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Science of predicting if, when, and how a given material will fail under loading
Material failure theory is an interdisciplinary field of materials science and solid mechanics which attempts to predict the conditions under which solid
Material_failure_theory
Mathematical model in materials science
engineering materials follow this rule in at least a portion of their shear failure envelope. Generally the theory applies to materials for which the
Mohr–Coulomb_theory
Composite materials failure criterion
Tsai–Hill failure criterion is one of the phenomenological material failure theories, which is widely used for anisotropic composite materials which have
Tsai-Hill_failure_criterion
Test for predicting engineering failures
The Tsai–Wu failure criterion is a phenomenological material failure theory which is widely used for anisotropic composite materials which have different
Tsai–Wu_failure_criterion
Equation for quantifying the effect of stress cycles on the working life of a material
Within the branch of materials science known as material failure theory, the Goodman relation (also called a Goodman diagram, a Goodman-Haigh diagram,
Goodman_relation
loading and its susceptibility to various failure modes takes into account the properties of the materials, such as yield strength, ultimate strength
Strength_of_materials
Failure Theory in continuum mechanics
material begins when the second invariant of deviatoric stress J 2 {\displaystyle J_{2}} reaches a critical value. It is a part of plasticity theory that
Von_Mises_yield_criterion
Branch of mechanics concerned with solid materials and their behaviors
solid mechanics examines the shear stress, deformation and the failure of solid materials and structures. The most common topics covered in solid mechanics
Solid_mechanics
strength theory (UST). proposed by Yu Mao-Hong is a series of yield criteria (see yield surface) and failure criteria (see Material failure theory). It is
Unified_strength_theory
Liquid, gas, or other continuously deforming and flowing material
In physics, a fluid is a liquid, gas, or other material that may continuously move and deform (flow) under an applied shear stress, or external force.
Fluid
Christensen failure criterion is a material failure theory for isotropic materials that attempts to span the range from ductile to brittle materials. It has
Christensen_failure_criterion
Principle relating to fluid dynamics
incorrect, explanations can be labeled the "Longer Path" theory, or the "Equal Transit Time" theory. Smith, Norman F. (November 1972). "Bernoulli and Newton
Bernoulli's_principle
Scientific law that a closed system's mass remains constant
processes in an isolated system, the total mass of the reactants, or starting materials, must be equal to the mass of the products. The concept of mass conservation
Conservation_of_mass
Materials engineered to have properties that have not yet been found in nature
; Itoh, T. (2002). "Application of the transmission line theory of left-handed (LH) materials to the realization of a microstrip "LH line"". IEEE Antennas
Metamaterial
Type of fluid
pour from the bottle. Under certain circumstances, flows of granular materials can be modelled as a continuum, for example using the μ(I) rheology. Such
Non-Newtonian_fluid
Study of propagation of cracks in materials
propagation of cracks in a material due to cyclic loading Fault (geology) – Fracture or discontinuity in displaced rock Material failure theory – Science of predicting
Fracture_mechanics
Relative deformation of a physical body
plastically-deforming materials and other fluids and biological soft tissue. Infinitesimal strain theory, also called small strain theory, small deformation theory, small
Strain_(mechanics)
Non-reversible deformation of a solid material in response to applied forces
of ductile materials could be explained in terms of the theory of dislocations. The mathematical theory of plasticity, flow plasticity theory, uses a set
Plasticity_(physics)
Deflection of a spinning object moving through a fluid
of the Mathematicks in the University of Cambridge; containing his new theory about light and colors: sent by the author to the publisher from Cambridge
Magnus_effect
Relationship between volume and temperature of a gas at constant pressure
temperature T (in degrees Celsius), V0 is the volume at 0 °C. The kinetic theory of gases relates the macroscopic properties of gases, such as pressure and
Charles's_law
Ability of a liquid to flow in narrow spaces
in a thin tube such as a straw, in porous materials such as paper and plaster, in some non-porous materials such as clay and liquefied carbon fiber, or
Capillary_action
State of matter
theory and advanced methods. Cambridge: Cambridge University Press. ISBN 978-0-521-89863-8. OCLC 869135580. Fisher, I.Z. (1964), Statistical Theory of
Liquid
Mathematical model for describing material deformation under stress
