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Syllabus for

Academic year
MHA043 - Material mechanics
Syllabus adopted 2021-02-11 by Head of Programme (or corresponding)
Owner: MPAME
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: Second-cycle
Main field of study: Mechanical Engineering, Civil and Environmental Engineering, Shipping and Marine Technology

Course round 1

Teaching language: English
Application code: 03129
Open for exchange students: Yes
Block schedule: A

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0116 Laboratory 4,5 c Grading: UG   4,5 c    
0216 Examination 1,5 c Grading: TH   1,5 c   03 Jun 2022 pm J_DATA,  09 Oct 2021 pm J   18 Aug 2022 am J_DATA
0316 Intermediate test 1,5 c Grading: UG   1,5 c    

In programs

MPAME APPLIED MECHANICS, MSC PROGR, Year 1 (compulsory elective)


Ragnar Larsson

  Go to Course Homepage


General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Basic courses in mechanics and strength of materials equivalent to the course offered by the Mechanical Engineering program, TKMAS, are required. Mathematics, in particular, linear algebra, calculus , and numerical methods. A basic course in FEM is strongly recommended but not a hard prerequisite for attendance to the course.
To be more specific, we assume:
  • 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 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.


Material mechanics plays a very important part in modeling and simulation of advanced components in automotive, aeronautics, 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 necessary 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.

Learning outcomes (after completion of the course the student should be able to)

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.


The course content is as follows:
  • L1 Introduction; "perfect plasticity".
  • L2 Thermomechanical basis for 1D problems: state equations and evolution rules for internal variables.
  • L3 Rate independent materials: linear hardening elastoplasticity.
  • L4 Elastoplasticity: time integration, tangent stiffness of stress-strain response.
  • L5 Elastoplasticity (cont'd): nonlinear hardening, mixed isotropic and kinematic hardening.
  • L6 Rate dependent materials: basic rheology, viscoelastic materials.
  • L7 Rate dependent material (cont'd): elastoviscoplastic materials; computational modeling/implementation.
  • L8 Basic continuum mechanics: 2nd order stress tensor, eigenbases, stress space.
  • L9 Basic continuum mechanics (cont'd): strong and weak equilibrium; formulation of yield criteria.
  • L10 Thermomechanical basis for multiaxial conditions: non-dissipative material, isotropic elasticity.
  • L11 J2-elastoplasticity: basic modelling, isotropic hardening.
  • L12 J2-elastoplasticity (cont'd): time integration and tangent stiffness.
  • L13 FEM for multiaxial material mechanics problems; Voight form of stress, strain and stiffness, Newton's method,
  • L14 J2-elastoplasticity (cont'd): mixed isotropic-kinematic hardening, computational aspects.
  • L15 Calibration of constitutive equations via optimization.
  • L16 Calibration of constitutive equations (cont'd); implementation
  • L17 Discussion on dugga- and exam questions.


Teories and concepts are presented at the lectures. In the problem classes and the computer assignments the theories outlined are applied at specified problems. The computer assignments also trains your ability in programming and systematic analysis of a given problem.


Cf. the course homepage.

Examination including compulsory elements

Mandatory graded Computer Assignments (CAs); Mandatory oral exam (dugga) and graded final exam.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.

Page manager Published: Thu 03 Nov 2022.