| Code |
18139
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
4
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| Workload |
TP(45H)
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| Scientific area |
Engenharia Mecânica
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Entry requirements |
N.A.
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Learning outcomes |
This course aims to provide a deep understanding of the concepts of continuum mechanics and the application of constitutive equations and fundamental relationships for the analysis of materials with nonlinear behavior under different types of loading. Additionally, it aims to develop the ability to create constitutive models by using a linear combination of various models. By the end of the course, students should
be able to:
-Consolidate and extend their knowledge in tensor algebra, linear operators, linearization, and directional and temporal derivatives.
-Apply the concepts of kinematics and conservation laws in analyzing the physical implications of the mechanical behavior of materials in different contexts.
-Apply constitutive models to the mechanical design of structures subjected to large deformations, with hyperelastic, elastoplastic, and viscoelastic mechanical behavior.
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Syllabus |
1 – Kinematics and conservation laws – Eulerian and Lagrangian approaches. Displacement and velocity fields. Velocity gradient. Rate of stretching and spin. Principle of Virtual Work applied to continuous media; Energetically conjugate stress and strain rate tensors; Conservation of momentum and angular momentum; Conservation of mass; Conservation of energy; 2nd law of thermodynamics applied to
continuum. Objectivity.
2 – Hyperelastic models; Hypoelasticity; Examples of functions for strain energy density.
3 – Elastoplastic models. Decomposition of strain into elastic and plastic parts; Yield criteria and yield surface; Hardening laws and plastic flow; Incremental kinematics.
4 – Nonlinear time-dependent constitutive models – Principle of superposition and linear combination of nonlinear models. Viscoelastic and viscoplastic models; Parallel network models.
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Main Bibliography |
Reddy, J.N., (2017) “Principles of Continuum Mechanics: An Introduction for Engineers”
Bergström J., (2015) “Mechanics of Solid Polymers: Theory and Computational Modeling”
Bonet J., Wood, R.D., (2008) “Nonlinear Continuum Mechanics for Finite Element Analysis – 2nd Edition”
Bower, A. F., (2009) “Applied Mechanics of Solids”
Holzapfel, G. A. (2000) “Nonlinear solid mechanics: a continuum approach for engineering”
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Teaching Methodologies and Assessment Criteria |
The Teaching/Learning assessment consists of two continuous assessment tests (F1) and (F2), with the final average of the Teaching/Learning assessment calculated using the formula: FINAL AVERAGE = (F1 + F2)/2.
The approval criteria for the Teaching/Learning assessment is defined as FINAL AVERAGE (FA) >= 9.5.
Students with a FINAL AVERAGE (FA) >= 6 are eligible for the exam.
The approval criteria for the Exam assessment is defined as EXAM >= 9.5.
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Language |
Portuguese. Tutorial support is available in English.
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