Course detail
Constitutive Equations in Computational Modelling
FSI-RK0Acad. year: 2012/2013
The coarse provides a comprehensive overview od constitutive dependencies of matters, not only solid (i.e. materials in the sens of mechanical engineering) but liquid and gaseous as well, it defines the term of constitutive dependencies and their mathematical descriptions (i.e. constitutive models). It systemizes constitutive models in three cathegories: basic constitutive models represent ideal states of matter, simple ones describe an only one major property (elasticity, viscosity, plasticity), combined ones create models of a more complex constitutive behaviour by synthesis of the simple ones on the base of the so called reological models (e.g. elasto-visco-plastic matter). For each of the models described, basic constitutive equations are created and dependencies of stress vs. strain, stress vs. strain rate, strain vs. time (creep) and stress vs. time (relaxation) are evaluated.
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Specification of controlled education, way of implementation and compensation for absences
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Basic literature
Holzapfel G.A.: Nonlinear Solid Mechanics
Lemaitre J., Chaboche J.-L.: Mechanics of Solid Materials
Recommended reading
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Lecture
Teacher / Lecturer
Syllabus
2. Basic constitutive models.
3. Simple constitutive models - overview. Linear and non-linear elastic models.
4. Revision of tensor calculus. Definitions of stress and deformation tensors under large strain conditions.
5. Hyperelastic models of isotropic hardly compressible elastomers.
6. Hyperelastic models of very compressible elastomers (foams).
7. Anisotropic hyperelastic models of elastomers with reinforcing fibres.
8. Constitutive models of Newtonian and non-Newtoniad liquids.
9. Combined models. Theories of viscoelasticity.
10. Models of linear viscoelasticity - response under static load.
11. Models of linear viscoelasticity - response under dynamic load. Complex modulus of elasticity.
12. Other combined models - basic constitutive characteristics.
13. Micropolar continuum models. Cosserat continuum.
Computer-assisted exercise
Teacher / Lecturer
Syllabus
2. Basic constitutive models - their specifics in FE analyses.
3. Multilinear elastic model.
4. Large displacements - geometrical non-linearity.
5. Hyperelasticity - tests of elastomers and their input into the constitutive model.
6. Choice of a suitable constitutive model of hardly compressible elastomers.
7. Adaptation of the constitutive model for the required strain range.
8. Use of constitutive models of foams.
9. Linear viscoelasticity - behaviour of Voigt model.
10. Linear viscoelasticity - behaviour of Maxwell model.
11. Linear viscoelasticity - behaviour of Kelvin and generalized Maxwell models.
12. Temperature dependence of viscoelastic parameters and application in FE analyses.
13. Semester project, course-unit credit.