An algorithmic stress formula for energy conserving time integration in a mixed framework for polyconvex large strain elasticity

AbstractIn this paper, an efficient and robust methodology to simulate saturated soils subjected to low-medium frequency dynamic loadings under large deformation regime is presented. The coupling between solid and fluid phases is solved through the dynamic reduced formulation $$u-p_\mathrm{w}$$ u - p w (solid displacement – pore water pressure) of the Biot’s equations. The additional novelty lies in the employment of an explicit two-steps Newmark predictor-corrector time integration scheme that enables accurate solutions of related geomechanical problems at large strain without the usually high computational cost associated with the implicit counterparts. Shape functions based on the elegant Local Maximum Entropy approach, through the Optimal Transportation Meshfree framework, are considered to solve numerically different dynamic problems in fluid saturated porous media.

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On the optimization of n-sub-step composite time integration methods

Nonlinear Dynamics ◽

10.1007/s11071-020-06020-8 ◽

2020 ◽

Vol 102 (3) ◽

pp. 1939-1962

Author(s):

Huimin Zhang ◽

Runsen Zhang ◽

Yufeng Xing ◽

Pierangelo Masarati

Keyword(s):

Time Integration ◽

Low Frequency ◽

Unconditional Stability ◽

Frequency Content ◽

Order Accuracy ◽

Integration Methods ◽

Universal Approach ◽

Energy Conserving ◽

Time Integration Methods ◽

Linear And Nonlinear Systems

AbstractA family of n-sub-step composite time integration methods, which employs the trapezoidal rule in the first $$n-1$$ n - 1 sub-steps and a general formula in the last one, is discussed in this paper. A universal approach to optimize the parameters is provided for any cases of $$n\ge 2$$ n ≥ 2 , and two optimal sub-families of the method are given for different purposes. From linear analysis, the first sub-family can achieve nth-order accuracy and unconditional stability with controllable algorithmic dissipation, so it is recommended for high-accuracy purposes. The second sub-family has second-order accuracy, unconditional stability with controllable algorithmic dissipation, and it is designed for heuristic energy-conserving purposes, by preserving as much low-frequency content as possible. Finally, some illustrative examples are solved to check the performance in linear and nonlinear systems.

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CDM Model and its Application to Numerical Simulation on Rotating Band’s Engraving Process

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.117-119.1672 ◽

2011 ◽

Vol 117-119 ◽

pp. 1672-1676 ◽

Cited By ~ 1

Author(s):

He Yang Sun ◽

Ji Sheng Ma ◽

Long Bo Sheng ◽

Wei Li ◽

Da Lin Wu

Keyword(s):

Damage Evolution ◽

Damage Mechanics ◽

Yield Criterion ◽

Large Strain ◽

Time Integration ◽

Continuum Damage Mechanics ◽

Thermal Softening ◽

Softening Effect ◽

Integration Algorithm ◽

Explicit Finite Element

A coupled constitutive model of viscoplasticity and ductile damage for penetration problems has been deduced. The model proposed by Lemaitre was based on the continuum damage mechanics. In the model, large strain, high strain-rate, thermal softening and damage evolution were taken into account. At the meanwhile, Von Mises yield criterion, Johnson-Cook hardening model and Johnson-Cook fracture strain model were adopted. The model was implemented in the explicit finite element code Abaqus\Explicit through the Vumat subroutine by using an efficient explicit time integration algorithm. Based on the model, the rotating band’s engraving process was simulated, at the same time the influence of the stress state on damage evolution and the thermal softening effect was discussed. An effective way to simulate the fire process of gun was afforded.

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