A5040697039- Numerical methods in engineering
- Composite Material Mechanics
- Advanced Mathematical Modeling in Engineering
- Geotechnical Engineering and Underground Structures
- Electromagnetic Simulation and Numerical Methods
- Rock Mechanics and Modeling
- Topology Optimization in Engineering
- Composite Structure Analysis and Optimization
- Advanced Numerical Methods in Computational Mathematics
- Photonic Crystals and Applications
- Metamaterials and Metasurfaces Applications
- Mechanical Behavior of Composites
- Numerical methods in inverse problems
- Electromagnetic Scattering and Analysis
- Fatigue and fracture mechanics
- Advanced Antenna and Metasurface Technologies
- Elasticity and Material Modeling
- Acoustic Wave Phenomena Research
- Photonic and Optical Devices
- Hydraulic Fracturing and Reservoir Analysis
- Optical Coatings and Gratings
- Advanced Materials and Mechanics
- Geotechnical and Geomechanical Engineering
- Thermal properties of materials
- Geophysical Methods and Applications
Louisiana State University
2014-2024
Worcester Polytechnic Institute
1993-2005
John Brown University
2004
United States Military Academy
2002
Rice University
1996
University of California, Berkeley
1990-1991
University of Minnesota
1990
Twin Cities Orthopedics
1990
Cornell University
1988
Courant Institute of Mathematical Sciences
1988
The paper addresses a numerical method for solving second order elliptic partial differential equations that describe fields inside heterogeneous media. scope is general and treats the case of rough coefficients, i.e., coefficients with values in $L^{\infty}(\Omega)$. This class includes as examples media microstructure well multiple nonseparated length scales. approach taken here based on generalized finite element (GFEM) introduced [I. Babuska, G. Caloz, J. E. Osborn, SIAM Numer. Anal., 31...
We consider the nonlocal formulation of continuum mechanics described by peridynamics. provide a link between peridynamic evolution and brittle fracture for broad class potentials associated with unstable constitutive laws. Distinguished limits evolutions are identified that correspond to vanishing horizon. The limit has both bounded linear elastic energy Griffith surface energy. corresponds simultaneous displacement fracture. For points in spacetime not on crack set field evolves according...
New variational principles are introduced, describing the eective conductivity tensor for anisotropic two-phase heat conducting composites with interfacial surface resistance between phases.These reduce to those of Hashin and Shtrikman in limit vanishing resistance.The new allow an unconstrained class trial elds.New bounds derived on composite phases.The upper bound is given terms two-point correlation function, component v olume fractions moment inertia each heterogeneity.The lower area, a...
Abstract An extension of recent work 1 on the simultaneous optimization material and structure to address design structures under multiple loading conditions is presented. Material properties are represented in most general form possible, namely, as elements unrestricted set positive‐semi‐definite constitutive tensors a linearly elastic continuum. Existence solutions can be shown when objective weighted average compliances resource constraint measured 2‐norm or trace included. The optimized...
Optical metamaterials manipulate light through various confinement and scattering processes, offering unique advantages like high performance, small form factor easy integration with semiconductor devices. However, designing metasurfaces suitable optical responses for complex metamaterial systems remains challenging due to the exponentially growing computation cost ill‐posed nature of inverse problems. To expedite design metasurfaces, a physics‐informed deep learning (DL) framework is used....
Synopsis We examine slow viscous flow past a concentrated bed of small stationary bubbles second fluid, and derive Darcy's law relating the average fluid velocity to overall pressure gradient body force.
Heat conduction in a fine scale mixture of two conductors is examined the presence contact resistance between phases. The problem studied rigorously context periodic homogenization. Unlike case perfect heat transmission phases, temperature gradients converge weakly as Radon measures. strict ellipticity homogenized transport equation depends upon geometry interface. effective conductivity associated with overall dissipation rate inside composite cube considered. It shown that this property...