A small-strain model to simulate the curing of thermosets

This contribution presents a newly developed phenomenological model to describe the curing process of thermosets undergoing small strain deformations. The governing equations are derived from a number of physical and chemical presuppositions and details of the numerical implementation within the finite element method are given. The curing of thermosets is a very complex process involving a series of chemical reactions which result in the conversion of liquid low molecular weight monomer mixtures into highly cross-linked solid macromolecular structures. This phase transition from a viscous fluid to a viscoelastic solid can be modelled by a constitutive relation which is based on a temporal evolution of shear modulus and relaxation time. Some numerical examples demonstrate the capability of the model to correctly represent the evolution of elastic and inelastic material properties as well as the volume shrinkage taking place during the curing process

A finite strain framework for the simulation of polymer curing. Part I: Elasticity

A phenomenologically motivated small strain model to simulate the curing of thermosets has been developed and discussed in a recently published paper (Hossain et al. in Comput Mech 43(6):769-779, 2009). Inspired by the concepts used there, this follow-up contribution presents an extension towards the finite strain regime. The thermodynamically consistent framework proposed here for the simulation of curing polymers particularly is independent of the choice of the free energy density, i.e. any phenomenological or micromechanical approach can be utilised. Both the governing equations for the curing simulation framework and the necessary details for the numerical implementation within the finite element method are derived. The curing of polymers is a very complex process involving a series of chemical reactions typically resulting in a conversion of low molecular weight monomer solutions into more or less cross-linked solid macromolecular structures. A material undergoing such a transition can be modelled by using an appropriate constitutive relation that is distinguished by prescribed temporal evolutions of its governing material parameters, which have to be determined experimentally. Part I of this work will deal with the elastic framework whereas the following Part II will focus on viscoelastic behaviour and shrinkage effects. Some numerical examples demonstrate the capability of our approach to correctly reproduce the behaviour of curing materials

Modeling and simulation of curing and damage in thermosetting adhesives

The curing of thermosetting adhesives is a complex polymerization process that involves the transition of a viscous liquid into a viscoelastic solid. This phase transition is frequently accompanied by a volume shrinkage of the material, which may induce mechanical strains and stresses. These, in turn, can lead to a reduced performance or even failure of the adhesive joint. The present contribution introduces a continuum mechanical model that is suited to describe the emergence of stresses and the corresponding initiation of material degradation in adhesive layers, both during the process of curing and, of course, during subsequent loading. The model is implemented into a finite element code and some numerical examples demonstrate the interaction of curing shrinkage, stress evolution, and damage

A finite strain framework for the simulation of polymer curing. Part II. viscoelasticity and shrinkage

A phenomenologically inspired, elastic finite strain framework to simulate the curing of polymers has been developed and discussed in the first part (Hossain et al. in Comput Mech 44(5):621-630, 2009) of this work. The present contribution provides an extension of the previous simulation concept towards the consideration of viscoelastic effects and the phenomenon of curing shrinkage. The proposed approach is particularly independent of the type of the free energy density, i.e. any phenomenologically or micromechanically based viscoelastic polymer model can be utilised. For both cases the same representatives that have been used for the elastic curingmodels, i.e. the Neo-Hookean model and the 21-chain microsphere model, are reviewed and extended accordingly. The governing equations are derived as well as the corresponding tangent operators necessary for the numerical implementation within the finite element method. Furthermore, we investigate two different approaches-a shrinkage strain function and a multiplicative decomposition of the deformation gradient-to capture the phenomenon of curing shrinkage, i.e. the volume reduction induced by the polymerisation reaction which may lead to significant residual stresses and strains in the fully cured material. Some representative numerical examples conclude this work and prove the capability of our approach to correctly capture inelastic behaviour and shrinkage effects in polymers undergoing curing processes

Numerical modelling of non-linear electroelasticity

The numerical modelling of non‐linear electroelasticity is presented in this work. Based on well‐established basic equations of non‐linear electroelasticity a variational formulation is built and the finite element method is employed to solve the non‐linear electro‐mechanical coupling problem. Numerical examples are presented to show the accuracy of the implemented formulation

Coupled modeling and simulation of electro-elastic materials at large strains

In the recent years various novel materials have been developed that respond to the application of electrical loading by large strains. An example is the class of so-called electro-active polymers (EAP). Certainly these materials are technologically very interesting, e.g. for the design of actuators in mechatronics or in the area of artificial tissues. This work focuses on the phenomenological modeling of such materials within the setting of continuum-electro-dynamics specialized to the case of electro-hyperelastostatics and the corresponding computational setting. Thereby a highly nonlinear coupled problem for the deformation and the electric potential has to be considered. The finite element method is applied to solve the underlying equations numerically and some exemplary applications are presented

An Arlequin-based method to couple molecular dynamics and finite element simulations of amorphous polymers and nanocomposites

A new simulation technique is introduced to couple a flexible particle domain as encountered in soft-matter systems and a continuum which is solved by the Finite Element (FE) method. The particle domain is simulated by a molecular dynamics (MD) method in coarse grained (CG) representation. On the basis of computational experiences from a previous study, a staggered coupling procedure has been chosen. The proposed MD–FE coupling approximates the continuum as a static region while the MD particle space is treated as a dynamical ensemble. The information transfer between MD and FE domains is realized by a coupling region which contains, in particular, additional auxiliary particles, so-called anchor points. Each anchor point is harmonically bonded to a standard MD particle in the coupling region. This type of interaction offers a straightforward access to force gradients at the anchor points that are required in the developed hybrid approach. Time-averaged forces and force gradients from the MD domain are transmitted to the continuum. A static coupling procedure, based on the Arlequin framework, between the FE domain and the anchor points provides new anchor point positions in the MD–FE coupling region. The capability of the new simulation procedure has been quantified for an atactic polystyrene (PS) sample and for a PS-silica nanocomposite, both simulated in CG representation. Numerical data are given in the linear elastic regime which is conserved up to 3% strain. The convergence of the MD–FE coupling procedure has been demonstrated for quantities such as reaction forces or the Cauchy stress which have been determined both in the bare FE domain and in the coupled system. Possible applications of the hybrid method are shortly mentioned