A type of nonlinearity in vibrational engineering systems emerges when the restoring force is a nonlinear function of displacement. The derivative of this function is known as stiffness. If the stiffness increases by increasing the value of displacement from the equilibrium position, then the system is known as hardening type oscillator and if the stiffness decreases by increasing the value of ...

Localized deformation such as shear bands, compaction bands, dilation bands, combined shear/compaction or shear/dilation bands, fractures, and joint slippage are commonly found in rocks. Thus, modeling their inception, development and propagation, and effect on stress response is important with regard to making informed engineering design decisions involving these materials. Following a GulfRoc...

The quasi-static problem of elastoplasticity with isotropic hardening is considered, with particular emphasis on its numerical solution by means of a Newton-like method. The smoothness properties necessary for such method can be ensured by Moreau-Yosida’s theorem. After time discretization, the classical formulation of the elastoplastic problem is transformed to a minimization problem. The conv...

K 〈x, y〉 dy = ‖x‖ By ‖·‖ we denote the standard Euclidean norm. The notion of isotropic position was extensively studied by V. Milman and A. Pajor [M-P]. Note that our definition is consistent with [K-L-S]. The normalization in [M-P] is slightly different. If the information about the body K is uncomplete it is impossible to bring it exactly to the isotropic position. So, the definition of the ...

The size-dependent response of metallic microwires under monotonic and cyclic torsion is modeled taking a reduced-order strain gradient crystal plasticity approach involving single scalar-valued micromorphic variable. It compared with the predicted by CurlFp model proposed in Kaiser Menzel (2019a), which based on complete dislocation density tensor. shown that, non-uniform plastic deformation p...

Abstract Female sterility is caused by Fallopian tube occlusions in one of three cases. Current treatment methods achieve unsatisfying pregnancy rates and are associated with high costs or significant psychological physiological stress. Our previously described microstent technology opens up new therapeutic possibilities to restore the lumen without surgery. In this work, a Finite Element Analy...

An experimental database of springback and twisting U-shaped elongated structures is available from a previous study. The materials are copper alloys: pure Cu, CuBe2, CuFe2P, provided in thin sheets thickness around 0.1 mm. After deep-drawing rectangular blanks, which can be aligned with the tools or slightly misaligned, tool withdrawal, structure exhibits an opening section (2D springback) (3D...

We propose an algorithm for the efficient parallel implementation of elastoplastic problems with hardening based on the so-called TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. We consider an associated elastoplastic model with the von Mises plastic criterion and the linear isotropic hardening law. Such a model is discretized by the implicit Euler method i...

In recent years, the studies on the enhancement of the prediction capability of the sheet metal forming simulations have increased remarkably. Among the used models in the finite element simulations, the yield criteria and hardening models have a great importance for the prediction of the formability and springback. The required model parameters are determined by using the several test results,...

The paper is devoted to the numerical solution of an elastoplastic constitutive initial value problem containing the Mohr-Coulomb yield criterion, a nonassociative plastic flow rule, and a nonlinear isotropic hardening. The constitutive problem is discretized by the implicit Euler method. Instead of the conventional Koiter formulations, we define the plastic flow rule using the subdifferential ...