First-order gradient damage theory

Taking the strain tensor, the scalar damage variable, and the damage gradient as the state variables of the Helmholtz free energy, the general expressions of the firstorder gradient damage constitutive equations are derived directly from the basic law of irreversible thermodynamics with the constitutive functional expansion method at the natural state. When the damage variable is equal to zero, the expressions can be simplified to the linear elastic constitutive equations. When the damage gradient vanishes, the expressions can be simplified to the classical damage constitutive equations based on the strain equivalence hypothesis. A one-dimensional problem is presented to indicate that the damage field changes from the non-periodic solutions to the spatial periodic-like solutions with stress increment. The peak value region develops a localization band. The onset mechanism of strain localization is proposed. Damage localization emerges after damage occurs for a short time. The width of the localization band is proportional to the internal characteristic length.

Physics of ferroelectric differential capacitance based upon free energy, and implications for use in electronic devices

In this paper,it is shown that for stable,steady state operation of devices typical of microwave and millimeter wave electronics,no negative differential capacitance is possible with conventional thinking.However,it may be possible,with strain engineering of materials,to obtain some if not all elements of the differential capacitance tensor which are negative.Rigorous derivations are provided based upon analyzing the physics using thermodynamic phenomenological free energy.It should be emphasized that,even with strain engineering,and possible discovery of some negative capacitive elements,stable operation will not be obtained because the thermodynamics precludes it.

Microstructure investigation of dynamic recrystallization in hard machining:From thermodynamic irreversibility perspective

The drastically changed thermal,mechanical,and chemical energies within the machined surface layer during hard machining tend to initiate microstructural alteration.In this paper,attention is paid to the introduction of thermodynamic potential to unravel the mechanism of microstructure evolution.First,the thermodynamic potential-based model expressed by the Helmholtz free energy was proposed for predicting the microstructure changes of serrated chip and the machined surface layer.Second,the proposed model was implemented into a validated finite element simulation model for cutting operation as a user-defined subroutine.In addition,the predicted irreversible thermodynamic state change in the deformation zones associated with grain size,which was reduced to less than 1 mm from the initial size of 1.5 mm on the machined surface,was provided for an in-depth explanation.The good consistency between the simulated results and experimental data validated the efficacy of the developed model.This research helps to provide further insight into the microstructure alteration during metal cutting.

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.