How To Solve Models of Extreme Deformation

The NAFEMS Computational Structural Mechanics Working Group (CSMWG) would like to commission a How-To guide for the modelling of extreme deformation. 


The intent of the document is to act as an introductory guide for analysts who, whilst experienced in small displacement finite element simulation, wish to understand the simulation challenges posed by systems with much greater deformation. Examples include high-speed impacts, blast response and penetration of materials and structures, slow-speed but severe forming processes (e.g. forging and extrusion) and simulation of parts containing elastomeric or foam materials.

The focus of the document should be on the challenges associated with the solution of these models, including discussion and comparison of the various points listed below. The use of explanatory example problems is strongly encouraged. These are to be used to illustrate the difficulties encountered in obtaining convergence to a realistic solution, e.g. due to excessive mesh distortion, and how alternative approaches can permit the simulation to proceed to completion.

Other aspects of extreme deformation modelling are of interest, but should not be the main focus. These aspects are listed under “additional points of interest” in the scope below.

The scope of the publication should cover the following concepts. Note, this list is not exhaustive and suggestions for additions are welcome:


The scope of the publication should cover the following concepts. Note, this list is not exhaustive and suggestions for modifications from potential authors are welcome:

  • Fundamental differences between static implicit, dynamic implicit, and dynamic explicit simulation schemes. Stress and strain measures for large deflections.
  • Wave propagation phenomena
  • Solution methods
  • Implicit vs explicit solution schemes
  • Computer requirements for implicit and explicit solvers, and scalability issues
  • The use of explicit dynamic schemes to solve implicit static problems with extreme deformation, and how to ensure a physically representative solution
  • Riks method and artificial stabilisation to assist in unstable static calculations
  • The transfer between solution schemes, or explicit-implicit switching, eg springback after forming
  • Finite element modelling
  • Lagrangian meshes (including deliberate pre-distortion to become progressively better shaped during the calculation)
  • Re-meshing and mapping of Lagrangian solutions from one mesh to another after excessive deformation
  • Purely Eulerian grids and interaction between Lagrangian meshes within Eulerian grids
  • Arbitrary Lagrangian-Eulerian adaptive meshing
  • Particle methods (SPH) and interactions between particle and Lagrangian regions
  • Common pitfalls and solution verification checking (eg Eulerian material leakage past Lagrangian boundaries).
  • Illustrative examples
  • Using benchmarks or NAFEMS publications (eg forging tutorials, R0117) From published material, e.g. conference or journal papers

Additional points of interest include:

  • Material modelling
  • Contact modelling, friction, erosion.

Intended Readership

Analysts who are experienced in small displacement or mildly non-linear problems who require knowledge of how to solve extreme deformation problems.

Cost / Timescale / Expected Length

The total cost is not expected to exceed £7,000 which should include responding to a single set of consolidated comments from the review panel.

The first draft for review must be complete within 12 months of placement of contract. Interim work-in-progress drafts may be requested by the review panel.

The publication is anticipated to be approximately 70 A5 pages in length.


Potential authors should submit the following:

  • A brief description of the main topics to be covered
  • Chapter and section headings with an approximate number of pages per chapter
  • Timescale for completing the book
  • Cost
  • CVs of the authors (Maximum  two-pages per author) 

Proposal should be sent to NAFEMS at  for a 1st of January 2021 submission deadline. 

Further details are available by contacting the NAFEMS Technical Officer