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III-Nitride Flexible Electronic Devices
Published in Chinmay K. Maiti, Fabless Semiconductor Manufacturing, 2023
The elastic model accounts for the strain caused by a lattice mismatch between materials. The material database for GaN is used to retrieve the lattice constants. In the simulation, all segments are subjected to an initial strain condition that forces their lattice constant to match that of the substrate segments. By solving the elastic equations, the system can relax and reduce its overall energy, resulting in the proper strain conditions at material interfaces. With the components C11, C12, and C44, the elasticity tensor defines the connection between stress and strain. The default material database is used to retrieve the components and lattice constants.
An energy-based anisotropic damage model and its engineering application
Published in Wang Sijing, Fu Bingjun, Li Zhongkui, st Century, 2020
Yang Qiang, Chen Xin, Zhou Weiyuan
In general, an elasticity tensor is subject to the following general principles of continuum mechanics (Malvern, 1969): (1) Symmetry condition requires Dijkl = Djikl = Dijlk = Dkllij; (2) positive definite condition requires the elastic potential function Dijkl0=λδijδkl+μ(δklδjl+δljδjk) is positive-definite as a function of strain εij; (3) Material symmetry condition requires that D(Ω) be an isotropic tensor function.
An Energy-Based Damage Model of Jointed Rockmass
Published in Hans-Peter Rossmanith, Mechanics of Jointed and Faulted Rock, 2018
G. Swoboda, Q. Yang, X.P. Shen
In general, an elasticity tensor is subject to the following general principles of continuum mechanics(Malvern, 1969): (1) Symmetry condition requires Dijkl = Djikl = Dijlk = Dklij; (2) Positive definite condition requires the elastic potential function W=12εijDijklεkl is positive-definite as a function of strain εij; (3) Material symmetry condition requires that D(Ω) be an isotropic tensor function.
Unified three-dimensional finite elements for large strain analysis of compressible and nearly incompressible solids
Published in Mechanics of Advanced Materials and Structures, 2023
A. Pagani, P. Chiaia, M. Filippi, M. Cinefra
In the framework of total-Lagrangian formulation of nonlinear problems, typically incremental formulations are considered. According to Holzapfel [27], the constitutive Eq. (6) can be rewritten in its incremental formulation by the total differential form: where is the so-called material Jacobian tensor. In the linearized framework of governing equation, in analogy with Hooke’s law, represents the tangent elasticity tensor and can be expressed as follows: