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COURSE 09 / COURSE

Continuum Mechanics

Treat matter as a field of material points.

OUTCOMEDefine stress and strain, derive balance laws, and understand how constitutive models turn general conservation into predictive mechanics.

PREREQUISITEMathematical methods plus dynamics and energy.

Continuum Mechanics: original course diagram — Course visual: a compact prompt for the physical ideas developed below.

12 CHAPTERS

Course map

01The continuum idealizationKnow when replacing atoms with fields is useful and where it fails.→02Deformation and displacementDescribe how a body changes shape in space.→03Strain and small-deformation kinematicsMeasure extension, shear, and volumetric change.→04Traction and the stress tensorRepresent internal force across arbitrary planes.→05Balance of massState continuity before choosing a material model.→06Balance of linear momentumDerive the continuum force balance from a control volume.→07Balance of angular momentumUnderstand why the Cauchy stress tensor is symmetric in the classical case.→08Constitutive lawsSeparate universal balances from material-specific behavior.→09Elastic solidsRelate stress and strain in a recoverable material model.→10Viscosity and Newtonian fluidsIntroduce rate-of-deformation and the linear viscous law.→11Boundary layers and no-slipExplain why boundaries organize gradients and resistance.→12Continuum studio: choose a modelSelect assumptions for a fountain component and state what evidence would falsify them.→