In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains
Finite_strain_theory
Branch of physics
University of Chicago Press. Temam, R. (2001). Navier-Stokes equations: theory and numerical analysis (Vol. 343). American Mathematical Society. Foias
Fluid_mechanics
Force needed to pull a spring grows linearly with distance
change of state. Many materials will noticeably deviate from Hooke's law well before those elastic limits are reached. The modern theory of elasticity generalizes
Hooke's_law
Buoyancy principle in fluid dynamics
analogous to the idea of Archimedes' principle. Ship stability – Archimedes's theory of displacement of fluid is a core principle of ship stability. List of
Archimedes'_principle
Physical property when materials or objects return to original shape after deformation
gradient (F) is the primary deformation measure used in finite strain theory. A material is said to be Cauchy-elastic if the Cauchy stress tensor σ is a function
Elasticity_(physics)
Concept in fluid dynamics
increasing Knudsen number, which implies increasing rarefaction, and gradual failure of the continuum approximation. The first-order expression, which is often
No-slip_condition
Law of physics and chemistry
everything is made. However, there is no particular reason to identify their theories with what we know today as "mass-energy" (for example, Thales thought it
Conservation_of_energy
Relation between gas pressure and volume
explanation for the observed relationship. Instead of a static theory, a kinetic theory is needed, which was developed over the next two centuries by Daniel
Boyle's_law
State of matter
Introduction to Plasma Theory. John Wiley & Sons. ISBN 978-0-471-09045-8. Hamrang, Abbas (2014). Advanced Non-Classical Materials with Complex Behavior:
Plasma_(physics)
Mathematical model for describing material deformation under stress
infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles
Infinitesimal_strain_theory
Force distributed over an area
term "pressure" will refer only to the scalar pressure. According to the theory of general relativity, pressure increases the strength of a gravitational
Pressure
Property of substances whose particles stick together
creating a "solid-like" state upon which light-weight or low-density materials can be placed. Water, for example, is strongly cohesive as each molecule
Cohesion_(chemistry)
Relationship between pressure and temperature of a gas at constant volume
published in 1809. Since there was no direct evidence for Avogadro's molecular theory, very few chemists adopted Avogadro's hypothesis as generally valid until
Gay-Lussac's_law
Process of a gas escaping through a small hole
equilibrated container into outside vacuum can be calculated based on kinetic theory. The number of atomic or molecular collisions with a wall of a container
Effusion
Property of materials with both viscous and elastic characteristics under deformation
viscoelastic materials exhibit rubber like behavior explained by the thermodynamic theory of polymer elasticity. Some examples of viscoelastic materials are amorphous
Viscoelasticity
Aspects of fluid mechanics involving fluid flow
accounts for the relativistic effects both from the special theory of relativity and the general theory of relativity. The governing equations are derived in
Fluid_dynamics
Quantity in fracture mechanics; predicts stress intensity near a crack's tip
applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials, and is a critical technique in the
Stress_intensity_factor
This article summarizes equations in the theory of fluid mechanics. Here t ^ {\displaystyle \mathbf {\hat {t}} \,\!} is a unit vector in the direction
List of equations in fluid mechanics
List_of_equations_in_fluid_mechanics
Equation in fluid dynamics
transferring more momentum to the pipe wall, as modeled in Blasius boundary layer theory. When the pipe surface's roughness height ε is significant (typically at
Darcy–Weisbach_equation
Research of materials
biomaterials, metallurgy, and nanotechnology. Materials science is also used by forensic engineers and failure analysts to understand why and how critical
Materials_science
Tendency of a liquid surface to shrink to reduce surface area
used to reduce it so there is more contact between the liquid and another material, for instance detergents. It can also lead to pressure inside water bubbles
Surface_tension
Mathematical model of how solid objects deform
loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics. The fundamental assumptions
Linear_elasticity
Study of the deformation of solids that touch each other
case of adhesive contact. This theory was rejected by Boris Derjaguin and co-workers who proposed a different theory of adhesion in the 1970s. The Derjaguin
Contact_mechanics
Type of fluid
demonstrated for monoatomic gas both experimentally and from the kinetic theory; for other gases and liquids, Stokes hypothesis is generally incorrect.
