10.10.2022 09:30 - 10.10.2022 16:30
TAV Konferans Salonu, Ayazağa Kampüsü
Akademik
Arizona Üniversitesi öğretim üyesi Prof.Dr. Erdoğan MADENCİ 10 Ekim 2022 Pazartesi günü 09.30–12.30 ve 13:30-16:30 saatleri arasında “ INTRODUCTION TO PERIDYNAMICS” başlıklı bir seminer verecektir.
Prof. MADENCİ’nin özgeçmişi ve seminer içeriği ekte gönderilmiş olup, ilgilenen tüm İTÜ'lüler davetlidir.
Uçak ve Uzay Bilimleri Fakültesi Dekanlığı
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INTRODUCTION TO PERIDYNAMICS
Course Description
The nonlocal peridynamic theory provides the capability for improved modeling of progressive failure in materials and structures. This course starts with an overview of the Peridynamic (PD) theory and derivation of its governing equations based on the balance laws of classical continuum mechanics. Subsequently, it presents derivation of the PD differential operator (PDDO) which enables the PD form of the governing equations of classical continuum mechanics. This course presents not only the theoretical basis but also its numerical implementation for the solution of governing field equations.
Course Objectives and Outcomes
The primary objective of the course is to acquaint students with the concept of PD, and derivation of the bond-based and state-based PD equilibrium equations through the Euler-Lagrange equations. Also, it acquaints the students with the derivation of PD differential operator, and its use in the construction of governing equations for elastic and elastic-plastic material response as well as the coupling of PD with the finite element analysis.
Course Outline
Review of Continuum Mechanics: Postulations, Kinematics, Cauchy’s hypothesis, Stress tensor, Balance laws in Mechanics, and limitations.
Peridynamic Theory: Concept of PD, PD states, PD form of deformation gradient, force density, PD form of strain energy density function, classification of PD equations of motion, surface effects, boundary conditions, and limitations.
PD Differential Operator (PDDO): PD functions and connection with PD theory, reduced order modeling, data recovery, Digital Image Correlation, discovery of equations, Physics Informed Neural Network (PINN)
Unification of Local and PD Theory: PD equilibrium equations for homogeneous deformation, PD form of local equilibrium and traction equations, imposition of boundary conditions
Failure Prediction: Bond breakage, local damage measure, critical stretch, kinetic theory of fracture for fatigue.
Numerical Implementation: Spatial discretization, family search, explicit and implicit solution
Modeling Material Nonlinearity: J2 Plasticity model
PD-FE Coupling: Direct coupling with finite elements in ANSYS