Introduction to Biomechanics and Mechanical Properties of Dental Materials

Fundamentals of Biomechanics in Dentistry

• Definitions and Primary Concepts:

  • Mechanics: The branch of science that studies the effect of force acting on physical bodies.

  • Biomechanics: The science that applies the principles of mechanics to study the structure, function, and effects of force on biological systems or living organisms (Hatze H, 1974; Hall SJ, 2019).

  • Dental Application: Biomechanics utilizes mechanical principles to analyze physiological functions and solve clinical problems related to human health, tissue injury, and functional rehabilitation in the oral cavity.

• Multidisciplinary Nature of Biomechanics:

  • Biomechanics sits at the intersection of numerous scientific and clinical disciplines:

  • Medicine & Dentistry: Guides medical therapy and dental restorative/regenerative therapy.

  • Health Sciences: Informs occupational therapy and physiotherapy.

  • Engineering: Underpins the design and structural testing of biomedical devices and implants.

  • Kinesiology: Examines movement science, motor control, and functional human physiology.

  • Sports Science: Focuses on optimizing athletic performance and reducing injury risk.

  • Natural Sciences: Informs structural biology and physical anthropology.

  • Mathematics: Provides analytical foundations through calculus and algebra.

• Biomaterials and Mechanical Behavior:

  • Biomaterial Definition: Any substance or material designed to interact with biological systems to replace, repair, or enhance injured or missing tissues and organs.

  • Functional Requirement: When introduced into a biological system, biomaterials are expected to withstand physiological loads and behave functionally like the natural anatomical structures they replace.

  • The Stomatognathic System:

  • The specific anatomical system of primary interest in dentistry.

  • Comprises the teeth, maxilla, mandible (jaws), temporomandibular joints (TMJ), periodontal apparatus, and all associated dynamic soft tissues (muscles, nerves, vasculature).

  • Primary functions include mastication, deglutition (swallowing), speech, and respiration.

  • All stomatognathic functions rely directly on dynamic and mechanical activities.

  • Environmental Challenges: Dental biomaterials placed in the stomatognathic environment face concurrent chemical, biological, physical, and mechanical stresses. To avoid clinical failure, materials must meet strict mechanical standards.

Clinical Scenarios and Challenges in Dental Specialties

• Restorative Dentistry:

  • Natural tooth structures—including enamel, dentin, cementum, and dental pulp—are subjected to continuous, cyclic mechanical loading and unloading during mastication and parafunction.

  • Restorative materials (such as dental composites, ceramics, and amalgams) must endure identical stress cycles without fracturing, deforming, or losing marginal integrity.

• Endodontics:

  • Endodontically treated teeth often suffer significant structural loss.

  • Fiber-reinforced posts placed within root canals to retain coronal restorations are subjected to repetitive fatigue loading, bending moments, and shear forces during function.

• Prosthodontics:

  • Fixed prostheses (crowns, bridges) and removable partial or complete dentures replace missing dental and oral structures.

  • Materials must tolerate long-term cyclical intraoral forces across broad surface areas while retaining dimensional stability and structural integrity.

• Implantology:

  • Dental implants serve as artificial root replacements anchorable directly in alveolar bone.

  • Implants and their associated abutments and crowns transfer high-magnitude occlusal loads directly to bone tissue, demanding high yield strength and resistance to fatigue failure.

• Temporomandibular Joint (TMJ) Prostheses:

  • Total TMJ replacement devices undergo lifetime cycles of joint loading, translation, and rotation.

  • Prosthetic joints require superior wear resistance, high fatigue strength, and mechanical durability.

• Orthodontics:

  • Orthodontic therapy deliberately applies controlled mechanical forces to induce bone remodeling and tooth movement.

  • Archwires, brackets, and elastomeric components depend on predictable mechanical behaviors (such as elastic storage and continuous force delivery) to achieve precise tooth realignment.

Biomechanical Axioms and Principles in the Oral Environment

• Axiomatic Parameters of Mechanics:

  • Axiom: An indemonstrable first principle, rule, or maxim accepted based on intrinsic merit or self-evidence.

  • Force (Load):

  • The physical action or interaction occurring between at least two bodies. When one body directly contacts or acts upon another, a force is generated.

  • Forces load interacting bodies reciprocally (one body loads the second, and the second loads the first).

  • Defined by three mandatory parameters: point of application, magnitude, and direction of application.

  • The terms force and load are used interchangeably in dental biomechanics.

  • Stress:

  • The internal reaction or resistance generated within a physical body subjected to an applied external load.

  • Stress cannot be measured directly; it is calculated as the ratio of applied force ($F$) to the cross-sectional area ($A$) over which it acts:

$\text{Stress} = \frac{\text{Force}}{\text{Area}}$

* Standard SI unit: Newtons per square meter ($\text{N/m}^2$) or Pascals ($\text{Pa}$).

• Mandibular Kinematics and Masticatory Forces:

  • Hinge Axis: An imaginary transverse line connecting the rotation centers of the mandibular condyles, around which the mandible can rotate purely without translational movement.