Newtonian_fluid
State of matter
much energy a material can absorb before mechanical failure, while fracture toughness (denoted KIc) describes the ability of a material with inherent
Solid
Resistance of a fluid to shear deformation
limit. Transport theory provides an alternative interpretation of viscosity in terms of momentum transport: viscosity is the material property which characterizes
Viscosity
Model of electrically conducting fluids
MHD theory for plasmas. This concerned the neglect of the "Hall current term" in Ohm's law, a frequent simplification made in magnetic fusion theory. Hall
Magnetohydrodynamics
Constitutive model for ideally elastic material
material is a special case of a Cauchy elastic material. For many materials, linear elastic models do not accurately describe the observed material behaviour
Hyperelastic_material
Study of the flow of matter, primarily in a fluid state
additives, bodily fluids (e.g., blood) and other biological materials, and other materials that belong to the class of soft matter such as food. Newtonian
Rheology
Equation describing the evolution of the vorticity of a fluid particle as it flows
\left({\frac {\mathbf {B} }{\rho }}\right)\end{aligned}}} where D/Dt is the material derivative operator, u is the flow velocity, ρ is the local fluid density
Vorticity_equation
Law describing the pressure drop in an incompressible and Newtonian fluid
wichtigsten Anwendungen. Basel: Birkhäuser Verlag. Stokes, G. G. (1845). "On the theories of the internal friction of fluids in motion, and of the equilibrium and
Hagen–Poiseuille_equation
Equation describing the transport of some quantity
density at each point, then j would be the mass flux, also known as the material discharge. In a well-known example, the flux of electric charge is the
Continuity_equation
Physical quantity that expresses internal forces in a continuous material
P. (1983). History of strength of materials: with a brief account of the history of theory of elasticity and theory of structures. Dover Books on Physics
Stress_(mechanics)
Molecular property
surroundings. There is no single theory covering adhesion, and particular mechanisms are specific to particular material scenarios. Five mechanisms of adhesion
Adhesion
National Defence, Canada, Valcartier, Quebec. http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA357607&Location=U2&doc=GetTRDoc.pdf Failure Material failure theory
Johnson–Holmquist damage model
Johnson–Holmquist_damage_model
Hyperelastic material model
incompressible neo-Hookean material. Mathematics and Mechanics of Solids, 20(2), 157–182. [1] "Abaqus (Version 6.8) Theory Manual". Strain energy density
Neo-Hookean_solid
Material designed to manipulate sound waves
Microwave Theory and Techniques. 45 (12): 2267. Bibcode:1997ITMTT..45.2267E. doi:10.1109/22.643830. A facility of the NSF provides added material to the
Acoustic_metamaterial
Perpendicular-axis marine propulsion system
of attack during each revolution, and their eccentric mounting could, in theory, produce nearly any combination of horizontal and vertical forces. The DVL
Cyclorotor
Set of laboratory techniques for separation of mixtures
a system (a column, a capillary tube, a plate, or a sheet) on which a material called the stationary phase is fixed. As the different constituents of
Chromatography
Sub-discipline of systems engineering that emphasizes dependability
engineering that emphasizes the ability of equipment to function without failure. Reliability is defined as the probability that a product, system, or service
Reliability_engineering
Process of pushing material through a die to create long symmetrical-shaped objects
process used to create objects of a fixed cross-sectional profile by pushing material through a die of the desired cross-section. Its two main advantages over
Extrusion
Equations of motion for viscous fluids
where D D t {\textstyle {\frac {\mathrm {D} }{\mathrm {D} t}}} is the material derivative, defined as ∂ ∂ t + u ⋅ ∇ {\textstyle {\frac {\partial }{\partial
Navier–Stokes_equations
Process of mechanically stirring a heterogeneous mixture to homogenize it
