Universitat Politècnica de Catalunya · BarcelonaTech

Continuum Mechanics (250401) – Course 2025/26 PDF

Contents

Introduction to the course and review of tensor algebra.

Dedication

2h Large group + 2h 48m Self Study
Total: 4h 48m

Reinforcement of basic concepts of Tensor Algebra: Concept of tensor, operations with tensors, index notation, differential operators.

Specific Objectives

Reinforce and review the basic concepts of Tensor Algebra: Concept of tensor, operations with tensors, index notation, differential operators.

Dedication

3h Large group + 4h 11m Self Study
Total: 7h 11m

Concept of the continuous medium, equations of motion, description of motion (material and spatial descriptions).

Dedication

3h 30m Large group + 2h 30m Medium group + 8h 23m Self Study
Total: 14h 23m

Concept of deformation and strain. Deformation gradient tensor, displacements, strain tensors, infinitesimal strain theory.

Dedication

7h 30m Large group + 2h 30m Medium group + 14h Self Study
Total: 24h

Compatibility equations of a potential vector field, compatibility equations of the infinitesimal strain tensor.

Dedication

2h Large group + 1h Laboratory classes + 4h 11m Self Study
Total: 7h 11m

Forces in a continuous medium, Cauchy's postulates, Cauchy's stress tensor, Mohr's circle.

Dedication

7h 30m Large group + 1h 30m Medium group + 12h 36m Self Study
Total: 21h 36m

Convective flux, material and local derivative of a volume integral, conservation of mass, Reynolds transport theorem, balance equations (linear momentum, angular momentum, mechanical energy, first and second laws of thermodynamics).

Dedication

9h Large group + 3h Medium group + 1h Laboratory classes + 18h 12m Self Study
Total: 31h 12m

Hypotheses of the linear elastic theory, constitutive equation of linear elasticity, isotropy, Lamé parameters and limits, the linear elastic problem, linear thermoelasticity.

Dedication

7h 30m Large group + 4h Medium group + 16h 6m Self Study
Total: 27h 36m

Plane linear elasticity theory, plane stress, plane strain, representative curves.

Dedication

2h Large group + 2h 48m Self Study
Total: 4h 48m

Principal stress space, stress tensor invariants, phenomenological behavior, 1D plasticity theory, 3D plasticity theory, yield surfaces.

Dedication

5h Large group + 3h 30m Medium group + 1h Laboratory classes + 13h 18m Self Study
Total: 22h 48m

Concept of fluid and pressure, constitutive equations in fluids, Newtonian fluids.

Dedication

2h Large group + 2h 48m Self Study
Total: 4h 48m

Governing equations, hydrostatics, perfect barotropic fluid, viscous Newtonian fluid, boundary conditions, laminar and turbulent flow.

Dedication

5h Large group + 3h Medium group + 11h 12m Self Study
Total: 19h 12m

Concept of a functional, Gâteaux derivative, variational principle, principle of virtual work, principle of minimum potential energy.

Dedication

1h Large group + 1h Laboratory classes + 2h 48m Self Study
Total: 4h 48m