scholarly journals Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics

2012 ◽  
Vol 205 (1) ◽  
pp. 59-118 ◽  
Author(s):  
Arash Yavari ◽  
Alain Goriely
Keyword(s):  
Cartan Geometry ◽  
Dislocation Mechanics

scholarly journals Cones and Cartan geometry

2021 ◽  
Vol 78 ◽  
pp. 101793
Author(s):  
Antonio J. Di Scala ◽  
Carlos E. Olmos ◽  
Francisco Vittone
Keyword(s):  
Cartan Geometry

scholarly journals On Computational Modelling Of Strain-Hardening Material Dynamics

2012 ◽  
Vol 11 (5) ◽  
pp. 1525-1546 ◽  
Author(s):  
Philip Barton ◽  
Evgeniy Romenski
Keyword(s):  
Relaxation Time ◽  
Stress Relaxation ◽  
Plastic Strain ◽  
Strain Hardening ◽  
Three Dimensional ◽  
Computational Modelling ◽  
Constitutive Models ◽  
Successful Implementation ◽  
Hardening Material ◽  
Dislocation Mechanics

AbstractIn this paper we show that entropy can be used within a functional for the stress relaxation time of solid materials to parametrise finite viscoplastic strain-hardening deformations. Through doing so the classical empirical recovery of a suitable irreversible scalar measure of work-hardening from the three-dimensional state parameters is avoided. The success of the proposed approach centres on determination of a rate-independent relation between plastic strain and entropy, which is found to be suitably simplistic such to not add any significant complexity to the final model. The result is sufficiently general to be used in combination with existing constitutive models for inelastic deformations parametrised by one-dimensional plastic strain provided the constitutive models are thermodynamically consistent. Here a model for the tangential stress relaxation time based upon established dislocation mechanics theory is calibrated for OFHC copper and subsequently integrated within a two-dimensional moving-mesh scheme. We address some of the numerical challenges that are faced in order to ensure successful implementation of the proposedmodel within a hydrocode. The approach is demonstrated through simulations of flyer-plate and cylinder impacts.

scholarly journals Plasticity of crystals and interfaces: From discrete dislocations to size-dependent continuum theory

2010 ◽  
Vol 37 (4) ◽  
pp. 289-332 ◽  
Author(s):  
Sinisa Mesarovic
Keyword(s):  
Unsolved Problem ◽  
Continuum Theory ◽  
Elastic Interaction ◽  
Interface Energy ◽  
Crystalline Materials ◽  
Size Dependent ◽  
Dislocation Mechanics ◽  
Pile Up ◽  
Slip Planes ◽  
Discrete Dislocations

In this communication, we summarize the current advances in size-dependent continuum plasticity of crystals, specifically, the rate-independent (quasistatic) formulation, on the basis of dislocation mechanics. A particular emphasis is placed on relaxation of slip at interfaces. This unsolved problem is the current frontier of research in plasticity of crystalline materials. We outline a framework for further investigation, based on the developed theory for the bulk crystal. The bulk theory is based on the concept of geometrically necessary dislocations, specifically, on configurations where dislocations pile-up against interfaces. The average spacing of slip planes provides a characteristic length for the theory. The physical interpretation of the free energy includes the error in elastic interaction energies resulting from coarse representation of dislocation density fields. Continuum kinematics is determined by the fact that dislocation pile-ups have singular distribution, which allows us to represent the dense dislocation field at the boundary as a superdislocation, i.e., the jump in the slip filed. Associated with this jump is a slip-dependent interface energy, which in turn, makes this formulation suitable for analysis of interface relaxation mechanisms.

CAN TORSION BE TREATED AS JUST ANOTHER TENSOR FIELD?

2012 ◽  
Vol 07 ◽  
pp. 158-164 ◽  
Author(s):  
JAMES M. NESTER ◽  
CHIH-HUNG WANG
Keyword(s):  
Gauge Theory ◽  
Tensor Field ◽  
Affine Connection ◽  
Cartan Geometry ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Alternative Gravity Theories ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity ◽  
Alternative Gravity

Many alternative gravity theories use an independent connection which leads to torsion in addition to curvature. Some have argued that there is no physical need to use such connections, that one can always use the Levi-Civita connection and just treat torsion as another tensor field. We explore this issue here in the context of the Poincaré Gauge theory of gravity, which is usually formulated in terms of an affine connection for a Riemann-Cartan geometry (torsion and curvature). We compare the equations obtained by taking as the independent dynamical variables: (i) the orthonormal coframe and the connection and (ii) the orthonormal coframe and the torsion (contortion), and we also consider the coupling to a source. From this analysis we conclude that, at least for this class of theories, torsion should not be considered as just another tensor field.

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