An Overview of the State of the Art in Atomistic and Multiscale Simulation of Fracture

The emerging field of nanomechanics is providing a new focus in the study of the mechanics of materials, particularly in simulating fundamental atomic mechanisms involved in the initiation and evolution of damage. Simulating fundamental material processes using first principles in physics strongly motivates the formulation of computational multiscale methods to link macroscopic failure to the underlying atomic processes from which all material behavior originates. This report gives an overview of the state of the art in applying concurrent and sequential multiscale methods to analyze damage and failure mechanisms across length scales

Coupling molecular dynamics and continua with weak constraints

One of the most challenging problems in dynamic concurrent multiscale simulations is the reflectionless transfer of physical quantities between the different scales. In particular, when coupling molecular dynamics and finite element discretizations in solid body mechanics, often spurious wave reflections are introduced by the applied coupling technique. The reflected waves are typically of high frequency and are arguably of little importance in the domain where the finite element discretization drives the simulation. In this work, we provide an analysis of this phenomenon.Based on the gained insight, we derive a new coupling approach, which neatly separates high and low frequency waves. Whereas low frequency waves are permitted to bridge the scales, high frequency waves can be removed by applying damping techniques without affecting the coupled share of the solution. As a consequence, our new method almost completely eliminates unphysical wave reflections and deals in a consistent way with waves of arbitrary frequencies. The separation of wavelengths is achieved by employing a discrete L2-projection, which acts as a low pass filter. Our coupling constraints enforce matching in the range of this projection. With respect to the numerical realization this approach has the advantage of a small number of constraints, which is computationally efficient. Numerical results in one and two dimensions confirm our theoretical findings and illustrate the performance of our new weak coupling approach

Multiscale Modelling of Molecules and Continuum Mechanics Using Bridging Scale Method

his PhD dissertation is about developing a multiscale methodology for coupling two different time/length scales in order to improve properties of new space materials. Since the traditional continuum mechanics models cannot describe the influence of the nanostructured upon the mechanical properties of materials and full atomistic description is still computationally too expensive, millions of degrees of freedom are needed just for modeling few hundred cubic nanometers, this leads to a coupled system of equations of finite element (FE) in continuum and molecular dynamics (MD) in atomistic domain. Coupling efficiently and accurately two dissimilar domains presents challenges especially in handshaking area where the two domains interact and transfer information. The objective of this study is (i) develop a novel nodal position FE method that can couple with the MD easily, (ii) develop a proper methodology to couple the FE with MD for FE/MD multi-scale modeling and let the information transfer in a seamless manner between the two domains, and (iii) implement complicated cases to confirm accuracy and validity of the proposed model

Computational Multiscale Methods

Computational Multiscale Methods play an important role in many modern computer simulations in material sciences with different time scales and different scales in space. Besides various computational challenges, the meeting brought together various applications from many disciplines and scientists from various scientific communities

Computational Multiscale Solvers for Continuum Approaches

Computational multiscale analyses are currently ubiquitous in science and technology. Different problems of interest-e.g., mechanical, fluid, thermal, or electromagnetic-involving a domain with two or more clearly distinguished spatial or temporal scales, are candidates to be solved by using this technique. Moreover, the predictable capability and potential of multiscale analysis may result in an interesting tool for the development of new concept materials, with desired macroscopic or apparent properties through the design of their microstructure, which is now even more possible with the combination of nanotechnology and additive manufacturing. Indeed, the information in terms of field variables at a finer scale is available by solving its associated localization problem. In this work, a review on the algorithmic treatment of multiscale analyses of several problems with a technological interest is presented. The paper collects both classical and modern techniques of multiscale simulation such as those based on the proper generalized decomposition (PGD) approach. Moreover, an overview of available software for the implementation of such numerical schemes is also carried out. The availability and usefulness of this technique in the design of complex microstructural systems are highlighted along the text. In this review, the fine, and hence the coarse scale, are associated with continuum variables so atomistic approaches and coarse-graining transfer techniques are out of the scope of this paper.Abengoa Researc

The Weak Coupling Method for Coupling Continuum Mechanics with Molecular Dynamics

For the global behavior of solids in structural mechanics of nonlinear processes, local effects on the atomistic level play an important role. Often a direct numerical simulation of the macroscopic behavior by a complete resolution of the microscale is for computational reason not possible. Thus, employing a multiscale strategy for an efficient and accurate modelling seems favorable since by separating the problem into two different frameworks, the accuracy of a fine scale model can be combined with the advantages of a computationally efficient model. More precisely a comparably small region of atoms e.g. surrounding the tip of a crack is modelled by molecular dynamics. Outside of this region, we take advantage of the fact that the displacement is almost homogeneous and can thus be modelled efficiently by a linear elastic continuum dynamical simulation. Clearly, both scales offer fundamentally different descriptions of the matter and they use different simulation methods. Whereas on the continuum scale the finite element method and a function space setting is used, the molecular dynamics is based on the movement of particles in the Euclidean space. Additionally, dynamical simulations with a transition zone (handshake region) between atomistic systems and the coarser finite element mesh suffer from unwanted (spurious) reflections, since the finite element method can not represent short wave length vibrational modes. Here a completely new approach is presented, which takes advantage of an infinite dimensional function space for the information transfer between the scales. Starting from a handshake region, the key idea is to construct a transfer operator between the different scales. This transfer operator is based on local averaging taken values. In order to construct the local weight functions, a partition of unity is assigned to the molecular degree of freedom. This allows us to decompose the micro scale displacement in the handshake region into a small and large wave number part by means of a weighted $L^2$ projection. In the first instance, this function space oriented interpretation of the atomistic displacement is applied in the context of a completely overlapping decomposition. More precisely, we consider the case, when the domain of the handshake region is conform with the domain of the molecular dynamics. In order to identify the displacements pertaining to the atomistic or continuum level respectively, we employ a multiscale decomposition. In particular, we decompose the micro scale displacement into a "low frequency'' and a "high frequency'' part in a weak sense. This new approach is also used in the context of a partly overlapping decomposition. Therein, the coarse and the fine scale simulation are matched by constraining the two displacements in the handshake region. The key issue in this context is, that our function space oriented approach allows us to interpret the constraints in a weak sense. Thus the "low frequent'' part can be captured by the coarse scale, whereas the "high frequent'' part of the displacement which has no meaning on the coarse scale is damped in the handshake region. Moreover numerical examples in 1d,2d and 3d show that this approach allows molecular displacements for entering into the continuum domain and the other way round flawlessly