Dept. of Theoretical and Applied Mechanics (1926-2006)
http://hdl.handle.net/2142/178
Wed, 23 May 2018 01:39:55 GMT2018-05-23T01:39:55ZMultiscale design of nonlinear materials using a shape optimization scheme based on an interface-enriched GFEM
http://hdl.handle.net/2142/95442
Multiscale design of nonlinear materials using a shape optimization scheme based on an interface-enriched GFEM
Raeisi Najafi, Ahmad
Motivated by key advances in manufacturing techniques, the tailoring of materials with specific macroscopic properties has been the focus of active research in mechanical engineering and materials science over the past decade. The key challenge in this line of work is how to optimize the material microstructure to achieve a desired macroscopic constitutive response. The overwhelming majority of this type of inverse design work relies on topology optimization based, primarily, on linear theory.
In this work, we develop and implement a method to design particulate composites at the mesoscale using a shape optimization scheme to minimize or maximize a nonlinear cost function at the macroscale while satisfying a set of constraints associated, for example, with the volume fraction of inclusions or with the manufacturing technique. The optimization method relies on three key ‘modules’: multiscale modeling, sensitivity analysis, and optimization.
The multiscale modeling is based on a nonlinear finite element solver, which combines a classical homogenization scheme with a NURBS-based Interface-enriched Generalized Finite Element Method (NIGFEM) used to capture accurately and efficiently the displacement field in a heterogeneous material with a finite element discretization that does not conform to the material interfaces. Damage evolution is captured using a three-parameter isotropic damage model able to simulate a wide range of failure responses.
The proposed gradient-based shape optimization scheme relies on the stationary nature of the non-conforming meshes used to discretize the periodic unit cell, thereby avoiding mesh distortion issues that plague conventional finite-element-based shape optimization studies. In the current approach, the finite element approximation space used in the NIGFEM is augmented with NURBS to allow for the accurate capture of the weak discontinuity present along complex, curvilinear material interfaces. NURBS are also used to parameterize the design geometry precisely and compactly by a small number of design variables.
To compute the derivatives of the cost and constraint functions with respect to the design variables, we also formulate an analytic nonlinear sensitivity, which is simplified by the fact that only the enrichment control points on material interfaces move, appear or disappear during the shape optimization process. The derivations uncover subtle but important new terms involved in the sensitivity of shape functions and their spatial derivatives. Our analytic nonlinear shape sensitivity avoids the technical difficulties encountered in the finite difference or semi-analytical schemes when the boundary intersects an element very close to a node in a non-conforming mesh. In these situations, the boundary may move to another element during the design perturbation step, resulting in changes of the mesh topology, making the differentiation of the stiffness matrix and load vector problematic.
We apply the NIGFEM shape optimization scheme to several 2D and 3D structural problems including some benchmark and application examples to demonstrate the performance and accuracy of the method. Based on the multiscale approach, we also design the microstructure of a periodic particulate composite to optimize the volume fraction and distribution of the inclusions for a desired macroscopic nonlinear stress-strain curve.
Gradient-based shape optimization scheme; Generalized Finite Element Method (GFEM)
Thu, 28 Jul 2016 00:00:00 GMThttp://hdl.handle.net/2142/954422016-07-28T00:00:00ZRaeisi Najafi, AhmadDimensional Stability of Multilayer Circuit Boards
http://hdl.handle.net/2142/87777
Dimensional Stability of Multilayer Circuit Boards
Shrotriya, Pranav
Numerical and experimental studies are performed to study residual deformation and warpage in a model multilayer circuit board construction of a common composite substrate (7628 fabric style). A numerical procedure based on classical lamination theory with non-isothermal viscoelastic constitutive relations is developed to predict the deformation and residual stress state due to relamination. Experimental values of the substrate stress relaxation modulus and coefficients of thermal expansion (CTE) are used as inputs in the numerical procedure to predict warpage of model circuit boards with a non-symmetric lay-up of 7628 style composite substrate. Boards with the exact same construction as used in the numerical analysis were fabricated according to the prescribed pressing cycle and the time dependent warpage measured using an ultrasonic contour scan technique. Comparison of the experimental warpage data with numerical predictions provides insight into the effects of processing cycle and substrate properties on residual stress development.
