{"id":3652,"date":"2026-02-20T17:18:08","date_gmt":"2026-02-20T16:18:08","guid":{"rendered":"https:\/\/dottorati.unica.it\/dotticar\/?p=3652"},"modified":"2026-02-20T17:18:08","modified_gmt":"2026-02-20T16:18:08","slug":"nonlinear-continuum-mechanics-and-applications-to-finite-element-analysis","status":"publish","type":"post","link":"https:\/\/dottorati.unica.it\/dotticar\/nonlinear-continuum-mechanics-and-applications-to-finite-element-analysis\/","title":{"rendered":"Nonlinear Continuum Mechanics and applications to finite element analysis"},"content":{"rendered":"

Professors:<\/strong><\/p>\n

Mario Spagnuolo, Researcher, DICAAR, Universit\u00e0 degli Studi di Cagliari<\/p>\n

Hours: <\/strong>30 hours<\/p>\n

Dates: <\/strong>[From Wednesday 4 March 2026 (18:00) and Thursday 5 March 2026 (15:00)]<\/p>\n

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Contents<\/strong><\/p>\n

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Tensor algebra and vector analysis<\/strong>: definition and properties of tensors; fundamental tensor operations; coordinate systems and transformations; vector and tensor differential analysis applied to problems in mechanics.<\/p>\n

Continuum kinematics:<\/strong> deformation; infinitesimal strain tensor and approaches to finite deformations; linear and nonlinear strain measures; motion and Eulerian and Lagrangian descriptions.<\/p>\n

Stress analysis:<\/strong> stress tensors; equilibrium equations; general formulations and specific applications.<\/p>\n

Constitutive relations:<\/strong> linear isotropic elastic materials; elastic moduli; generalized Hooke\u2019s law; anisotropic and orthotropic materials; elasticity criteria and practical applications.<\/p>\n

Principle of virtual work and energy methods<\/strong>: virtual work; elastic potential energy; energy-based methods for solving elasticity problems.<\/p>\n

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Duration:<\/strong> 30 hours distributed within the second semester<\/p>\n

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Extended description<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Lecture<\/td>\nDate<\/td>\nTopic<\/td>\nDetailed topic<\/td>\nPages<\/td>\n<\/tr>\n
1<\/td>\n04.03.2026<\/td>\nIntroduction to the course<\/td>\nSimple examples of nonlinear structural behavior: Cantilever; Column.<\/td>\n1–18<\/td>\n<\/tr>\n
2<\/td>\n05.03.2026<\/td>\nIntroduction<\/td>\n1D nonlinear strain measures. Directional derivative, linearization and equation solution.<\/td>\n1–18<\/td>\n<\/tr>\n
3<\/td>\n11.03.2026<\/td>\nMathematical Preliminaries (1)<\/td>\nVector and Tensor algebra.<\/td>\n22–46<\/td>\n<\/tr>\n
4<\/td>\n12.03.2026<\/td>\nMathematical Preliminaries (2)<\/td>\nVector and Tensor algebra.<\/td>\n<\/td>\n<\/tr>\n
5<\/td>\n18.03.2026<\/td>\nNumerical Application<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
6<\/td>\n19.03.2026<\/td>\nMathematical Preliminaries (3)<\/td>\nLinearization and the directional derivative. Tensor analysis.<\/td>\n47–62<\/td>\n<\/tr>\n
7<\/td>\n25.03.2026<\/td>\nKinematics (1)<\/td>\nThe motion. Material and spatial descriptions.<\/td>\n94–104<\/td>\n<\/tr>\n
8<\/td>\n26.03.2026<\/td>\nKinematics (2)<\/td>\nDeformation gradient. Strain.<\/td>\n94–104<\/td>\n<\/tr>\n
9<\/td>\n15.04.2026<\/td>\nNumerical Application<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
10<\/td>\n16.03.2026<\/td>\nKinematics (3)<\/td>\nPolar decomposition. Volume change. Distortional component of the deformation gradient. Area change. Linearized kinematics.<\/td>\n105–118<\/td>\n<\/tr>\n
11<\/td>\n22.04.2026<\/td>\nKinematics (3)<\/td>\nVelocity and material time derivatives.<\/td>\n118–133<\/td>\n<\/tr>\n
12<\/td>\n23.04.2026<\/td>\nKinematics (4)<\/td>\nRate of deformation. Spin tensor. Rate of change of volume. Superimposed rigid body motions and objectivity.<\/td>\n118–133<\/td>\n<\/tr>\n
13<\/td>\n29.04.2026<\/td>\nNumerical Application<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
14<\/td>\n30.04.2026<\/td>\nStress and Equilibrium (1)<\/td>\nCauchy stress tensor. Equilibrium.<\/td>\n134–143<\/td>\n<\/tr>\n
15<\/td>\n06.05.2026<\/td>\nStress and Equilibrium (2)<\/td>\n\u00a0Principle of Virtual Work.<\/td>\n134–143<\/td>\n<\/tr>\n
16<\/td>\n07.05.2026<\/td>\nStress and Equilibrium (3)<\/td>\nAlternate stress representations.<\/td>\n144–154<\/td>\n<\/tr>\n
17<\/td>\n13.05.2026<\/td>\nNumerical Application<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
18<\/td>\n14.05.2026<\/td>\nHyperelasticity (1)<\/td>\nHyperelasticity. Elasticity Tensor. Isotropic Hyperelasticity. Incompressible and nearly incompressible materials.<\/td>\n155–173<\/td>\n<\/tr>\n
19<\/td>\n20.05.2026<\/td>\nHyperelasticity (2)<\/td>\nIsotropic elasticity in principal directions.<\/td>\n174–184<\/td>\n<\/tr>\n
20<\/td>\n21.05.2026<\/td>\nLinearized Equilibrium Equations<\/td>\nLinearization and Newton-Raphson process. Lagrangian linearized internal Virtual Work. Eulerian linearized internal Virtual Work. Linearized external Virtual Work. Variational methods and incompressibility.<\/td>\n216–231<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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Contact and registration<\/strong><\/p>\n

Mario Spagnuolo, <\/strong>mario.spagnuolo@unica.it<\/a><\/p>\n

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The certificate is issued for participants that attend more than 80% of the lectures and successfully pass a written exam.<\/p>\n

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Bibliography <\/strong><\/p>\n

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