scholarly journals A matrix‐free approach for finite‐strain hyperelastic problems using geometric multigrid

2020 ◽  
Vol 121 (13) ◽  
pp. 2874-2895 ◽  
Author(s):  
Denis Davydov ◽  
Jean‐Paul Pelteret ◽  
Daniel Arndt ◽  
Martin Kronbichler ◽  
Paul Steinmann
Keyword(s):  
Finite Strain ◽  
Matrix Free ◽  
Geometric Multigrid

Stress and Deformation

1996 ◽  
Author(s):  
Gerhard Oertel
Keyword(s):  
Differential Equations ◽  
Mathematical Description ◽  
Finite Strain ◽  
Stress Strain ◽  
Complex Problems ◽  
Vector Algebra ◽  
Stress And Deformation

Students of geology who may have only a modest background in mathematics need to become familiar with the theories of stress, strain, and other tensor quantities, so that they can follow, and apply to their own research, developments in modern, quantitative geology. This book, based on a course taught by the author at UCLA, can provide the proper introduction. Included throughout the eight chapters are 136 complex problems, advancing from vector algebra in standard and subscript notations, to the mathematical description of finite strain and its compounding and decomposition. Fully worked solutions to the problems make up the largest part of the book. With their help, students can monitor their progress, and geologists will be able to utilize subscript and matrix notations and formulate and solve tensor problems on their own. The book can be successfully used by anyone with some training in calculus and the rudiments of differential equations.

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