Engineering, Materials Science
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/2142/877772001-01-01T00:00:00ZShrotriya, PranavThe Structure of Turbulence Over Smooth and Rough Walls
http://hdl.handle.net/2142/87778
The Structure of Turbulence Over Smooth and Rough Walls
Tomkins, Christopher David
Several spanwise lengthscales are shown to vary linearly with distance from the wall, revealing self-similar growth of spanwise structure in an average sense. However, inspection of the data suggests individual structures do not grow strictly self-similarly in time. It is proposed that additional scale growth occurs by the merging of vortex packets on an eddy-by-eddy basis via a vortex leg-annihilation mechanism similar to that suggested by Perry and Chong (1982). The proposed mechanism provides a link between vortex-pairing concepts and the observed coalescence of streaky low-speed regions in the inner layer.
Engineering, Aerospace
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/2142/877782001-01-01T00:00:00ZTomkins, Christopher DavidThe Spatial Structure of Turbulent Rayleigh-Benard Convection
http://hdl.handle.net/2142/87776
The Spatial Structure of Turbulent Rayleigh-Benard Convection
Fernandes, Richard Lawrence Joseph
The circulation cells visualized in the present study are a manifestation, in the fully turbulent regime, of the cellular structures commonly observed at low Rayleigh numbers. The circulation cells are proposed as a physical description (not an explanation) of the phenomenon referred to in the literature as the wind of turbulence. They were found to contain approximately 40% of the total kinetic energy, and this fraction was found to be approximately independent of the Rayleigh number. This leads to the conclusion that the wind of turbulence (U) scales with the velocity fluctuations (ufluct), U ∼ u fluct. The visualizations indicate that the large-scale circulation engulfs the small-scale structures and advect them across the layer. The engulfment of small-scale buoyant elements may be the mechanism by which the large-scale circulation obtains the buoyancy required to maintain its kinetic energy.
Physics, Fluid and Plasma
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/2142/877762001-01-01T00:00:00ZFernandes, Richard Lawrence JosephGranular Wave Patterns in a Horizontal Rotating Cylinder
http://hdl.handle.net/2142/87774
Granular Wave Patterns in a Horizontal Rotating Cylinder
Shen, Qing Amy
Our long-term objective is to combine our experimental and computational results to determine the values of the critical constitutive parameters that appear in our theory.
Geophysics
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/2142/877742000-01-01T00:00:00ZShen, Qing AmyToward Ideal Large -Eddy Simulation
http://hdl.handle.net/2142/87775
Toward Ideal Large -Eddy Simulation
Langford, Jacob Anthony
In the second case, a coarse finite-volume representation defines the LES scales. Optimal flux models are expressed as modifications of standard fourth-order schemes, so that numerical and subgrid effects are treated simultaneously. The LES obeys only a bulk conservation of mass, but it is shown that errors introduced by enforcing a second-order divergence-free condition are small.
Applied Mechanics
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/2142/877752000-01-01T00:00:00ZLangford, Jacob AnthonyStudy of the Effect of Interface Slip and Diffusion Mechanisms on the Creep of Metal and Intermetallic Matrix Composites
http://hdl.handle.net/2142/87773
Study of the Effect of Interface Slip and Diffusion Mechanisms on the Creep of Metal and Intermetallic Matrix Composites
Nimmagadda, Prasad B.R.
The influence of the two mechanisms on the transient stress redistribution between the composite constituents is investigated. For a composite whose matrix-reinforcement interface is either perfectly bonded, freely slipping, or rapidly diffusive, the transient solution scales with the applied load and the matrix creep viscous modulus. The transient solutions at large times are found to approach the corresponding solutions obtained from the direct steady state analysis.
