysteresis = Energy lost as heat during loading-unloading cycles
- Strain-rate sensitivity = Stiffer and stronger at higher loading rates
Examiner's Pearls
- "All biological tissues are viscoelastic
- "Ligaments, tendons, and intervertebral discs exhibit strong viscoelastic behavior
- "Creep explains loss of fracture reduction over time
- "Stress relaxation explains why initial cast tension decreases
Critical Viscoelasticity Concepts
Creep Definition
Progressive increase in deformation under constant load. Example: Disc height decreases throughout the day. Scoliosis brace applies constant force causing gradual correction.
Stress Relaxation
Progressive decrease in force at constant deformation. Example: Cast becomes loose as swelling subsides. Initial graft tension decreases over time.
Hysteresis
Energy dissipation as heat during loading-unloading cycles. Loading and unloading curves do not overlap. Area between curves = energy lost. Protective mechanism in tissues.
Strain-Rate Sensitivity
Materials are stiffer and stronger at higher loading rates. High-energy trauma causes different injury patterns. Explains why impact testing differs from static testing.
At a Glance
Viscoelasticity describes time-dependent mechanical behavior combining both viscous (fluid-like) and elastic (solid-like) properties, exhibited by all biological tissues. Four key phenomena: Creep (progressive deformation under constant load—explains disc height loss throughout the day and loss of fracture reduction), Stress relaxation (force decreases at constant deformation—explains why cast tension decreases over time), Hysteresis (energy dissipated as heat during loading-unloading cycles—area between curves represents lost energy), and Strain-rate sensitivity (materials are stiffer and stronger at higher loading rates—explains different injury patterns in high vs low energy trauma). Mechanical models include Maxwell (spring-dashpot in series, models relaxation), Kelvin-Voigt (parallel, models creep), and Standard Linear Solid (combined).
CRHSViscoelastic Phenomena
Memory Hook:CRHS = The four key viscoelastic behaviors all tissues show!
MKSViscoelastic Models
Memory Hook:MKS models = Maxwell Series, Kelvin parallel, Standard combined!
DISCClinical Examples
Memory Hook:DISC = Clinical examples where viscoelasticity matters!
Overview
Viscoelasticity describes time-dependent mechanical behavior that combines characteristics of both viscous fluids and elastic solids. Unlike purely elastic materials that immediately return to their original shape when unloaded, viscoelastic materials exhibit time-dependent strain and stress responses.
Definition
Viscoelastic materials exhibit both elastic and viscous behavior. The elastic component stores energy and provides immediate reversible deformation. The viscous component dissipates energy and causes time-dependent irreversible flow. All biological tissues demonstrate viscoelastic properties.
Clinical Significance
Understanding viscoelasticity is essential in orthopaedics because all biological tissues behave viscoelastically. This affects how tissues respond to loading, how implants interact with tissues, and how injuries occur. Viscoelastic properties determine tissue response to both physiological and traumatic loads.
Principles and Mechanisms
Elastic vs Viscous vs Viscoelastic
Elastic materials (ideal solid) obey Hooke's Law. Stress is proportional to strain. Deformation is instantaneous and completely reversible. Energy is stored. There is no time dependence.
Viscous materials (ideal fluid) obey Newton's law of viscosity. Stress is proportional to strain rate. Deformation is permanent. Energy is dissipated as heat. Behavior is rate-dependent.
Viscoelastic materials combine both behaviors. Response depends on both strain magnitude and strain rate. Deformation has immediate and time-dependent components. Some energy is stored, some is dissipated.
Time-Dependent Behavior
Viscoelastic behavior manifests in several ways. The response to loading depends on how fast the load is applied. The material continues to deform even after the load stops changing. When held at constant deformation, the force required decreases over time.
Temperature Dependence
Viscoelastic properties are temperature-dependent. Higher temperatures increase viscous behavior. Lower temperatures increase elastic behavior. This is relevant for cryopreserved tissues and temperature effects on implants.
Key Viscoelastic Phenomena
Creep
Definition: Progressive increase in deformation under constant load over time.
Mechanism: The viscous component allows continued deformation even though load remains constant. Initially rapid, then slows asymptotically toward equilibrium.
