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Hydromechanical coupling and basin tectonic compression
Published in J.-F. Thimus, Y. Abousleiman, A.H.-D. Cheng, O. Coussy, E. Detournay, Poromechanics, 2020
J.P. Radu, R. Charlier, J.D. Barnichon
The incremental stress-strain relation relates the Jaumann’s derivative of the effective stress rate tensor to the strain rate tensor : σ∇_=σ′∇_−pfI_=C__ε_.
Continuum theory of granular materials
Published in M. Oda, K. Iwashita, Mechanics of Granular Materials, 2020
where ε˙ijvp is the viscop lastic strain rate tensor, is the elastic strain rate tensor and is the total strain rate tensor. ε˙ijeε˙ij
A Review on Plasticity and the Finite Element Method
Published in Uday S Dixit, Seikh Mustafa Kamal, Rajkumar Shufen, Autofrettage Processes, 2019
Uday S. Dixit, Seikh Mustafa Kamal, Rajkumar Shufen
where vi represents a component of velocity as a function of spatial coordinates. Eulerian formulation uses strain rate as the measure of deformation. In the textbooks on continuum mechanics, strain rate tensor is called rate of deformation tensor.
Anisotropic mechanical behavior prediction of aluminum alloy sheet based on an anisotropic GTN model: Modeling, simulation and experimental investigation
Published in Mechanics of Advanced Materials and Structures, 2022
The stress updating procedure can be divided into an elastic stress prediction and plastic stress correction [41]. The elastic stress prediction is firstly conducted for predicting the elastic stress and after that the plastic stress correction is performed on that basis. Hence it is usually assumed that the total strain rate of a small-deformed metal material consists of elastic and plastic parts as presented by where denotes the elastic strain rate tensor, and denotes the plastic strain rate tensor. The elastic Cauchy stress rate tensor can be calculated by where denotes a fourth-order elastic tensor that satisfies with and being the bulk modulus and shear modulus, respectively.
Non-classical continuum theories for solid and fluent continua and some applications
Published in International Journal of Smart and Nano Materials, 2019
K.S. Surana, D. Mysore, J.N. Reddy
represents the usual strain rate tensor (symmetric part of the velocity gradient tensor) used in fluid mechanics., , are antisymmetric tensor containing rotation rates, hence are not measures of strain rate.Based on (1) and (2) is not a strain rate tensor, but rather addition of strain rate tensor and the internal and Cosserat rotation rates and .
Smooth particle hydrodynamics for the analysis of stresses in soil around Jack-in Pile
Published in European Journal of Environmental and Civil Engineering, 2022
Perpetua Aaniya Cyril, Sien Ti Kok, Myung Kyu Song, Andy Chan, Jing-Ying Wong, Wee Kang Choong
To begin with, total strain rate tensor for an elastic-perfectly plastic constitutive relationship is expressed as: where and are the elastic strain rate tensor and plastic strain rate tensor respectively. and denote and coordinate directions. This is because, for plane strain condition, the components of the total strain rate tensor along the direction are zero.