Acceleration and higher order waves in a mixture of chemically reacting elastic materials

1969 ◽  
Vol 33 (3) ◽  
pp. 169-180 ◽  
Author(s):  
Ray M. Bowen
Keyword(s):  
Higher Order ◽  
Elastic Materials ◽  
Chemically Reacting

The Higher Order Crack Tip Fields for Special FGM Functions

2012 ◽  
Vol 476-478 ◽  
pp. 1472-1475
Author(s):  
Yao Dai ◽  
Lei Zhang ◽  
Xiao Chong ◽  
Jun Feng Liu
Keyword(s):  
Numerical Simulation ◽  
Theoretical Basis ◽  
Superposition Principle ◽  
Crack Tip ◽  
Higher Order ◽  
Elastic Materials ◽  
Crack Tip Fields ◽  
Complex Models ◽  
Special Complex ◽  
Order Element

Superposition principle and the higher order crack tip fields for power function are used to obtain the higher order crack tip fields for several special complex models. A new effective way is provided to solve the fracture problems of different structures and special non-homogeneous elastic materials, which establishes a theoretical basis for determing stress intensity factor, numerical simulation of higher order element and experimental analysis

scholarly journals Anisotropic effective higher-order response of heterogeneous Cauchy elastic materials

2013 ◽  
Vol 54 ◽  
pp. 63-71 ◽  
Author(s):  
M. Bacca ◽  
F. Dal Corso ◽  
D. Veber ◽  
D. Bigoni
Keyword(s):  
Higher Order ◽  
Elastic Materials

On the Theory of Elastic Undamageable Materials

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
George Z. Voyiadjis ◽  
Peter I. Kattan
Keyword(s):  
Elastic Material ◽  
Deformation Process ◽  
Strain Energy ◽  
Damage Mechanics ◽  
Materials Science ◽  
Higher Order ◽  
Damage Variable ◽  
Elastic Materials ◽  
Nonlinear Elastic Material ◽  
Nonlinear Elastic

In this work, both the concepts of Voyiadjis–Kattan materials and undamageable materials are introduced. The Voyiadjis–Kattan material of order n is defined as a nonlinear elastic material that has a higher-order strain energy form in terms of n. The undamageable material is obtained as the limit of the Voyiadjis–Kattan material of order n as n goes to infinity. The relations of these types of materials to other nonlinear elastic materials from the literature are outlined. Also, comparisons of these types of materials with rubber materials are presented. Finally, a proof is given to show that the value of the damage variable remains zero in an undamageable material throughout the deformation process. It is hoped that these proposed new types of materials will open the way to new areas of research in both damage mechanics and materials science.

scholarly journals Unified analytical expressions of the three-dimensional fundamental solutions and their derivatives for linear elastic anisotropic materials

2016 ◽  
Vol 472 (2186) ◽  
pp. 20150272 ◽  
Author(s):  
Longtao Xie ◽  
Chuanzeng Zhang ◽  
Jan Sladek ◽  
Vladimir Sladek
Keyword(s):  
Three Dimensional ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Higher Order ◽  
The Novel ◽  
Elastic Materials ◽  
Linear Elastic ◽  
Second Derivatives ◽  
Analytical Expressions ◽  
Derivatives Of

Novel unified analytical displacement and stress fundamental solutions as well as the higher order derivatives of the displacement fundamental solutions for three-dimensional, generally anisotropic and linear elastic materials are presented in this paper. Adequate integral expressions for the displacement and stress fundamental solutions as well as the higher order derivatives of the displacement fundamental solutions are evaluated analytically by using the Cauchy residue theorem. The resulting explicit displacement fundamental solutions and their first and second derivatives are recast into convenient analytical forms which are valid for non-degenerate, partially degenerate, fully degenerate and nearly degenerate cases. The correctness and the accuracy of the novel unified and closed-form three-dimensional anisotropic fundamental solutions are verified by using some available analytical expressions for both transversely isotropic (non-degenerate or partially degenerate) and isotropic (fully degenerate) linear elastic materials.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

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