of ergodic theory, itself a part of chaos theory. The type of operation and equipment used during mixing depends on the state of materials being mixed
Mixing_(process_engineering)
Hyperelastic material model
1948, Large elastic deformations of isotropic materials. IV. Further developments of the general theory, Philosophical Transactions of the Royal Society
Mooney–Rivlin_solid
Fluid whose properties can be changed by applying an electric or magnetic field
Continuum mechanics – Branch of physics which studies the behavior of materials modeled as continuous media Electrorheological fluid – Type of chemical
Smart_fluid
Smart fluid whose viscosity increases in a magnetic field
model the fluid mathematically, a task slightly complicated by the varying material properties (such as yield stress). As mentioned above, smart fluids are
Magnetorheological_fluid
Failure of the heart to provide sufficient blood flow throughout the body
Heart failure (HF), also known as congestive heart failure (CHF), is a syndrome caused by an impairment in the heart's ability to fill with and pump blood
Heart_failure
Concept in physics
criterion are Yield surface Yield (engineering) Plasticity (physics) Material failure theory Daniel C. Drucker William Prager Drucker, D. C. and Prager, W.
Drucker–Prager yield criterion
Drucker–Prager_yield_criterion
Branch of physics which studies the behavior of materials modeled as continuous media
elastic material Configurational mechanics Curvilinear coordinates Equation of state Finite deformation tensors Finite strain theory Hyperelastic material Knudsen
Continuum_mechanics
Ability to attribute mental states to oneself and others
joint-attention behaviors, which may lead to a failure to form a full theory of mind. It has been speculated that theory of mind exists on a continuum as opposed
Theory_of_mind
Mathematical model of the stresses within flat plates under loading
Kirchhoff–Love theory of plates (classical plate theory) The Reissner–Mindlin theory of plates (first-order shear plate theory) The Kirchhoff–Love theory is an
Plate_theory
Liquid that is attracted by poles of a magnet
using a surfactant, and thus ferrofluids are colloidal suspensions – materials with properties of more than one state of matter. In this case, the two
Ferrofluid
Theory describing the behaviour of three-layered structures or materials
most commonly used sandwich theory is linear and is an extension of first-order beam theory. The linear sandwich theory is of importance for the design
Sandwich_theory
Enrichment of atoms, ions, and molecules
segregation behavior that results in the intergranular failures of engineering materials. More complex theories are detailed in the work by Guttmann and McLean
Segregation (materials science)
Segregation_(materials_science)
Concept in contact mechanics
angle θ0 can not be derived from the theory. They must be measured. For a given system — given diameters and materials —, thus for given K and clearance
Bearing_pressure
Scientific instrument used to measure fluid flow (rheology)
as well as for quality control in the manufacturing of a wide range of materials. Dynamic shear rheometers have been used since 1993 when Superpave was
Rheometer
Transformation of a body from a reference configuration to a current configuration
expressed by constitutive equations, e.g., Hooke's law for linear elastic materials. Deformations which cease to exist after the stress field is removed are
Deformation_(physics)
Initiation and propagation of cracks in a material due to cyclic loading
the material, producing rapid propagation and typically complete fracture of the structure. Fatigue has traditionally been associated with the failure of
Fatigue_(material)
Physical condition
leave a body in a compatible state. In the context of infinitesimal strain theory, these conditions are equivalent to stating that the displacements in a
Compatibility_(mechanics)
Calculation of strain energy release rate
of Materials," 445–448. Yoda, M., 1980, The J-integral fracture toughness for Mode II, Int. J. Fracture, 16(4), pp. R175–R178. "J-integral Theory". COMSOL