Clinical Examples:
- Intervertebral disc height decreases during the day under body weight
- Fracture reduction may be lost over time in cast or external fixator
- Scoliosis bracing applies constant force causing gradual correction
- Total disc replacement devices may subside into endplates
- Ligament grafts elongate under constant tension
Three Phases of Creep:
- Primary creep: Rapid initial deformation, decreasing rate
- Secondary creep: Constant steady-state deformation rate
- Tertiary creep: Accelerating deformation leading to failure
Stress Relaxation
Definition: Progressive decrease in force required to maintain constant deformation over time.
Mechanism: At constant strain, internal stresses redistribute and decrease. The viscous component allows molecular rearrangement.
Clinical Examples:
- Casts become loose as initial swelling subsides and tissues relax
- Fracture reduction maintained by ligamentotaxis loses tension over time
- ACL graft initial tension decreases requiring retensioning
- Circular external fixator wires lose tension over days
- Compression plates lose some compression over weeks
Time Course: Exponential decay. Most relaxation occurs in first minutes to hours. Continues at slower rate for days to weeks.
Hysteresis
Definition: Energy dissipation when a material is loaded and then unloaded. The loading and unloading curves do not overlap.
Mechanism: Energy absorbed during loading is not completely recovered during unloading. The difference is dissipated as heat. Area between loading and unloading curves represents lost energy.
Clinical Significance:
- Protective mechanism - tissues absorb impact energy
- Ligaments and intervertebral discs show significant hysteresis
- Repeated loading causes cumulative energy dissipation
- May contribute to tissue heating during repetitive loading
- Affects damping of vibrations and impacts
Measurement: Hysteresis loop area on stress-strain curve. Larger area means more energy dissipation.
Strain-Rate Sensitivity
Definition: Mechanical properties depend on the rate at which load is applied.
Behavior: Materials are stiffer and stronger at higher strain rates. They are more compliant at lower rates.
Mechanism: At high rates, viscous component has less time to flow. Material behaves more elastically. At low rates, viscous flow contributes more.
Clinical Examples:
- Bone is stronger and fails more brittly in high-energy trauma
- Ligament tears in sports occur at higher loads than in clinical testing
- Dashboard injuries differ from gradual compression injuries
- Impact testing gives different results than quasi-static testing
Testing Implications: Static tests underestimate tissue strength during dynamic activities. Physiological loading rates should be used when testing.
Mathematical Models
Maxwell Model
Structure: Spring (elastic element) and dashpot (viscous element) connected in series.
Behavior: Models stress relaxation well. Predicts instantaneous elastic deformation followed by continued viscous flow under constant load. Under constant strain, stress decreases exponentially.
Equation: Relaxation time equals viscosity divided by elastic modulus.
Limitation: Does not model creep accurately. Predicts infinite deformation under constant load.
Kelvin-Voigt Model
Structure: Spring and dashpot connected in parallel.
Behavior: Models creep well. Predicts gradual deformation under constant load reaching equilibrium. Cannot model stress relaxation.
Response: Delayed elastic response. Deformation is time-dependent but ultimately reaches elastic equilibrium value.
Limitation: Predicts no instantaneous deformation, which is unrealistic. Does not model stress relaxation.
Standard Linear Solid Model
Structure: Combination of Maxwell and Kelvin-Voigt elements. Three-parameter model.
Behavior: Models both creep and stress relaxation. Most realistic simple model for biological tissues.
Response: Instantaneous elastic response, followed by time-dependent viscoelastic response, approaching equilibrium.
Application: Better approximates actual tissue behavior. Used in finite element modeling.
More Complex Models
Generalized Maxwell: Multiple Maxwell elements in parallel. Better fits stress relaxation data.
Generalized Kelvin-Voigt: Multiple Kelvin-Voigt elements in series. Better fits creep data.
Quasi-linear Viscoelasticity: Advanced model for soft tissues proposed by Fung. Separates time-dependent and strain-dependent responses.
Tissue Composition and Viscoelasticity
Tissue Components
Solid Phase:
- Collagen fibers (structural framework)
- Proteoglycans (hydration, resistance)
- Elastin (elastic recoil)
Fluid Phase:
- Interstitial water (60-80% of tissue)
- Fluid flow through matrix
- Contributes to viscous behavior
Tissue Composition
| Tissue | Water Content | Viscoelasticity |
|---|---|---|
| Articular cartilage | 60-80% | High (biphasic) |
| Intervertebral disc | 70-90% | Very high |
| Ligament | 60-70% | Moderate-high |
| Bone | 10-20% | Low-moderate |
Classification of Viscoelastic Behavior
By Phenomenon
Four Key Types (CRHS):
Viscoelastic Phenomena
| Phenomenon | Definition | Clinical Example |
|---|---|---|
| Creep | Constant load, increasing deformation | Disc height loss during day |
| Relaxation | Constant deformation, decreasing force | Cast loosening over time |
| Hysteresis | Energy loss in loading cycles | Shock absorption |
| Strain-rate | Rate-dependent properties | High-energy fracture patterns |
Clinical Applications in Orthopaedics
Bone
Viscoelastic Properties: Bone is moderately viscoelastic. More viscous when wet. Shows strain-rate sensitivity.
