Computational Mechanics Research Research Articles

Documenting research in simulation science to enhance understanding for reusability

One goal of Open Science is to promote reusability, which requires understanding and documentation. Reusability spans a spectrum from the straightforward reuse of existing materials to the extraction and adaptation of specific elements, depending on the maturity of the reused research and the research context. Beyond knowledge, understanding is crucial for enabling reusability. Simply reading an article is often insufficient; thus, publishing the underlying data and software is recommended. While the FAIR principles (Findable, Accessible, Interoperable, Reusable) facilitate the discovery and legal reuse of data and software through metadata, they fall short of promoting comprehensive understanding. By applying insights from the epistemology of simulation to computational mechanics research cases, we tested our hypothesis that the simulation process involves critical components beyond software and data that are essential to understand for reuse. Our findings indicate that reusability in these cases predominantly involves adjusting existing methodologies—a combination of different process steps from an epistemological perspective. Therefore, it is imperative to document not only learned knowledge but also the decisions regarding adjustments, assumptions and applications that concern the entire simulation process. Documentation is vital for understanding and herby enabling true reusability in scientific research, aligning with philosophical considerations of transparency and the nature of scientific knowledge.

JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science

This paper introduces JAX-FEM, an open-source differentiable finite element method (FEM) library. Constructed on top of Google JAX, a rising machine learning library focusing on high-performance numerical computing, JAX-FEM is implemented with pure Python while scalable to efficiently solve problems with moderate to large sizes. For example, in a 3D tensile loading problem with 7.7 million degrees of freedom, JAX-FEM with GPU achieves around 10× acceleration compared to a commercial FEM code depending on platform. Beyond efficiently solving forward problems, JAX-FEM employs the automatic differentiation technique so that inverse problems are solved in a fully automatic manner without the need to manually derive sensitivities. Examples of 3D topology optimization of nonlinear materials are shown to achieve optimal compliance. Finally, JAX-FEM is an integrated platform for machine learning-aided computational mechanics. We show an example of data-driven multi-scale computations of a composite material where JAX-FEM provides an all-in-one solution from microscopic data generation and model training to macroscopic FE computations. The source code of the library and these examples are shared with the community to facilitate computational mechanics research. Program summaryProgram Title: JAX-FEMCPC Library link to program files:https://doi.org/10.17632/hgwshjbcw6.1Developer's repository link:https://github.com/tianjuxue/jax-am/tree/main/jax_am/femLicensing provisions: GPLv3Programming language: PythonNature of problem: Implementation of the finite element method (FEM) with several appealing features that classic FEM software typically does not have: realized with pure Python; running on CPU/GPU; differentiable for solving PDE-constrained optimization problems; seamless integration with machine learning.Solution method: Our framework JAX-FEM is based on Google JAX, a high-performance numerical computing library with automatic differentiation features and supporting both CPU/GPU. Unlike classic FEM software written in Fortran or C/C++, JAX-FEM is implemented with pure Python and can easily be installed as a Python package. We demonstrate our software by solving problems including forward PDE prediction, inverse design/optimization, and data-driven analysis.

Non-parametric material state field extraction from full field measurements

Data-driven computations propose a completely new paradigm to the computational mechanics research community and to experimentalists. Classically, admissible material states can only be obtained experimentally for homogeneous stress/strain configurations or using a parametric optimization of material laws based on heterogeneous tests. Data-driven algorithms aim at circumventing these limitations. However, data-driven algorithms require a large database of admissible material states, otherwise extrapolation is required and some limitations of the classical constitutive equation based approach remain. In this paper, an inverse data-driven approach based on full field measurements is presented. The main idea is to extract, with no assumption on the constitutive equations, rich (i.e. heterogeneous and multiaxial) material state fields from displacement fields and external load measurements. The capability of the proposed method to extract databases of admissible material states and to evaluate stress fields without parametric constitutive equations is illustrated through three examples dedicated to non-linear elasticity, plasticity and dynamics.