J-integral
Measurement of fluid flow
experimental techniques used to determine the rheological properties of materials, that is the qualitative and quantitative relationships between stresses
Rheometry
strength Fracture Creep (deformation) Material Failure Theory H., Courtney, Thomas (2005). Mechanical behavior of materials. Waveland Press. ISBN 978-1577664253
Theoretical strength of a solid
Theoretical_strength_of_a_solid
Deviation with the scale in the theories of elastic or plastic structures
According to the classical theories of elastic or plastic structures made from a material with non-random strength (ft), the nominal strength (σN) of a
Size effect on structural strength
Size_effect_on_structural_strength
{\displaystyle \alpha } is the grain angle. Material failure theory Linear elasticity Hooke's law Orthotropic material Transverse isotropy Hankinson, R. L.,
Hankinson's_equation
mechanics of a material with a cubic representative volume element containing eight chains along the diagonal directions. The material is assumed to be
Arruda–Boyce_model
Taylor & Francis, 9780891165224 Salvi Rodolfo, The Navier Stokes equation theory and numerical methods, 2002, M. Dekker, 9780824706722 Fox, Robert W.; Alan
Non-dimensionalization and scaling of the Navier–Stokes equations
Non-dimensionalization_and_scaling_of_the_Navier–Stokes_equations
Type of chemical suspension
two main theories to explain the effect: the interfacial tension or 'water bridge' theory, and the electrostatic theory. The water bridge theory assumes
Electrorheological_fluid
Yield criterion
Mohr–Coulomb. Yield surface Yield (engineering) Plasticity (physics) Material failure theory Compaction of ceramic powders The Bigoni-Piccolroaz yield surface
Bigoni–Piccolroaz yield criterion
Bigoni–Piccolroaz_yield_criterion
The theory of micro-mechanics of failure aims to explain the failure of continuous fiber reinforced composites by micro-scale analysis of stresses within
Micro-mechanics_of_failure
Study of the deformation of bodies in the presence of frictional effects
existence and uniqueness theories. Over time, these grew into finite element approaches for contact problems with general material models and geometries
Frictional_contact_mechanics
Systemic risk of failure
A cascading failure is a failure in a system of interconnected parts in which the failure of one or few parts leads to the failure of other parts, growing
Cascading_failure
McIntyre (1981) Holm (2002) Andrews, D. G.; McIntyre, M. E. (1978a), "An exact theory of nonlinear waves on a Lagrangian-mean flow" (PDF), Journal of Fluid Mechanics
Generalized_Lagrangian_mean
times divergence of material flow equals deviatoric stress tensor times divergence of material flow minus pressure times material flow. h = e + p ρ {\displaystyle
First law of thermodynamics (fluid mechanics)
First_law_of_thermodynamics_(fluid_mechanics)
Conservable measure of the wave part of a motion
1098/rspa.1970.0205 Sturrock, P.A. (1962), "Energy and momentum in the theory of waves in plasmas", in Bershader, D. (ed.), Plasma Hydromagnetics. Sixth
Wave action (continuum mechanics)
Wave_action_(continuum_mechanics)
Strain caused by an external load
Sandwich theory Vibration Vibration of plates Boresi, A. P. and Schmidt, R. J. and Sidebottom, O. M., 1993, Advanced mechanics of materials, John Wiley
Bending
they sought an extension of the concept of an elastic material. The key assumption of their theory was that the local stress value at a time t depends upon
Materials_with_memory
Model of rubber elasticity
The Gent hyperelastic material model is a phenomenological model of rubber elasticity that is based on the concept of limiting chain extensibility. In
Gent_hyperelastic_model
Analysis of potential system failures
Failure mode and effects analysis (FMEA; often written with "failure modes" in plural) is the process of reviewing as many components, assemblies, and
Failure mode and effects analysis
Failure_mode_and_effects_analysis
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MATERIAL FAILURE-THEORY
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