Solid Mechanics

Solid mechanics , also known as the mechanics of solids , is the branch of continuum mechanics that studies the behavior of solid materials, particularly their motion and deformation under the action of forces , temperature changes, phase changes, and other external or internal agents.

Solid mechanics is fundamental to civil , aerospace , nuclear , biomedical and mechanical engineering , to geology , and to many branches of material science such as materials science. [1] It has specific applications in many other areas, such as understanding the anatomy of living beings, and the design of dental prostheses and surgical implants . One of the most common practical applications of solid mechanics is the Euler–Bernoulli beam equation . Solid mechanics extensively to describe stresses, stresses, and the relationships between them. Uses tensors. Solid mechanics is a vast subject because of the wide range of solid materials available, such as steel, wood, concrete, organic materials, textiles, geological materials and plastics.

Fundamental aspect

A solid is a material that can support a substantial amount of shear force over a given time scale during a natural or industrial process or action . This is what separates solids from liquids , because liquids also support normal forces which are those that force the material across the plane perpendicular to the direction from which they act and the normal stress is the normal force that per unit area of ​​the material plane. Shear forces act parallel rather than perpendicular to the physical plane, unlike normal forces, and the shear force per unit area is called shear stress .

Therefore, solid mechanics investigates the shear stress, deformation, and failure of solid materials and structures.

The most common topics covered in solid mechanics include:

  1. Stability of structures – checking whether structures can return to a given equilibrium after perturbation or partial/complete failure
  2. Dynamic systems and chaos – dealing with mechanical systems that are highly sensitive to their given initial state
  3. Thermomechanics – Analysis of materials with models derived from principles of thermodynamics
  4. Biomechanics – solid mechanics applied to biological materials such as bone, heart tissue
  5. Geomechanics – solid mechanics applied to geological materials such as ice, soil, rock
  6. Vibration of solids and structures – investigating vibration and wave propagation from vibrating particles and structures i.e. important in mechanical, civil, mining, aeronautical, marine/marine, aerospace engineering
  7. Fracture and damage mechanics – dealing with crack-growth mechanics in solid materials
  8. Composite materials – concrete mechanics applied to materials composed of more than one compound such as reinforced plastics , reinforced concrete , fiberglass
  9. Variable Formulation and Computational Mechanics – Numerical solutions of mathematical equations arising from various branches of solid mechanics such as Finite Element Method (FEM)
  10. Experimental mechanics – the design and analysis of experimental methods to investigate the behavior of solid materials and structures

Relation to continuum mechanics

As shown in the following table, solid mechanics occupies a central position within continuum mechanics. The field of rheology presents an overlap between solid and fluid mechanics .

continuum mechanics
the study of the physics of continuous materials
Solid mechanics
The study of the physics of continuous materials with a defined rest shape.
Elasticity
describes materials that return to their resting shape after applied stresses have been removed.
Plasticity
describes materials that deform permanently after sufficiently applied stress.
Rheology
The study of substances having both solid and liquid characteristics.
Fluid mechanics
is the study of the physics of a continuous material that deforms when subjected to a force.
Non-Newtonian fluid
does not undergo strain rates proportional to the applied shear stress.
Newtonian fluids undergo a strain rate proportional to the applied shear stress.

Response model

A material has a rest shape and its shape moves away from the rest shape due to stress. The amount of departure from the remaining shape is called the deformation , the ratio of the original size to the deformation is called the strain. If the applied stress is sufficiently low (or the applied stress is small enough), almost all solids behave in such a way that the stress is directly proportional to the strain; The coefficient of the ratio is called the modulus of elasticity . This region of deformation is known as the linearly elastic region.

Because of the ease of calculation, it is most common for analysts in solid mechanics to use linear material models. However, the actual material often exhibits non-linear behavior. As new materials are used and old ones are pushed to their limits, non-linear material models are becoming more common.

These are the basic models that describe how a solid responds to an applied stress:

  1. Elasticity – When an applied stress is removed, the material returns to its deformed state. Linearly elastic materials, which deform proportionally to the applied load, can be described by linear elasticity equations such as Hooke’s law .
  2. Viscoelasticity – These are materials that behave elastically, but also have damping: when stress is applied and removed, work has to be done against damping effects and converted into heat within the material , resulting in a hysteresis loop in the stress–strain curve. , This implies that the physical reaction has a time-dependence.
  3. Plasticity – Materials that behave elastically typically do so when the applied stress is less than the yield value. When the stress stress is greater than the stress, the material behaves plastically and does not return to its previous state. That is, the post-harvest deformation is permanent.
  4. Viscoplasticity – combines the principles of viscosity and plasticity and is applicable to materials such as gels and clays.
  5. Thermoelasticity – the coupling of mechanical with thermal reactions. In general, thermoelastic refers to an elastic solid under conditions that are neither isothermal nor adiabatic. In contrast to advanced theories with more physically realistic models, the simplest theory involves Fourier’s law of heat conduction.