The cyclic instability phenomenon is investigated at the modeling of large elasto-plastic strains. The instability is observed at
large strains for some elasto-plastic material models with a kinematic hardening in contrast to the small strain case. The
cyclic instability manifests itself as a changing of shape, sizes or location of the hysteresis loop during cycling. In partial case
the cyclic instability leads to the stress ratcheting. Responses of 50 various models of elasto-plastic material have been
considered under proportional loading (cyclic simple shear) and non-proportional loading (combined cyclic simple shear and
tension-compression). Causes of the cyclic instability are analyzed and conditions ensuring the cyclic stability of elasto-plastic
models are proposed.
Ferroelectroelastic materials exhibit nonlinear behavior when they are subjected to high electromechanical loadings.
Using the standard formulation with the scalar potential as electric nodal variable in the nonlinear finite element analysis
can lead to a low convergence of the iteration procedures. Therefore the formulation with a vector potential as electric
nodal variable is developed, which ensures a positive definite stiffness matrix. Solutions of boundary value problems
using the scalar potential formulation lie on a saddle point in the space of the nodal degrees of freedom, whereas
solutions for the vector potential formulation are in a minimum. Unfortunately, the latter solutions involving the "curlcurl"
operator are non-unique in the three-dimensional case. A Coulomb gauge condition imposed on the electric vector
potential improves the convergence behavior of nonlinear problems, and in combination with appropriate boundary
conditions, it can enforce unique vector potential solutions. A penalized version of the weak vector potential formulation
with the Coulomb gauge is proposed and tested on some numerical examples in ferroelectricity.
Response of various elasto-plastic models is compared at large strains under cyclic loading. In contrast to the small strain case, the cyclic instability is observed at large strains for some elasto-plastic material models with a kinematic hardening. The cyclic instability manifests itself as changing of shape, size or location of the hysteresis loop during cycling. Causes of the cyclic instability are analyzed. Conditions ensuring the cyclic stability of elasto-plastic models are proposed.
Experimental - theoretical research of the plastic deformation of thin-walled steel and nickel tubular specimens was done. The experimental results and forecasts of the kinematical hardening model and multisurface model with one active surface were compared. A modification of the plasticity theory was gone. The modification takes into account character of a loading path. The constitutive equation gives the possibility to make predictive calculations when either loading or strain path (in whole strains) is known. The research is performed for complex periodic loading paths, containing partial and complete unloading.
KEYWORDS: Mechanics, Data modeling, Finite element methods, Process control, Process modeling, Computer simulations, Chemical elements, Numerical modeling, Kinematics, Nondestructive evaluation
The influence of crack path configuration on its growth rate is considered. The straight and zigzag-like crack models are compared for the different stages of propagation and various loading conditions. Comparison of numerical results based on elasto-plastic finite element analysis and experimental data has been presented and discussed. The possible modification of classical fatigue lifetime prediction equations are discussed with aim to take into consideration the kinking effect at the initial stage of crack propagation.
KEYWORDS: Mechanics, Computer simulations, Modeling, Finite element methods, Chemical elements, Data modeling, Aluminum, Solids, 3D modeling, Numerical analysis
The direct modeling of fatigue cracks propagation with nonlinear paths is carried out on the base of continuum damage mechanics concept. The crack initiation and propagation is assumed to occur within the current plane of maximal damage. The various damage measures are introduced and compared for the prediction of the crack growth direction. The influence of the crack configuration on the effect of crack closure and propagation rate is investigated for the different types of crack trajectory. Elasto-plastic finite element analysis of the steel sharp notched specimens with a single crack under plane cyclic bending is performed for the different cases of loading. Comparison of numerical results and experimental data has been presented and discussed.
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