Solid mechanics
Solid mechanics describes how a body with a preferred reference shape deforms and carries load. A solid can sustain shear at rest: that is why a beam, a soil specimen, or a battery electrode holds its form until the stress is large enough to yield, crack, or buckle.
The usual ingredients are kinematics (how strain is measured from motion), stress (internal force per area), balance of momentum, and a constitutive model that relates stress to strain or strain history. Linear elasticity is the small-strain starting point. Plasticity, viscoelasticity, hyperelasticity, damage, and contact extend it when the material or the geometry is no longer linear.
- Small-strain vs finite-deformation kinematics, including Green and logarithmic strain
- Constitutive models: elasticity, plasticity, viscoelasticity, hyperelasticity
- Equilibrium, buckling, fracture, and contact as typical boundary-value problems
- FEM as the standard discretization: weak form, elements, assembly, Newton–Raphson
Fluid mechanics
Fluid mechanics describes liquids and gases, which cannot support a static shear stress. In a fluid, shear is resisted only while the material is deforming: the constitutive response depends on the rate of strain, not on a remembered solid-like shape.
Mass conservation (continuity), momentum balance, and an energy equation close the problem together with a constitutive law. For a Newtonian fluid that is Newton’s law of viscosity, and the momentum statement becomes the Navier–Stokes equations. The Reynolds number compares inertia to viscous diffusion and organizes laminar, transitional, and turbulent regimes. Many engineering flows are treated as incompressible; high-speed gas dynamics needs compressibility and thermodynamics.
- Continuity, Navier–Stokes, and energy; inviscid Euler flow as a limiting model
- Viscosity, Reynolds number, laminar vs turbulent, boundary layers
- Incompressible vs compressible flow; internal flow, aerodynamics, free surfaces
- Shared numerical ideas with solids: conservation form, stabilization, and coupled fluid–structure problems