  • Terminal Hinge Position: The most retruded physiological position of the mandible along the hinge axis. It represents a learnable, repeatable, and recordable position that coincides with Centric Relation (CR).

  • Occlusal Force Distribution:

  • Maximum occlusal forces in humans range from $200\,\text{N}$ to $3500\,\text{N}$.

  • Force magnitude varies anatomically: it is highest in the posterior regions (molars) due to proximity to the mandibular hinge axis and muscle attachments, and progressively decreases toward the anterior regions (incisors).

  • Occlusal force increases nonlinearly with age and skeletal growth in developing children.

  • Magnitude varies significantly between individuals based on age, gender, facial skeletal morphology, and neuromuscular efficiency/tonus.

• Key Restorative Planning Factors:

  • When designing dental restorations and selecting materials, three primary factors must be evaluated:

  1. Anatomical Tooth Location: Dictates the direction and magnitude of functional loads (posterior vs. anterior).

  2. Force-Generating Capacity: Individual patient variation in muscle tonus and bite force capability (e.g., severe bruxers vs. light biters).

  3. Type of Opposing Dentition: Restorative choices depend heavily on whether the opposing arch consists of natural dentition, ceramic restorations, metallic prostheses, or removable dentures.

  • Clinical evidence of previous restoration failure or natural tooth fracture serves as a direct indicator of elevated mechanical demands in a given patient.

Mechanical Properties and Stress-Strain Behavior of Dental Biomaterials

• Core Mechanical Property Definitions:

  • Mechanical properties quantify a material's capacity to resist deformation, structural fatigue, crack propagation, or outright fracture under applied loads.

  • Mechanical performance depends directly on internal material atomic structure, environmental intraoral conditions (moisture, thermal changes, pH), and masticatory load profiles.

• The Stress-Strain Relationship:

  • Stress-Strain Curve: A graphical plot depicting internal stress generated in a material relative to the resulting deformation (strain) across varying increments of load.

  • The curve is unique to each individual material composition and structure.

  • Strain: The relative linear or volumetric deformation caused by applied stress ($\text{Strain} = \frac{\Delta L}{L_0}$).

• Critical Points on the Stress-Strain Curve:

  • Proportional Limit (PL) / Elastic Limit (EL): The maximum stress at which stress remains directly proportional to strain (the linear portion of the curve). Below the PL, material deformation is purely elastic; removing the load allows the material to return completely to its original dimensions.

  • Yield Stress (YS) / Yield Strength: The stress threshold marking the boundary between elastic deformation and permanent (plastic) deformation. For most dental biomaterials, the Proportional Limit, Elastic Limit, and Yield Stress coincide functionally.

  • Ultimate Tensile Strength (UTS): The maximum stress a material withstands before structural failure under tensile (pulling) loading.

  • Ultimate Compressive Strength (UCS): The maximum stress a material withstands before structural failure under compressive (crushing) _.

  • Fracture Stress: The precise stress level recorded at the moment of material fracture. Can result from tensile, compressive, shear, or flexural stresses.

• Elastic and Energy Absorption Properties:

  • Modulus of Elasticity (Elastic Modulus or Young's Modulus, $E$):

  • Calculated as the slope (ratio of stress to strain) within the linear elastic region of the stress-strain curve:

$E = \frac{\text{Stress}}{\text{Strain}}$

* Measures a material's intrinsic stiffness or rigidity. A high elastic modulus indicates a stiff material that resists elastic deflection; a low modulus indicates a flexible material.

• Resilience:

  • The capacity of a material to absorb energy when deformed elastically without undergoing permanent deformation.

  • Quantified as the total area under the elastic region of the stress-strain curve (from zero up to the proportional limit).

• Toughness:

  • The total energy required to cause complete fracture of a material.

  • Quantified as the total area under both the elastic and plastic regions of the stress-strain curve (from zero to the point of fracture).

  • Summary Table of Biomaterial Mechanical Properties:

• Proportional & Elastic Limits: Define elastic resistance and the upper boundary of non-permanent elastic deformation.

• Yield Strength: Represents the borderline threshold between elastic and plastic (permanent) deformation.

• Resilience: Measures material resistance to permanent plastic deformation under energy input.

• Toughness: Measures material resistance to ultimate mechanical fracture.

• Elastic Modulus ($E$): Quantifies the degree of rigidity or flexibility of a material.

• Tensile Strength: Measures ultimate resistance to fracture when pulled along a single axis.

• Compressive Strength: Measures ultimate resistance to fracture when compressed or crushed along a single axis.

• Fatigue Resistance: Represents the ability to withstand cyclic, repeated mechanical loading and unloading cycles without sub-critical crack growth.

• Hardness: Measures surface resistance to permanent penetration, indentation, or scratching.

• Flexural Strength: Measures resistance to fracture when subjected to complex combined tensile, compressive, and shear forces (bending).