Course syllabus

MHA043 Material mechanics lp4 VT22 (7.5 hp). The course is offered by the department of Industrial and Materials Science

Contact details

Course purpose

Material mechanics plays a very important part in modeling and simulation of advanced components in automotive, areonautics, civil, maritime and other engineering branches. In fact, all load bearing components deviate from the ideal linear response under service conditions. The nonlinear effects depend on the loading on the structure, whether it is sustained, time-dependent of impact dynamic character, quasistatic with cyclic variation or due to elevated temperature.

One aim is to develop mathematical model concepts, named constitutive modeling, to describe the nonlinear material response of the components. Presented constitutive theories are: elasticity, viscoelasticity, plasticity and viscoplasticity for the material modeling of physically observed behavior. In the end, the observed behavior becomes more or less well represented by the material model, involving additional material parameters as compared to linear elasticity. The procedure nessesscary for the parameter identification for a given experiment is named material model calibration.

Another aim is to develop computational procedures for material model implementation to facilitate model calibration and finite element simulation of real world components. Here, the material mechanics based modeling is the heart in the finite element simulation!

Schedule

cf. the detailed course plan

Course literature

The following main texts are used in the course:

  1. CONSTITUTIVE MODELING OF ENGINEERING MATERIALS - THEORY AND COMPUTATION,  The Primer, Kenneth Runesson and Ragnar Larsson, Department of Industrial and Materials Science, Chalmers University of Technology, Göteborg.

  2. A COURSE ON COMPUTATIONAL SOLID MECHANICS, Ragnar Larsson, Chalmers University of Technology, Göteborg 2018.

Course design

The course comprises 34 hours of lectures, L1-L17 in the detailed course outline, 30 hours of exercises, E1-E15, and 14 hours of scheduled computer assignment classes, C1-C7. In addition, 4 hours of oral exam time (or dugga time), D-D4 in the course-pm.

As mentioned in the aim of the course, the major purpose is to outline the fundamental basis and the relevant computational procedures for material model implementation in the finite element context. The theoretical and computational basis is outlined in the lectures. In the exercises hands-on examples of material mechanics are demonstrated. In the computer assignments, concrete problems are handled based on material model implementation in Matlab/Abaqus and the consequent verification/validation against experimental evidence. During the oral exams (or duggas) you will present in front of each other (in small seminar groups) the dugga questions of the course.

The CANVAS platform is used for formal interaction between you and the teachers. All the formal material and information about the course are placed in the CANVAS course homepage. Hence, there will be no other course-pm handed out. In CANVAS, announcements about special events in the course are made, so you are advised to visit CANVAS on a daily basis during the course. In CANVAS the reports for the computer assignments are handed in electronically with due consideration to the deadlines, cf. the detailed course-pm.

Digitals tools like Matlab and Abaqus are used in the course work. For the report writing, MS-office tools or equivalent softwares (e.g. overleaf) may be used. 

Changes since last occasion

Changes in the wording to make the dugga-questions clearer; minor updates in the primer; new and clearer formulations of CA1 and CA2; CA1 has been updated with a task introducing nonlinear FE-modeling using Abaqus.

Prerequisites

Before coming to the course you should have basic knowledge in:

  • mechanics and strength of materials. Concepts of stress and strain. Elasticity and other stress-strain phenomena. Yielding and deformation mechanisms in metals.
  • mathematics. Your skills in calculus, linear algebra with eigenvalues and numerical methods are needed. Concepts of vectors and tensors are exploited.
  • finite element methodology. Weak forms. Nodal forces. Element stiffness. Assembly of global arrays.
  • programming. The Matlab software is extensively used in the course. 

Learning objectives

After the completion of the course you should be able to:

  • Formulate and implement the basic concepts of elastoplastic and elastoviscoplastic stress-strain phenomena for 1D problems.
  • Formulate and implement elastoplastic stress-strain relations for multiaxial problems.
  • Formulate and carry out nonlinear finite element analyses of elastoplastic material response.
  • Formulate, implement and conduct calibration of material parameters using experimental data based on concepts of optimization.
  • Formulate the links between observed phenomena, continuum/material mechanics and finite element simulation.

Link to the syllabus on Studieportalen.

Study plan

Examination form

The examination of the course is based on work done in the computer assignment, work done for the oral exams and work done for the written exam. The detailed description is given in the module "examination" of this CANVAS homepage.