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Fertig Research Group: Multiscale Failure of Materials
Приєднався 19 гру 2013
Material Fracture (Ductile vs. Brittle Fracture)
Introduces ductile and brittle fracture. Describes the macroscopic appearance of both types of cracking. Describes the microscopic mechanism that are responsible for each type. Briefly covers fractography and shows cup-and-cone fracture for ductile materials and chevron markings for brittle materials. Introduces the ductile to brittle transition. Gives example of Liberty Cargo Ships in WWII.
Переглядів: 2 272
Відео
Material Fracture (Theoretical Fracture Strength)
Переглядів 916Рік тому
Introduces the idea of fracture as the creation of two new surfaces. Develops the idea of theoretical fracture strength on the basis of elastic modulus, lattice spacing, and surface energy.
Linear Elastic Constitutive Behavior: Hooke's Law
Переглядів 7842 роки тому
Develops a linear elastic constitutive law in both tensor notation and Voight notation. Gives the form of the compliance matrix for an orthotropic material.
Review of Strain: (Definition of Small Strain Tensor)
Переглядів 8082 роки тому
Defines the small strain tensor in terms of displacement gradients. Shows how this intuitively yields the same solution as the simple change in length divided by original length.
Review of Strain: Types of Deformation
Переглядів 4182 роки тому
Shows how strain tensor can be used to compute changes in length, changes in angle, and changes in volume leading to normal engineering strain, engineering shear strain, and volumetric strain, respectively.
Simulated Rockwell B Hardness Test for 1018 Steel
Переглядів 1,1 тис.2 роки тому
This is an axisymmetric simulation in Abaqus of a Rockwell B hardness test with material properties that are nominally 1018 Steel. The left-hand animation shows the von Mises stress evolution; the right-hand animation shows the plastic strain magnitude.
Variational Principles of Elasticity (Principle of Virtual Work)
Переглядів 1,7 тис.2 роки тому
Develops the Principle of Virtual Work from the idea of work done by virtual displacements. Demonstrates that the Principle of Virtual Work is an equivalent statement to the equations of equilibrium.
Variational Methods (Parametric Representations)
Переглядів 2912 роки тому
Expands the discussion of optimization of functionals to include parametric representations so that functions need not be single-valued. Shows that any solution (even a non-single-valued function like a circle) that satisfies the conventional Euler-Lagrange equation is a valid extremizing function.
Variational Methods (Finite Constraints - Geodesics Example)
Переглядів 3252 роки тому
Develops the solution of a simple geodesic optimization in 3D where the curve length to be minimized lies on a sphere centered at the origin. The solution ultimately shows that the optimized path lies at the intersection of the sphere and a plane through the origin, which leads to solution that is a great circle of the sphere.
Variational Methods (Finite and Differential Constraints)
Переглядів 6202 роки тому
Develops the methodology to optimize a functional subject to finite equation constraints and differential equation constraints. Introduces the concept of a Lagrange multiplier function. Shows how to create an auxiliary functional that can be optimized to yield the Euler-Lagrange equations.
Variational Methods (Isoperimetric Example)
Переглядів 3362 роки тому
Develops the solution to an example of extremizing (maximizing) the area under the curve subject to the constraint that the curve be of some fixed length L. Uses Lagrange multipliers to form an augmented functional from the constraint functional and shows how to compute the solution.
Variational Methods (Ritz Method and Finite Element Analysis)
Переглядів 3 тис.3 роки тому
Begins with the total potential energy for an elastic body and uses the Ritz method to develop the governing system of matrix equations for FEA. It returns the identical result to the methods that were developed previously by solving the equations of motion in their weak form.
Variational Methods (Rayleigh-Ritz Method)
Переглядів 8 тис.3 роки тому
Develops the Rayleigh-Ritz method for approximating functionals. Shows how extremization of a functional can be reduced to extremization of a function. Goes through an example problem developing a 1-term Ritz solution to an example functional.
Variational Methods (Potential Energy of an Elastic Body)
Переглядів 1,5 тис.3 роки тому
Develops the functional describing the potential energy of an elastic body. Demonstrates that extremizing this functional to get the stationary potential energy yields the Principle of Virtual Work, which is the weak form of the equations of equilibrium. Thus, the lecture validates using the extremization of the potential energy functional for solving for elastic solutions.
Variational Methods (Principle of Stationary Total Potential Energy)
Переглядів 2,3 тис.3 роки тому
Defines the Principle of Stationary Total Potential Energy. Gives a simple example for its use with a linear spring under axial load. Discusses strain energy potential and potential energy due to applied loading.
Variational Methods (Functionals with Multiple Independent Variables)
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Variational Methods (Functionals with Multiple Independent Variables)
Variational Methods (Functionals with Multiple Dependent Variables)
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Variational Methods (Functionals with Multiple Dependent Variables)
Variational Methods (Functionals with Higher Order Derivatives)
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Variational Methods (Functionals with Higher Order Derivatives)
Variational Methods (Natural Boundary Conditions)
Переглядів 2,3 тис.3 роки тому
Variational Methods (Natural Boundary Conditions)
Variational Methods (Delta Operator)
Переглядів 1,8 тис.3 роки тому
Variational Methods (Delta Operator)
Variational Methods (First Integrals of the Euler-Lagrange Equation)
Переглядів 1,7 тис.3 роки тому
Variational Methods (First Integrals of the Euler-Lagrange Equation)
Variational Methods (Example - Surface of Revolution)
Переглядів 5803 роки тому
Variational Methods (Example - Surface of Revolution)
Variational Methods (Example - Shortest Path)
Переглядів 8053 роки тому
Variational Methods (Example - Shortest Path)
Variational Methods (Fundamental Lemma of Variational Calculus)
Переглядів 2,4 тис.3 роки тому
Variational Methods (Fundamental Lemma of Variational Calculus)
Variational Methods (Functionals and Extremization)
Переглядів 2,8 тис.3 роки тому
Variational Methods (Functionals and Extremization)
4-4: Dynamic FEA (Mode Superposition - Modal Analysis)
Переглядів 1,3 тис.3 роки тому
4-4: Dynamic FEA (Mode Superposition - Modal Analysis)
4-2: Dynamic FEA (Newmark-beta Implicit Integration)
Переглядів 3,9 тис.3 роки тому
4-2: Dynamic FEA (Newmark-beta Implicit Integration)
4-1: Dynamic Finite Element Analysis (Natural Frequencies and Mode Shapes)
Переглядів 3 тис.3 роки тому
4-1: Dynamic Finite Element Analysis (Natural Frequencies and Mode Shapes)
3-3: Nonlinear Finite Elements in 3-D (Updated Lagrangian Formulation)
Переглядів 9073 роки тому
3-3: Nonlinear Finite Elements in 3-D (Updated Lagrangian Formulation)