Plasticity in modern engineering practice.

A brief history of plasticity theory

The origins of theoretical work on permanent deformation, known as plasticity, date back to the second half of the 19th century. However, it was only after World War II that the development of this field accelerated significantly. This was led by the following milestones:

• 1864 – Henri E. Tresca publishes the results of experiments on sheet metal stamping and formulates the criterion of plastic flow.
• Pre-1945 – St. Venant and Lévy lay the foundations of modern plasticity theory, which was further developed by von Mises, Prandtl, Hencky, and Huber.
• Post-1945 – The formulation of a unified mathematical theory of plasticity based on macroscopic approaches and experimental research.

Unified theory of plasticity includes such phenomena as:

• Bauschinger effect,
• anisotropy beyond the yield point,
• effect of strain rate,
• effect of temperature,
• creep,
• stress relaxation,
• hydrostatic pressure.

The starting point for all considerations within this framework is the stress-strain curve obtained in a strength laboratory through tensile tests on the material being studied.

Development of computer-based simulation tools for permanent deformations in the second half of the 20th century

The 1960s witnessed rapid advancements in computer technology, which enabled the application of previously developed theories to the computer simulation of plastic phenomena. As computing speeds increased and device memory expanded, the accuracy of Finite Element Method (FEM) calculations improved, as did the accessibility of computers necessary for such simulations.

In the 1970s, the first commercial software was developed, transitioning from predominantly linear calculations to advanced nonlinear analyses, including plasticity calculations. In the decades that followed, computer developments allowed the use of FEM spatial models and rapid iterations of nonlinear processes for large models.

Examples of application of plasticity knowledge

Based on the simulation of nonlinear interactions on FEM spatial models, such tasks as:

Product testing using plasticity

• crash tests of vehicles, such as cars and trains.
• design and selection of impact energy absorbers.
• drop tests for electronic devices.

Technological processes using plasticity

• manufacturing with sheet metal stamping, extrusion, etc.
• design of assembly joints, e.g., rivets.
• centrifugation of turbine rotor and last stage blades.

Design new structures using plasticity

• turbine body design with considerations for creep and plasticity.
• blast-resistant casings, including escape tunnels on oil rigs.
• missile-resistant shields, including armor for tanks and armored vehicles.
• combat aircraft design, such as landing gear for takeoffs and landings.
• sports cars design, e.g., subframe structure.
• design of earthquake-resistant structures.

Root Cause Analyses (RCA) using plasticity:

• a bridge that falls into a river.
• a hall roof that collapses.
• a turbine rotor that explodes.
• collisions of means of transportation, such as motor vehicles, railroads, ships.
• many other types of extraordinary events.

Benefits of including plasticity in simulations and calculations

Including plasticity in simulations and calculations provides a number of benefits related to issues such as:

• getting closer to the realistic behavior of the structure and better exhausting its load carrying capacity by moving from a linear to a nonlinear approach;
• elimination of the occurrence of singularities at corners typical of linear elastic theory and thus making stress peaks more realistic;
• the ability to plan manufacturing, assembly, and work deformations for plasticized components by taking into account loading and unloading histories;
• accurate determination of low-cycle fatigue life and precise prediction of the permissible number of cycles of the tested structure through the use of deformation Wöhler (E-N) curves;
• the possibility of conducting detailed analyses of extraordinary events in the field of fracture mechanics, and, as a result, accurately determining their cause and preventing them in the future.

Future prospects for technology development using plasticity theory

Already today, calculations implemented on the basis of plasticity theory are of great importance for the design of durable and safe structures. It can be expected that in the coming years the importance of such simulations will grow in such contexts as:

• ensuring safety in more areas of life through virtual emergency event testing of various everyday devices;
• increasing the safety of structures, thanks to virtual earthquake tests;
• increasing the safety of vehicles, thanks to virtual crash tests;
• better utilizing the load-bearing capacity of structural components and reducing the need for raw materials for their construction;
• detailed analysis of extraordinary events and explanation of their causes to avoid similar events in the future;
• use of “material memory” as a logical element;
• application of repeatable nonlinear elements in nanotechnology.

Feel free to contact Endego’s CAE team. We perform computationally demanding advanced simulations for automotive and other sectors.

Grzegorz Wiśniewski

CAE Technical Expert

Senior specialist in areas such as mechanics and strength of materials, non-linear issues, plasticity (PhD ETH Zürich), strength of thermal turbines, rail vehicles, ship structures. He has professional experience in conducting and coordinating development projects in the above-mentioned fields, as well as teaching and implementing the Finite Element Method (including ETH Zürich and Gdansk University of Technology).