Algorithmic tangent modulus at finite strains based on multiplicative decomposition

The algorithmic tangent modulus at finite strains in current configuration plays an important role in the nonlinear finite element method. In this work, the exact tensorial forms of the algorithmic tangent modulus at finite strains are derived in the principal space and their corresponding matrix expressions are also presented. The algorithmic tangent modulus consists of two terms. The first term depends on a specific yield surface, while the second term is independent of the specific yield surface. The elastoplastic matrix in the principal space associated with the specific yield surface is derived by the logarithmic strains in terms of the local multiplicative decomposition. The Drucker-Prager yield function of elastoplastic material is used as a numerical example to verify the present algorithmic tangent modulus at finite strains.

ter Multiplicative Decomposition Applied to Thermoelastic Geometrically-Exact Rods Dedicated to Professor Karl Stark Pister for his 95th birthday

This paper addresses the application of the continuum mechanics-based multiplicative decomposition for thermohyperelastic materials by Lu and Pister to Reissner’s structural mechanics-based,geometrically exact theory for finite strain plane deformations of beams,which represents a geometrically consistent non-linear extension of the linear shear-deformable Timoshenko beam theory.First,the Lu-Pister multiplicative decomposition of the displacement gradient tensor is reviewed in a three-dimensional setting,and the importance of its main consequence is emphasized,i.e.,the fact that isothermal experiments conducted over a range of constant reference temperatures are sufficient to identify constitutive material parameters in the stress-strain relations.We address various isothermal stress-strain relations for isotropic hyperelastic materials and their extensions to thermoelasticity.In particular,a model belonging to what is referred to as Simo-Pister class of material laws is used as an example to demonstrate the proposed procedure to extend isothermal stress-strain relations for isotropic hyperelastic materials to thermoelasticity.A certain drawback of Reissner’s structural-mechanics based theory in its original form is that constitutive relations are to be stipulated at the one-dimensional level,between stress resultants and generalized strains,so that the standardized small-scale material testing at the stress-strain level is not at disposal.In order to overcome this,we use a stress-strain based extension of the Reissner theory proposed by Gerstmayr and Irschik for the isothermal case,which we utilize here in the framework of the considered thermoelastic extension of the Simo-Pister stressstrain law.Consistent with the latter extension,we derive non-linear thermo-hyperelastic constitutive relations between stress-resultants and general strains.Special emphasis is given to linearizations and their consequences.A numerical example demonstrates the efficacy of the structural-mechanics approach in large-deformation problems.

Simulation of texture evolution during plastic deformation of FCC,BCC and HCP structured crystals with crystal plasticity based finite element method

Two alternative formulations of single crystal plasticity model were introduced respectively and two schemes were implemented in the explicit FE code with software ABAQUS/Explicit by writing the user subroutine VUMAT.Meshes containing material data were created with solid elements.Each element represented an individual grain,and the grain orientations were explicitly stored and updated at each increment.Tangential modulus method was employed to calculate the plastic shear strain increment of deformation systems in combination with a hardening law to describe the hardening responses.Both two developed subroutines were applied to simulate the texture evolution during the uniaxial tension of copper（FCC）,cold rolling of IF steel（BCC） and uniaxial compression of AZ31 magnesium alloy（HCP）.The predicted texture distributions are in qualitative agreement with the experimental results.

GRAPHICAL-BASED RELIABILITY EVALUATION OF MULTIPLE DISTINCT PRODUCTION LINES

This paper proposes a graphical-based methodology to evaluate the performance of a manufacturing system in terms of network model.We focus on a manufacturing system which consists of multiple distinct production lines.A transformation technique is developed to build the manufacturing system as a manufacturing network.In such a manufacturing network,the capacity of each machine is multistate due to failure,partial failure,or maintenance.Thus,this manufacturing network is also regarded as a multistate network.We evaluate the probability that the manufacturing network can meet a given demand,where the probability is referred to as the system reliability.A simple algorithm integrating decomposition technique is proposed to generate the minimal capacity vectors that machines should provide to eventually satisfy demand.The system reliability is derived in terms of such capacity vectors afterwards.A practical application in the context of IC card manufacturing system is utilized to demonstrate the performance evaluation procedure.

In-situ EXAFS study on the thermal decomposition of TiH_2

Thermal decomposition behaviors of TiH_2 powder under a flowing helium atmosphere and in a low vacuum condition have been studied using an in situ EXAFS technique.By an EXAFS analysis containing the multiple scattering paths including H atoms,the changes of the hydrogen stoichiometric ratio and the phase transformation sequence are obtained.The results demonstrate that the initial decomposition temperature is dependent on experimental conditions,which occurs,respectively,at about 300 and 400℃ in a low vacuum condition and under a flowing helium atmosphere.During the decomposition process of TiH_2 in a low vacuum condition,the sample experiences a phase change process：δ（TiH_2）→δ（TiH_x）→δ（TiH_1）＋β（TiH_x）→δ（TiH_x）＋β（TiH_x）＋α（Ti）→β（TiH_x）＋α（Ti）→α（Ti）＋β（Ti）.This study offers a way to detect the structural information of hydrogen.A detailed discussion about the decomposition process of TiH_2 is given in this paper.

A new interpretation of internal-variable theory in finite thermo-viscoelasticity

Based on the non-equilibrium thermodynamics,an internal-variable theory in thermo-viscoelasticity at finite deformation was proposed by Huang in 1999.In this theory,a modified stretch of the molecular chain was introduced,and hence the molecular network model in rubber elasticity was extended to take into account the viscous and thermal effects of the material.The viscous dissipation of the material can then be described by means of these internal variables,which appear in the expression of the modified stretch.In order to give a clearer explanation on the physical implication of the internal variables,a connection between the internal-variable theory and theoretical formulation based on the multiplicative decomposition of the deformation gradient in existing literature is presented in this paper,which allows the above internal-variable theory to be more systematic.

Theoretical and Numerical Modeling of Nonlinear Electromechanics with applications to Biological Active Media

We present a general theoretical framework for the formulation of the nonlinear electromechanics of polymeric and biological active media.The approach developed here is based on the additive decomposition of the Helmholtz free energy in elastic and inelastic parts and on the multiplicative decomposition of the deformation gradient in passive and active parts.We describe a thermodynamically sound scenario that accounts for geometric and material nonlinearities.In view of numerical applications,we specialize the general approach to a particular material model accounting for the behavior of fiber reinforced tissues.Specifically,we use the model to solve via finite elements a uniaxial electromechanical problem dynamically activated by an electrophysiological stimulus.Implications for nonlinear solid mechanics and computational electrophysiology are finally discussed.