Creep: Minimal compared to soft tissues. Relevant in long-term loading scenarios.
Rate Effects: Much stronger and stiffer at impact rates. Fails more brittly in high-energy trauma. Cortical bone Young's modulus increases approximately thirty percent at physiological strain rates compared to quasi-static loading.
Clinical Relevance: High-energy fractures have more comminution. Bone density measurement may vary with loading rate.
Articular Cartilage
Viscoelastic Properties: Highly viscoelastic due to fluid flow through solid matrix. Biphasic model required (solid matrix plus fluid).
Creep: Fluid exudes under constant load. Cartilage thickness decreases with sustained loading. Recovery occurs when load removed.
Clinical Relevance: Joint loading patterns affect cartilage health. Cyclic loading may be protective. Prolonged static loading may be harmful.
Ligaments and Tendons
Viscoelastic Properties: Strongly viscoelastic. Exhibit all four key phenomena (creep, stress relaxation, hysteresis, rate-dependence).
Creep: ACL grafts elongate over time under constant tension. May contribute to residual laxity after reconstruction.
Stress Relaxation: Initial graft tension decreases. Surgeons may retension grafts or account for expected relaxation.
Rate Effects: Ligaments fail at higher loads when loaded rapidly. Low-rate testing underestimates functional strength.
Hysteresis: Energy dissipation protects joint during impact. Repeated loading causes progressive damage.
Preconditioning: Cyclical loading stabilizes viscoelastic response. Done before mechanical testing to obtain reproducible results.
Intervertebral Disc
Viscoelastic Properties: Highly viscoelastic. Fluid movement through nucleus pulposus and annulus fibrosus.
Creep: Disc height decreases during day due to fluid exudation under body weight loading. Height recovers overnight when unloaded in recumbent position. Young adults may lose up to twenty millimeters of height during a typical day.
Stress Relaxation: Intradiscal pressure decreases when spine held in fixed position.
Clinical Relevance: Diurnal variation affects spinal mechanics. Morning stiffness relates to overnight fluid accumulation. Disc degeneration alters viscoelastic properties.
Meniscus
Viscoelastic Properties: Moderately viscoelastic. Collagen fiber orientation affects behavior.
Role in Load Distribution: Viscoelastic damping absorbs impact. Protects articular cartilage from shock loading.
Effect of Injury: Meniscal tears alter viscoelastic properties. Meniscectomy removes shock-absorbing function.
Clinical Implications
Fracture Fixation
Creep of Fracture Reduction: Fracture alignment maintained by cast or external fixator may worsen over time due to creep of soft tissues. Serial radiographs monitor for loss of reduction.
Plate Relaxation: Compression plates lose some compression force over weeks. Dynamic compression continues as bone resorbs and remodels.
Wire Tension Loss: External fixator wires and circular frame wires lose tension. May require retensioning.
Ligament Reconstruction
Graft Tensioning: Initial tension applied during ACL reconstruction decreases due to stress relaxation. Some surgeons pretension grafts cyclically. Others account for expected relaxation.
Graft Elongation: Viscoelastic creep may contribute to residual laxity after reconstruction. Proper initial tension important.
Spinal Biomechanics
Disc Loading: Viscoelastic properties of disc allow load sharing with facets over time. Affects intradiscal pressure measurements.
Spinal Instrumentation: Viscoelastic settling affects construct behavior. Loss of disc height after fusion affects adjacent segments.
Arthroplasty
Polyethylene Creep: Ultra-high molecular weight polyethylene is viscoelastic. Creep contributes to deformation and wear. Highly crosslinked polyethylene reduces creep.
Soft Tissue Balancing: Ligament stress relaxation affects stability. Initial tight soft tissue balance may loosen.
