Solid mechanics
Solid mechanics, also known as mechanics of solids, is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents. Solid mechanics is fundamental for civil, aerospace, nuclear, biomedical and mechanical engineering, for geology, and for many branches of physics such as materials science. 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 uses tensors to describe stresses, strains, and the relationship between them. Solid mechanics is a vast subject because of the wide range of solid materials available, such as steel, wood, concrete, biological materials, textiles, geological materials, and plastics. Fundamental aspects. A "solid" is a material that can support a substantial amount of shearing force over a given time scale during a natural or industrial process or action. This is what distinguishes solids from fluids, because fluids also support "normal forces" which are those forces that are directed perpendicular to  the material plane across from which they act and "normal stress" is the normal force per unit area of that material plane. "Shearing forces" in contrast with "normal forces", act parallel rather than perpendicular to the material plane and the shearing force per unit area is called "shear stress". Therefore, solid mechanics examines the shear stress, deformation and the failure of solid materials and structures. The most common topics covered in solid mechanics include: Relationship to continuum mechanics. As shown in the following table, solid mechanics inhabits a central place within continuum mechanics. The field of rheology presents an overlap  between solid and fluid mechanics. Response models. A material has a rest shape and its shape departs away from the rest shape due to stress. The amount of departure from rest shape is called deformation, the proportion of deformation to original size is called strain. If the applied stress is sufficiently low (or the imposed strain is small enough), almost all solid materials behave in such a way that the strain is directly proportional to the stress; the coefficient of the proportion is called the modulus of elasticity. This region of deformation is known as the linearly elastic region. It  is most common for analysts in solid mechanics to use linear material models, due to ease of computation. However, real materials often exhibit 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 basic models that describe how a solid responds to an applied stress: