Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

The method we introduced in 1992 for measuring hardness and elastic modulus by instrumented indentation techniques has widely been adopted and used in the characterization of small-scale mechanical behavior. Since its original development, the method has undergone numerous refinements and changes brought about by improvements to testing equipment and techniques as well as from advances in our understanding of the mechanics of elastic–plastic contact. Here, we review our current understanding of the mechanics governing elastic–plastic indentation as they pertain to load and depth-sensing indentation testing of monolithic materials and provide an update of how we now implement the method to make the most accurate mechanical property measurements. The limitations of the method are also discussed.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0884291400085800

Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology

An elastic-plastic finite element model for the frictionless contact of a deformable sphere pressed by a rigid flat is presented. The evolution of the elastic-plastic contact with increasing interference is analyzed revealing three distinct stages that range from fully elastic through elastic-plastic to fully plastic contact interface. The model provides dimensionless expressions for the contact load, contact area, and mean contact pressure, covering a large range of interference values from yielding inception to fully plastic regime of the spherical contact zone. Comparison with previous elastic-plastic models that were based on some arbitrary assumptions is made showing large differences. ©2002 ASME

Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat

Failure of metals I : brittle and ductile fracture

This work presents a finite element study of elasto-plastic hemispherical contact. The results are normalized such that they are valid for macro contacts (e.g., rolling element bearings) and micro contacts (e.g., asperity contact), although micro-scale surface characteristics such as grain boundaries are not considered. The material is modeled as elastic-perfectly plastic. The numerical results are compared to other existing models of spherical contact, including the fully plastic truncation model (often attributed to Abbott and Firestone) and the perfectly elastic case (known as the Hertz contact). This work finds that the fully plastic average contact pressure, or hardness, commonly approximated to be a constant factor of about three times the yield strength, actually varies with the deformed contact geometry, which in turn is dependent upon the material properties (e.g., yield strength). The current work expands on previous works by including these effects and explaining them theoretically. Experimental and analytical results have also been shown to compare well with the current work. The results are fit by empirical formulations for a wide range of interferences (displacements which cause normal contact between the sphere and rigid flat) and materials for use in other applications.

/pdf/a-finite-element-study-of-elasto-plastic-hemispherical-5dpeutoisj.pdf

A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat

The finite–element method is used to perform an accurate numerical study of the normal indentation of an elastic–plastic half–space by a rigid sphere. The effects of elasticity and strain–hardening rate of the half–space are explored, and the role of friction is assessed by analysing the limiting cases of frictionless contact and sticking friction. Indentation maps are constructed with axes of contact radius a (normalized by the indenter radius R and the yield strain of the half–space. Competing regimes of deformation mode are determined and are plotted on the indentation map: (i) elastic Hertzian contact; (ii) elastic–plastic deformation; (iii) plastic similarity regime; (iv) finite–deformation elastic contact; and (v) finite–deformation plastic contact. The locations of the boundaries between deformation regimes change only slightly with the degree of strain–hardening rate and of interfacial friction. It is found that the domain of validity of the rigid–strain–hardening similarity solution is rather restricted: it is relevant only for solids with a yield strain of less than 2 x 10 −4 and a / R

/pdf/spherical-indentation-of-elastic-plastic-solids-fqir4354yx.pdf

Spherical indentation of elastic–plastic solids

http://www-mech.eng.cam.ac.uk/profiles/fleck/papers/102.pdf

Frictionless indentation of dissimilar elastic-plastic spheres

We examine the process of decohesion of two adhering elastic–plastic spheres following mutual indentation beyond their elastic limit. In the first instance, it is assumed that during unloading to the point of pull-off, the deformation is predominantly elastic. First, elastic–plastic loading is modelled by a fine grid finite element analysis revealing that, for elastic–perfectly plastic materials, the contact pressure at the end of loading p o is approximately uniform. Next, the contact size and pressure distribution during elastic unloading from a uniform pressure, in the absence of adhesion, is found by the method of rigid punch decomposition. The pressure distribution approaches that of Hertz as the contact size approaches zero. The distribution of adhesive traction has been found in two ways. First, using the singular traction distribution of linear elastic fracture mechanics, and second, using a step cohesive law, whereby a constant adhesive stress σ o acts between surfaces separated by less than δ o , while the surfaces separated by more than δ o , are traction-free. The cohesive zone solution depends on two non-dimensional parameters, while the asymptotic singular solution depends on one non-dimensional parameter only. The limit where the singular model provides a good approximation for the more accurate cohesive zone solution is defined. Finally, a decohesion map is deduced, which divides the parameter space into the regions where decohesion process is governed by different physical mechanisms. The deduced mechanisms are compared with the existing experimental data.

Adhesive contact of elastic–plastic spheres

A constitutive model proposed by McCormick [(1988) Theory of flow localization due to dynamic strain ageing. Acta. Metall. 36, 3061–3067] based on dislocation-solute interaction and describing dynamic strain aging behavior, is analyzed for the simple loading case of uniaxial tension. The model is rate dependent and includes a time-varying state variable, representing the local concentration of the impurity atoms at dislocations. Stability of the system and its post-instability behavior are considered. The methods used include analytical and numerical stability and bifurcation analysis with a numerical continuation technique. Yield point behavior and serrated yielding are found to result for well defined intervals of temperature and strain rate. Serrated yielding emerges as a branch of periodic solutions of the relaxation oscillation type, similar to frictional stick-slip. The distinction between the temporal and spatial (loss of homogeneity of strain) instability is emphasized. It is found that a critical machine stiffness exists above which a purely temporal instability cannot occur. The results are compared to the available experimental data.

Dynamic strain aging and plastic instabilities

In simulations of representative volume elements (RVEs) of materials with disordered microstructures, commonly used rigid and periodic boundary conditions (BCs) introduce additional constraints, causing: (i) boundary effects, (ii) unrealistic stiff response, (iii) artificial wavelengths in the solution fields, and (iv) suppression of solutions with localized deformation that otherwise may occur in the simulation. In this paper we define the minimal kinematic boundary conditions such that only the desired overall strain is imposed on the RVE, with no other undesirable constraints. We prove that such BCs result in a unique solution for the linear elastic case, and that the uniqueness for nonlinear problems is dependent on the pointwise positive definiteness of the incremental stiffness tensor. Upon incorporating the minimal BCs into the finite element framework, we consider, as an example, two-dimensional, linear elastic, disordered polycrystals and perform a systematic study of the effects of boundary conditions while varying the RVE size and controlling the sampling error. The results demonstrate that the minimal BCs, applicable to a RVE of any shape, are superior to other BCs, in that they give more realistic overall behaviour, reduce the required size of the RVE, and eliminate the superficial wavelengths in the solution field, ubiquitous in simulations with other boundary conditions.

Sinisa Dj. Mesarovic

Papers

Spherical indentation of elastic–plastic solids

Frictionless indentation of dissimilar elastic-plastic spheres

Adhesive contact of elastic–plastic spheres

Dynamic strain aging and plastic instabilities

Minimal kinematic boundary conditions for simulations of disordered microstructures