Engineering, Materials Science
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/2142/877732000-01-01T00:00:00ZNimmagadda, Prasad B.R.Integrable Vortex Motions in Unbounded and Periodic Domains
http://hdl.handle.net/2142/87771
Integrable Vortex Motions in Unbounded and Periodic Domains
Stremler, Mark Andrew
In each of the vortex systems investigated, the motion of a passive particle in the field of the vortices is, in general, chaotic. One means of characterizing the advected field is through Thurston-Nielsen theory from topology. Using only information about the motions of the vortices themselves and the fact that the advected fluid is a continuous field, Thurston-Nielsen theory establishes a lower bound on the stretching in the advected field. Some of the vortex motions investigated produce exponential stretching in the flow field. This stretching is as violent as any in turbulent flow, which suggests that the problem of point vortices in two-dimensional flow may lend itself to an understanding of some of the physics present in fully turbulent two-dimensional flows.
Physics, Fluid and Plasma
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/2142/877711998-01-01T00:00:00ZStremler, Mark AndrewOn the Continuum-Mechanics of Nematic Elastomers
http://hdl.handle.net/2142/87772
On the Continuum-Mechanics of Nematic Elastomers
Anderson, David Robert
A nematic elastomer is a rubber-like solid formed by the cross-linking of a polymeric fluid that includes nematic liquid crystalline molecules. We develop a continuum theory with the basic kinematic ingredients being the deformation of material particles and the orientation of the nematic microstructure. The kinetics of our theory consist of separate momentum balances for forces acting conjugate to each kinematic variable. We restrict our attention to a purely mechanical setting, so the thermodynamic structure rests on an energy imbalance that serves in lieu of the first and second laws of thermodynamics. We consider only nematic elastomers that are incompressible and microstructurally inextensible. In our treatment of these material constraints, we start with a mathematical decomposition of the dependent fields based on the geometry of the constraint manifold. This naturally gives rise to active and reactive components, where only the former enter into the energy imbalance because the latter automatically expend zero power in processes consistent with the constraints. The reactive components are scaled by constitutively indeterminate multipliers. We introduce constitutive equations for the active components, and the requirement that these equations be consistent with the energy imbalance in all processes leads to the active components being determined by an energy density response function depending on the deformation gradient, the orientation, and the orientation gradient. After enforcing the requirements of observer independence and material symmetry for such a function, the representation is expressed in terms of 40 scalar invariants. To obtain a reduced form of the energy response function, we use a polynomial approximation, in terms of the invariants in which we view the principal extension ratios and the magnitude of the nondimensionalized orientation gradient as small quantities. Our energy density encompasses the successful Mooney-Rivlin description of rubber and the Oseen-Zocher-Frank description of nematic fluids as specializations. To investigate the nature of solutions, we derive a necessary and sufficient condition for ellipticity of the equilibrated governing system of equations. In situations where the ellipticity condition fails, we examine the existence of solutions that allow for surface defects. Several example energy densities are considered to study the implications of these conditions.
Applied Mechanics
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/2142/877721999-01-01T00:00:00ZAnderson, David RobertCord-Reinforced Cylindrical Shells
http://hdl.handle.net/2142/87768
Cord-Reinforced Cylindrical Shells
Paris, Anthony James
In this work, an analytical approach is used to develop the equations for the displacements from the loads on a cord-reinforced cylindrical shell. The load-deformation relations are developed by considering the mechanics of the matrix, the cords, and the shell. The matrix is modeled using the generalized Hooke's law for an isotropic linear-elastic material. The theory that is used to model the cords was developed by Costello and includes the extension-twist coupling of the cords. For the shell, a set of differential equations for the displacements is derived based upon the analysis of the bending of circular cylindrical shells by Flugge, an equilibrium approach. These equations are solved analytically in closed form for axisymmetric loading. The resulting load--deformation relations are strongly dependent upon the properties of the constituents, including the extension-twist coupling of the cords, and the geometry, boundary conditions, and loading of the cord-reinforced cylindrical shell.
Engineering, Automotive
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/2142/877681997-01-01T00:00:00ZParis, Anthony James