Multi‐scale modeling of plastic deformations in nano‐scale materials; Transition to plastic limit

SummaryA large amount of research in computational mechanics has biased toward atomistic simulations. This trend, on one hand, is due to the increased demand to perform computations in nanoscale and, on the other hand, is due to the rather simple applications of pairwise potentials in modeling the interactions between atoms of a given crystal. The Cauchy–Born (CB) hypothesis has been used effectively to model the behavior of crystals under different loading conditions, in which the comparison with molecular dynamics simulations presents desirable coincidence between the results. A number of research works have been devoted to the validity of CB hypothesis and its application in post‐elastic limit. However, the range of application of CB hypothesis is limited, and it remains questionable whether it is still applicable beyond the validity limit. In this paper, a multi‐scale technique is developed for modeling of plastic deformations in nanoscale materials. The deformation gradient is decomposed into the plastic and elastic parts, i.e., F = FpFe. This decomposition is in contrast to the conventional decomposition, F = FeFp, generally encountered in continuum and crystal plasticity. It is shown that the former decomposition is more appropriate for the problem dealt within this work. Inspired by crystal plasticity, the plastic part is determined from the slip on potential slip systems. Based on the assumption that the CB hypothesis remains valid in the homogeneous deformation, the elastic deformation gradient resulting from the aforementioned decomposition is employed in conjunction with the CB hypothesis to update the state variables for face‐centered cubic crystals. The assumption of homogeneity of elastic deformation gradient is justified by the fact that elastic deformations are considerably smaller than the plastic deformations. The computational algorithms are derived in details, and numerical simulations are presented through several examples to demonstrate the capability of the proposed computational algorithm in the modeling of golden crystals under different loading conditions. Copyright © 2016 John Wiley & Sons, Ltd.

Isogeometric dual mortar methods for computational contact mechanics

In recent years, isogeometric analysis (IGA) has received great attention in many fields of computational mechanics research. Especially for computational contact mechanics, an exact and smooth surface representation is highly desirable. As a consequence, many well-known finite element methods and algorithms for contact mechanics have been transferred to IGA. In the present contribution, the so-called dual mortar method is investigated for both contact mechanics and classical domain decomposition using NURBS basis functions. In contrast to standard mortar methods, the use of dual basis functions for the Lagrange multiplier based on the mathematical concept of biorthogonality enables an easy elimination of the additional Lagrange multiplier degrees of freedom from the global system. This condensed system is smaller in size, and no longer of saddle point type but positive definite. A very simple and commonly used element-wise construction of the dual basis functions is directly transferred to the IGA case. The resulting Lagrange multiplier interpolation satisfies discrete inf–sup stability and biorthogonality, however, the reproduction order is limited to one. In the domain decomposition case, this results in a limitation of the spatial convergence order to O(h32) in the energy norm, whereas for unilateral contact, due to the lower regularity of the solution, optimal convergence rates are still met. Numerical examples are presented that illustrate these theoretical considerations on convergence rates and compare the newly developed isogeometric dual mortar contact formulation with its standard mortar counterpart as well as classical finite elements based on first and second order Lagrange polynomials.

India's Declining Share in Computational Mechanics Research

Modern science began with Galileo's discourses on two new sciences, name ly kinematics and materials science. Over five centuries, the discipline of mechanics which emerged from such studies has played a leading role in many engineering disciplines. Over the last five decades, with the advent of digital computing, mechanics has become 'algorithmized' and this new discipline of computational mechanics has played a very significant role in modern science and engineering, from the execution of megaprojects to the fabrication of nano and quantum devices. In this communication, using bibliometric techniques, we examine India's current place in the area of computational mechanics research and see stagnation and may be a steady decline.

