4C600 - Continuum mechanics for advanced manufacturing technologies


The course is composed of two major parts. The first part is devoted to the theoretical basis of continuum mechanics. After a short introduction on vector and tensor analysis, the 3D kinematics is extended in detail to large deformations, rotations and strains. New kinematical quantities arise, e.g. the Cauchy-Green deformation tensors, stretch tensors, velocity gradient tensor, the rate-of-deformation tensor, the spin tensor, etc. The experimental identification and quantification of these kinematical quantities is addressed and illustrated with practical examples. New stress measures (Kirchhoff, first and second Piola-Kirchhoff stress tensors) are introduced and the balance equations are consistently derived. Special attention is given to constitutive principles like objectivity, which are essential in the elaboration of material constitutive laws. The second part of the course presents the geometrically nonlinear description of three categories of materials, illustrated with several applications. The first category envelopes large strain elastic materials, whereby a clear distinction is made between hypo- and hyperelasticity. Various formulations for elastic material behaviour at large strains (Neo-Hookean, Mooney-Rivlin) are detailed. The second category represents time-dependent or viscous materials, relying on a description of a Newtonian fluid and the generalization thereof. This type of material behaviour is important for the analysis of polymer processing, but also for metals in e.g. aluminium extrusion. The third category treats plastic material behaviour, whereby a rigid plastic, a visco-elastic and a J2 elasto-plastic material behaviour is elaborated. The application of these models is illustrated by means of a few examples of forming processes taken from the industrial practice.

Learning objectives

The manufacturing of a diversity of components, parts, structures and devices, consists in making products on the basis of material forming through multiple processing steps. These forming processes are essentially characterized by large deformations, for which the mechanical descriptions change substantially. The design of a product and the chain of manufacturing processes providing its final shape, is strongly governed by the kinematics of large deformations and stress evolution in the underlying material. Most technical problems arise from the behaviour of a specific material under a process deformation step. This basic course constitutes the kernel of the description of the behaviour of materials at large deformations, which is an indispensable tool for the predictive analysis of most forming processes in the industrial practice. The course also offers the theoretical basic knowledge as required in many courses on the numerical simulation of non-linear mechanical processes.