Injury Biomechanics
Loading Rate Effect: High-energy trauma produces different injury patterns than low-energy trauma. Bone fragments differ. Soft tissue damage differs.
Energy Absorption: Viscoelastic tissues absorb impact energy through hysteresis. Protects deeper structures.
Testing and Measurement
Creep Test
Protocol: Apply constant load. Measure deformation over time. Plot strain versus time.
Result: Creep curve showing primary, secondary, and sometimes tertiary creep.
Parameters Measured: Initial elastic strain, time-dependent strain, creep rate, equilibrium strain.
Stress Relaxation Test
Protocol: Apply constant deformation. Measure force over time. Plot stress versus time.
Result: Exponential decay curve.
Parameters Measured: Initial stress, relaxation time constant, equilibrium stress.
Hysteresis Measurement
Protocol: Cyclically load and unload specimen. Plot stress versus strain for complete cycle.
Result: Hysteresis loop. Loading curve above unloading curve.
Parameters Measured: Area of hysteresis loop (energy dissipated), loop width.
Dynamic Mechanical Analysis
Protocol: Apply sinusoidal oscillating load. Measure resulting strain.
Result: Storage modulus (elastic component), loss modulus (viscous component), phase lag.
Application: Characterizes frequency-dependent viscoelastic properties.
Laboratory Testing Methods
Testing Protocols
Creep Testing:
- Apply constant load
- Measure deformation over time
- Plot strain vs time curve
Stress Relaxation Testing:
- Apply constant deformation
- Measure force decay over time
- Plot stress vs time curve
Testing Methods
| Test Type | Control Variable | Measured Variable |
|---|---|---|
| Creep | Constant load | Deformation over time |
| Relaxation | Constant strain | Force over time |
| Hysteresis | Cyclic loading | Energy dissipation |
| DMA | Sinusoidal load | Phase lag, moduli |
Clinical Applications
Managing Viscoelastic Effects
Fracture Fixation:
- Account for creep in reduction
- Serial X-rays for alignment loss
- Consider stress relaxation in casts
Ligament Reconstruction:
- Pretensioning minimizes relaxation
- Account for expected tension loss
- Cyclic conditioning of grafts
Clinical Considerations
| Procedure | Viscoelastic Issue | Management |
|---|---|---|
| Casting | Stress relaxation | Serial checks, rewedging |
| ACL recon | Graft relaxation | Pretension, account for loss |
| External fix | Wire tension loss | Retensioning protocol |
Surgical Considerations
Intraoperative Factors
Graft Tensioning:
- Apply cyclic pretensioning
- Allow for stress relaxation
- Final tension after settling
Reduction Maintenance:
- Viscoelastic settling occurs
- Initial over-correction may help
- Serial imaging essential
Surgical Techniques
| Procedure | Technique | Rationale |
|---|---|---|
| ACL graft | Cyclic pretensioning | Reduce relaxation |
| Fracture | Slight over-reduction | Account for settling |
| Wire fixation | Retension at 2 weeks | Relaxation occurs |
Complications from Viscoelastic Behavior
Clinical Consequences
Creep-Related:
- Loss of fracture reduction
- ACL graft laxity over time
- Disc subsidence in spine surgery
Relaxation-Related:
- Cast loosening
- External fixator wire loosening
- Plate compression loss
Prevention Strategies
| Problem | Cause | Prevention |
|---|---|---|
| Reduction loss | Creep | Serial imaging, timely revision |
| Graft laxity | Relaxation | Pretensioning, proper initial tension |
| Cast loosening | Relaxation | Serial assessment, rewedging |
Postoperative Considerations
Rehabilitation Implications
Loading Protocols:
- Progressive loading respects tissue adaptation
- Cyclic loading can be protective
- Avoid prolonged static loading
Monitoring:
- Serial imaging for alignment
- Clinical assessment for stability
- Early intervention if settling
Postoperative Monitoring
| Procedure | Timepoint | Assessment |
|---|---|---|
| Fracture | Weekly x 3 | Alignment, reduction |
| ACL recon | 3, 6, 12 months | Laxity, function |
| External fix | 2 weeks | Wire tension |
Outcomes and Clinical Relevance
Clinical Significance
Understanding Improves Outcomes:
- Better fracture management
- Improved graft tensioning
- Appropriate material selection
Key Takeaways:
- All tissues are viscoelastic
- Time-dependent behavior affects surgery
- Material properties influence implant success
Clinical Applications
| Area | Application | Benefit |
|---|---|---|
| Fracture care | Account for settling | Better alignment |
| ACL surgery | Pretensioning | Reduced laxity |
| Arthroplasty | HXLPE selection | Reduced wear |
Evidence Base
- Comprehensive treatment of viscoelasticity in biological tissues
- Quasi-linear viscoelastic theory developed
- Mathematical models for tissue behavior
- Foundation for modern tissue biomechanics
- Comprehensive coverage of viscoelastic theory
- Mathematical models and measurement techniques
- Applications to biomedical materials
- Creep and stress relaxation detailed
- Developed models for soft tissue viscoelasticity
- Accounted for large deformations
- Experimental validation on ligaments
- Improved prediction of tissue response
- Characterized viscoelastic properties of knee ligaments
- Demonstrated strain-rate sensitivity
- Showed hysteresis and preconditioning effects
- Clinical implications for ACL reconstruction
Exam Viva Scenarios
Practice these scenarios to excel in your viva examination
Scenario 1: Explaining Viscoelasticity
"What is viscoelasticity and how is it relevant to orthopaedic tissues?"
