Non-linear solid mechanics, past, present and future

1969 ◽  
pp. 77-99 ◽  
Author(s):  
F. K. G. Odqvist
Keyword(s):  
Solid Mechanics ◽  
Non Linear

scholarly journals Advances in the DEM and Coupled DEM and FEM Techniques in Non Linear Solid Mechanics

2017 ◽  
pp. 309-335 ◽  
Author(s):  
Eugenio Oñate ◽  
Francisco Zárate ◽  
Miguel A. Celigueta ◽  
José M. González ◽  
Juan Miquel ◽  
...  
Keyword(s):  
Solid Mechanics ◽  
Non Linear

scholarly journals A stabilized mixed implicit Material Point Method for non-linear incompressible solid mechanics

2018 ◽  
Vol 63 (6) ◽  
pp. 1243-1260 ◽  
Author(s):  
I. Iaconeta ◽  
A. Larese ◽  
R. Rossi ◽  
E. Oñate
Keyword(s):  
Solid Mechanics ◽  
Material Point Method ◽  
Material Point ◽  
Point Method ◽  
Non Linear

scholarly journals On a class of non-linear differential equations with exact solution

2012 ◽  
Vol 34 (1) ◽  
pp. 7-17
Author(s):  
Dao Huy Bich ◽  
Nguyen Dang Bich
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Exact Solutions ◽  
Solid Mechanics ◽  
Linear Equations ◽  
Linear Differential Equations ◽  
Second Order Differential Equations ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

The present paper deals with a class of non-linear ordinary second-order differential equations with exact solutions. A procedure for finding the general exact solution based on a known particular one is derived. For illustration solutions of some non-linear equations occurred in many problems of solid mechanics are considered.

scholarly journals Teaching solid mechanics to artificial intelligence—a fast solver for heterogeneous materials

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Jaber Rezaei Mianroodi ◽  
Nima H. Siboni ◽  
Dierk Raabe
Keyword(s):  
Deep Neural Network ◽  
Solid Mechanics ◽  
Local Stress ◽  
Percentage Error ◽  
Elastic Media ◽  
Fast Solver ◽  
Plastic Materials ◽  
Local Stresses ◽  
Non Linear ◽  
Elastic Plastic Materials

AbstractWe propose a deep neural network (DNN) as a fast surrogate model for local stress calculations in inhomogeneous non-linear materials. We show that the DNN predicts the local stresses with 3.8% mean absolute percentage error (MAPE) for the case of heterogeneous elastic media and a mechanical contrast of up to factor of 1.5 among neighboring domains, while performing 103 times faster than spectral solvers. The DNN model proves suited for reproducing the stress distribution in geometries different from those used for training. In the case of elasto-plastic materials with up to 4 times mechanical contrast in yield stress among adjacent regions, the trained model simulates the micromechanics with a MAPE of 6.4% in one single forward evaluation of the network, without any iteration. The results reveal an efficient approach to solve non-linear mechanical problems, with an acceleration up to a factor of 8300 for elastic-plastic materials compared to typical solvers.

scholarly journals Explicit mixed strain-displacement finite element for dynamic geometrically non-linear solid mechanics

2015 ◽  
Vol 55 (3) ◽  
pp. 543-559 ◽  
Author(s):  
N. M. Lafontaine ◽  
R. Rossi ◽  
M. Cervera ◽  
M. Chiumenti
Keyword(s):  
Finite Element ◽  
Solid Mechanics ◽  
Non Linear

Edge-based finite element techniques for non-linear solid mechanics problems

2001 ◽  
Vol 50 (9) ◽  
pp. 2053-2068 ◽  
Author(s):  
Alvaro L. G. A. Coutinho ◽  
Marcos A. D. Martins ◽  
Jos� L. D. Alves ◽  
Luiz Landau ◽  
Anderson Moraes
Keyword(s):  
Finite Element ◽  
Solid Mechanics ◽  
Non Linear ◽  
Edge Based
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