Special Issue: Recent Advances in Structural Engineering

Papers were presented by the international and regional scholars in the area of Structural Engineering. The Special Issue is a collection of the peer adjudged 18 papers from the Conference, including 4 keynote papers. Exciting new developments in the world of computational mechanics and materials are leading the way to advances in Structural Engineering. Computational modeling developments are the catalyst for a new wave of research into problems addressing nanoand micromechanical behavior, in addition to provide improved constitutive models for monotonic, cyclic and dynamic loading of structures. Innovations in materials engineering include the use of nano-technology in the production of superior concretes and adhesives, smart materials and their use in retrofitting of damaged structures, and use of new superplasticizers and mineral admixtures in the production of ultra-high strength concrete. Such developments in the world of structural mechanics and materials make demands on structural engineering researchers to match the advances, and to conceive and design structures that would take full advantage of the innovations. The use of these models and the new generation of materials by structural engineers in traditional and innovative structures are now allowing the buildings to reach higher into the skies, for bridges to traverse distances and terrain not dreamt of before and to provide for safe and stable foundations for such structures. The structural engineer has to interface with the geotechnical engineer and be cognizant of developments in geotechnical engineering. The 18 papers in the Special Issue address subjects in various broad groups, including three papers in concrete materials and durability modeling (including two keynote papers, one on nano-concrete and another on improvement of durability of post-tensioned reinforced concrete bridges), five papers in precast and prestressed concrete and bridges (including a keynote presentation on the challenge of using CFRP cables in ultra-long span suspension bridges), and two papers including a keynote address on ferrocement and fiber reinforced concrete. Considering the recent natural disasters that have occurred around the world, two papers on earthquake engineering, including a theme presentation addressing this very important topic in the regional context, have been included. Three papers on the use of FRP’s in retrofitting and repair of reinforced concrete structures, two papers on composites including a theme presentation on the design of composite columns, and one paper addressing soil–structure interaction complete the list of eighteen papers selected for inclusion. It is hoped that this Special Issue will provide researchers and practicing professionals in the Gulf region with valuable information which can be incorporated in the design of new structures and stimulate further research in structural design, constitutive modeling and computational mechanics, and concrete materials. The team of Technical Editors would like to express their deepest gratitude and appreciation first to KFUPM for hosting the 11th ASEC Conference, allowing regional and international scholars to share their experiences with the engineering community in the Kingdom. The Editors also offer thanks to the authors who responded spontaneously to the invitation to submit enhanced versions of their 11th ASEC papers for review for possible inclusion in this Special Issue. Special thanks are due to the referees for their meticulous reviews, and for their role in improving the presentations and the discussions in the papers.

Internal variable formulations of elastic-plastic dynamic problems

The paper reviews work that has been carried out in recent years in the Centre for Research in Computational and Applied Mechanics (CERECAM) at the University of Cape Town on the compact internal variable formulation of the problem of an elastic-plastic body subject to incremental loading. The fundamental problem is expressed as a convex nonlinear programming problem. The simplest two step algorithm for the solution of this programming problem is shown to be the standard Newton-Raphson algorithm, and the formulation permits a discussion of the convergence of the iterative solution procedure. It is shown that this static formulation is readily extended to include inertia and linear damping terms, leading to an identical basic formulation in which the stiffness matrix and the residual are redefined for the dynamic problem. The static problem, and hence any software written for its solution, can thus be simply modified to include dynamic effects. The essential analogy between the static and dynamic problems was first presented as a master's thesis (R.D. Isted, 1988); subsequently there have been a number of additional contributions to the basic formulation for static problems, in which the internal variable framework was extended and clarified. Further contributions have also been made in respect of the dynamic problem, and these developments are summarised. Some of this later work has been directed at improvements in the implicit solution algorithms. These aspects will not be discussed in detail, however, the main purpose of this review is to demonstrate the formal relationship between the static and dynamic problems.

Interactive-adaptive, large displacement analysis with real-time computer graphics

This paper presents an investigation of interactive-adaptive techniques for large displacement analysis of frames based on vector refresh graphic terminals and 32-bit, virtual-memory, minicomputers. The first aspect of this investigation is a review of interactive graphics techniques to monitor results and control the flow of the analysis. The concepts of parallel analyses and analysis sequences are also introduced as means to facilitate selection of analysis parameters and comprehension of nonlinear behavior. Examples are presented to illustrate the techniques and demonstrate their power for both practical nonlinear analysis and computational mechanics research.