What to Calculate: The deformed shape of a structure or component subjectedto mechanical, thermal, or electrical loading: The forces required to cause a particular shape change. The stiffness of a structure or component: The internal forces (stresses) in a structure or component. The critical forces that lead to failure by structuralinstability (buckling)? Natural frequencies of vibration for a structure orcomponent16
• The deformed shape of a structure or component subjected to mechanical, thermal, or electrical loading • The forces required to cause a particular shape change • The stiffness of a structure or component • The internal forces (stresses) in a structure or component • The critical forces that lead to failure by structural instability (buckling) • Natural frequencies of vibration for a structure or component What to Calculate 16
What to Calculate. Predicting the critical loads to cause fracture in a brittle orductile solid containing a crack. Predicting the fatigue life of a component under cyclicloading? Predicting the rate of growth of a stress-corrosion crack ina component? Predicting the creep life of a component? Finding the length of a crack that a component can containand still withstand fatigue or fracture? Predicting the wear rate of a surface under contact loading? Predicting the fretting or contact fatigue life of a surface17
• Predicting the critical loads to cause fracture in a brittle or ductile solid containing a crack • Predicting the fatigue life of a component under cyclic loading • Predicting the rate of growth of a stress-corrosion crack in a component • Predicting the creep life of a component • Finding the length of a crack that a component can contain and still withstand fatigue or fracture • Predicting the wear rate of a surface under contact loading • Predicting the fretting or contact fatigue life of a surface What to Calculate 17
What to Calculate. Calculating the properties (e.g., elastic modulus, yield stress, stress-strain curve,fracture toughness, etc.) of a composite material in terms of those of itsconstituents. Predicting the influence of the microstructure (e.g., texture, grain structure,dispersoids, etc.) on the mechanical properties of metals such as modulus, yieldstress, strain hardening, etc.. Modeling the physics of failure in materials, including fracture, fatigue, plasticityand wear, and using the models to design failure resistant materials: Modeling materials processing, including casting and solidification, alloy heattreatments, and thin-film and surface-coating deposition (e.g., by sputtering,vapor deposition, or electroplating) Modeling biological phenomena and processes, such as bone growth, cellmobility, cell wall/particle interactions, and bacterial mobility18
• Calculating the properties (e.g., elastic modulus, yield stress, stress-strain curve, fracture toughness, etc.) of a composite material in terms of those of its constituents • Predicting the influence of the microstructure (e.g., texture, grain structure, dispersoids, etc.) on the mechanical properties of metals such as modulus, yield stress, strain hardening, etc. • Modeling the physics of failure in materials, including fracture, fatigue, plasticity, and wear, and using the models to design failure resistant materials • Modeling materials processing, including casting and solidification, alloy heat treatments, and thin-film and surface-coating deposition (e.g., by sputtering, vapor deposition, or electroplating) • Modeling biological phenomena and processes, such as bone growth, cell mobility, cell wall/particle interactions, and bacterial mobility What to Calculate 18
Geometry: Geometry is important for modeling brittle fracture.fatigue failure, or for calculating critical loads required toinitiate plastic flow in a component.? Less important for creep damage, large-scale plasticdeformation (e.g., metal forming) or vibration analysis: Geometrical features typically only influence localstresses. (≤ 3L): Start with the simplest possible model and graduallyrefine the calculation19
• Geometry is important for modeling brittle fracture, fatigue failure, or for calculating critical loads required to initiate plastic flow in a component. • Less important for creep damage, large-scale plastic deformation (e.g., metal forming) or vibration analysis. • Geometrical features typically only influence local stresses. (≤ 3L) • Start with the simplest possible model and gradually refine the calculation. Geometry 19
Loading.Displacement boundary conditions S,: Traction boundary conditions, either normal or tangential or both, S. Mixed boundary conditions, e.g. horizontal displacements + verticaltraction at a point. Gravitational or electromagnetic body forces.Contactforces: Nonuniform thermal expansion Materials process such as phase transformation that causes the solidto change its shape20
• Displacement boundary conditions Su • Traction boundary conditions, either normal or tangential or both, St • Mixed boundary conditions, e.g. horizontal displacements + vertical traction at a point • Gravitational or electromagnetic body forces • Contact forces • Nonuniform thermal expansion • Materials process such as phase transformation that causes the solid to change its shape Loading 20