Planar deformation in geometrically nonlinear elasticity

1994 ◽  
Vol 35 (1) ◽  
pp. 100-116
Author(s):  
V. D. Bondar'
Keyword(s):  
Nonlinear Elasticity ◽  
Geometrically Nonlinear ◽  
Planar Deformation

An efficient grid-based direct-volume integration BEM for 3D geometrically nonlinear elasticity

2017 ◽  
Vol 62 (4) ◽  
pp. 603-616 ◽  
Author(s):  
Yani Deng ◽  
Junjie Rong ◽  
Wenjing Ye ◽  
L. J. Gray
Keyword(s):  
Nonlinear Elasticity ◽  
Geometrically Nonlinear ◽  
Volume Integration ◽  
Grid Based

scholarly journals Phase-Field Approximation of Functionals Defined on Piecewise-Rigid Maps

2021 ◽  
Vol 31 (5) ◽  
Author(s):  
Marco Cicalese ◽  
Matteo Focardi ◽  
Caterina Ida Zeppieri
Keyword(s):  
Brittle Fracture ◽  
Nonlinear Elasticity ◽  
Phase Field ◽  
Field Approximation ◽  
Variational Approximation ◽  
Geometrically Nonlinear

AbstractWe provide a variational approximation of Ambrosio–Tortorelli type for brittle fracture energies of piecewise-rigid solids. Our result covers both the case of geometrically nonlinear elasticity and that of linearised elasticity.

scholarly journals Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity

2017 ◽  
Vol 473 (2203) ◽  
pp. 20170235 ◽  
Author(s):  
S. Conti ◽  
M. Klar ◽  
B. Zwicknagl
Keyword(s):  
Nonlinear Elasticity ◽  
Inclusion Problem ◽  
Geometrically Nonlinear ◽  
Austenitic Matrix ◽  
Continuous Solutions ◽  
Nonlinear Elasticity Theory ◽  
Piecewise Affine ◽  
Specific Parameter ◽  
Partial Differential Inclusion ◽  
Differential Inclusion Problem

We consider a partial differential inclusion problem which models stress-free martensitic inclusions in an austenitic matrix, based on the standard geometrically nonlinear elasticity theory. We show that for specific parameter choices there exist piecewise affine continuous solutions for the square-to-oblique and the hexagonal-to-oblique phase transitions. This suggests that for specific crystallographic parameters the hysteresis of the phase transformation will be particularly small.

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