Scenario 2: Creep vs Stress Relaxation
"Explain the difference between creep and stress relaxation with clinical examples."
Scenario 3: Clinical Application
"How does strain-rate sensitivity affect injury patterns in high-energy versus low-energy trauma?"
MCQ Practice Points
Creep Definition
Q: What is creep in viscoelastic materials? A: Progressive increase in deformation under constant load. Example: disc height decreases during the day under body weight.
Stress Relaxation Definition
Q: What is stress relaxation? A: Progressive decrease in force required to maintain constant deformation. Example: casts become loose as tissues relax.
Hysteresis
Q: What does hysteresis represent? A: Energy dissipation during loading-unloading cycles. Area between loading and unloading curves represents energy lost as heat.
Maxwell Model
Q: What does the Maxwell viscoelastic model consist of? A: Spring and dashpot in series. Models stress relaxation behavior well.
Kelvin-Voigt Model
Q: What does the Kelvin-Voigt model consist of? A: Spring and dashpot in parallel. Models creep behavior well.
Strain-Rate Sensitivity
Q: How do materials behave at higher strain rates? A: Stiffer and stronger. High-energy trauma produces more comminuted fractures because bone is stronger but more brittle at impact rates.
Australian Context
Clinical Practice: Understanding viscoelasticity informs fracture management, ligament reconstruction techniques, and spinal surgery in Australia. Strain-rate effects relevant for trauma management.
Research: Australian biomechanics laboratories study viscoelastic properties of tissues and implant materials. Finite element modeling incorporates viscoelastic behavior.
Education: Viscoelasticity is core curriculum for orthopaedic training. Essential for understanding tissue mechanics and injury biomechanics.
Management Algorithm
VISCOELASTICITY
High-Yield Exam Summary
Core Concepts
- •Time-dependent behavior combining elastic and viscous properties
- •All biological tissues are viscoelastic
- •Four key phenomena: CRHS mnemonic
- •Temperature-dependent behavior
Creep
- •Constant load → increasing deformation
- •Example: disc height loss during day
- •Example: fracture reduction loss in cast
- •Three phases: primary, secondary, tertiary
Stress Relaxation
- •Constant deformation → decreasing force
- •Example: cast becomes loose over time
- •Example: ACL graft loses initial tension
- •Exponential decay with time
Hysteresis
- •Energy dissipation in loading cycles
- •Loading and unloading curves differ
- •Area between curves = lost energy
- •Protective impact absorption
Strain-Rate Sensitivity
- •Higher rates → stiffer and stronger
- •High-energy trauma causes comminution
- •Static testing underestimates dynamic strength
- •Physiological rates needed for testing
Mathematical Models
- •Maxwell (series): stress relaxation
- •Kelvin-Voigt (parallel): creep
- •Standard Linear Solid: both behaviors
- •QLV for soft tissues (Fung)
Clinical Applications
- •Bone: moderate viscoelasticity, rate-sensitive
- •Ligaments: strong viscoelasticity, all phenomena
- •Disc: highly viscoelastic, diurnal variation
- •Cartilage: biphasic, fluid flow effects
Key Numbers
- •Disc height: up to 20mm loss per day
- •Bone modulus: ~30% higher at impact rates
- •Wire tension: decreases over days-weeks
- •Preconditioning: stabilizes tissue response