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Course description: “Multiscale and Multiphysics Constitutive Modelling”

Course description: “Multiscale and Multiphysics Constitutive Modelling”

Starting with the next summer semester the Institute of Contiuum Mechanics will offer a new course to Master students given in English language.


The description of the mechanical response of materials is a main issue for the development of physically-consistent computational models of structures in civil, mechanical and biomedical engineering. The constitutive behaviour of materials is highly affected by the multiscale arrangement of their constituents. Methods for incorporating nano/microscale properties on the macroscale response allow to gain a deep insight on the design and the assessment of structures and devices. Moreover, since modern applications require to employ non-standard materials, mechanics is usually coupled with multiphysics mechanisms, such as thermal effects, moisture movements, phase change, electrical dipoles, deposition/loss of mass.

This course discusses constitutive laws by means of theoretical approaches, technical results and computational methods based on a continuum mechanical framework. This course aims to bridge the gap between the material model response and the physical mechanisms occurring in crystals, concretes, composites, metals and biological tissues. Graduates of this course are familiar with the mathematical concepts behind constitutive models for a wide range of materials, being able to discuss their limitations. They are qualified for the computational implementation of constitutive models, also addressing finite element (FE) calculations, and for the assessment of the correctness of computational results. They are able to verify and validate constitutive models, to obtain parameters from mechanical tests and to propose experimental campaigns for model calibration. They are experienced on understanding and discussing the published literature in the field and on the defence of their findings by an oral presentation. 


  • Review of fundamental principles for the development of constitutive models: objectivity, material symmetry, thermodynamic principles.
  • Technical results for the homogenization of composite materials. Laminate theory.
  • Computational homogenization techniques: scale separation, local periodicity, the Representative Volume Element, Hill-Mandel theorem.
  • Hyperelastic constitutive models under finite-strain regime: invariant-based formulations, notion of material stability, polyconvexity.
  • Structure-based models for specific classes of materials in elastic regime: crystals, polymers and rubber, soft biological tissues. Optimization problems for parameters identification.
  • Multiphysics effects in material response:
    • hygrothermal properties of concrete;
    • thermomechanical response of shape memory alloys;
    • electromechanical properties of piezoelectric materials;
    • growth and remodelling of biological tissues.


  • Prior Knowledge: Continuum Mechanics and Computational Techniques (FE method)
  • Literature: Subject specific recommendation of textbooks and journal articles
  • Media: Power-Point presentations + blackboard, practical training in the computer lab (with Matlab and other FE environments)
  • Examination: Semester project and oral presentation
  • Language: English
  • Semester: Summer semester
  • Level: Master Degree
  • Lecturer and examiner: Dr.-Ing. Michele Marino

Michele Marino has done his PhD in Structural Engineering, University of Rome "Tor Vergata", Italy. He is now group leader for „predictive simulation in biomechanics" in the program „SmartBioTecs“ ot the State of Lower Saxony and  loacted at the Institute of Continuum Mechanics.

source: ikm