Dynamic Behavior of Materials. Constitutive Relations and Applications
In this chapter a particular attention has been directed on the dynamic behavior of materials and structures subjected to dynamic loading. Based on experimental observations, it is clear that the homogeneous material behavior of metals has several non lin
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Laboratory of mechanics, Biomechanics, Polymers, Structures, National engineering School of Metz, 1 route d’Ars Laquenexy, 57000 Metz, France Institute of Structural Engineering, Poznan University of Technology, Piotrowo 5, 60-965 Pozna, Poland Abstract Abstract. In this chapter a particular attention has been directed on the dynamic behavior of materials and structures subjected to dynamic loading. Based on experimental observations, it is clear that the homogeneous material behavior of metals has several non linearities related for example to the strain rate and temperature sensitivity. Therefore, the material description and more precisely the constitutive relation used during numerical simulations for example must include all macroscopic observations. It has to be noticed that constitutive relations described in this chapter are defined in a macroscopic scale. Considering some examples, it is clear that the constitutive relation that was used is the key point to simulate a global problem allowing to avoid as frequently used some numerical tricks to obtain an agreement between experiments and numerical predictions. Following the concept described in this part, the reader will be available to propose new models to fit precisely their own materials for specific applications.
Introduction It is frequently observed that the structure is loaded dynamically by unique loading during special events as crashes in case of vehicles, impacts or perforations in case of military structures and blast in case of public and military structures. These kinds of loadings create in the structures large strains ε and strain rates ε. ˙ It generates also the high increase of the temperature T . Many experiments show that behavior of materials is dependent on: 1. Strain sensitivity, ε 2. Strain rate sensitivity, ε˙ 3. Temperature sensitivity, T T. àodygowski, A. Rusinek (Eds.), Constitutive Relations under Impact Loadings, CISM International Centre for Mechanical Sciences, DOI 10.1007/978-3-7091-1768-2_3, © CISM, Udine 2014
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A. Rusinek and T. Jankowiak
In addition the loading process can be complex following several loading paths. For this reason, the material behavior σ (ε, ε, ˙ T ) used to design a structure must be studied in a precise way to include all above effects. However sometimes some additional effects must be considered to understand the macroscopic description of the material as for example the process of phase transformation, the pre-plastic deformation or the industrial process induced to the considered material. It has to be noticed that the kinetic of phase transformation is also depending on temperature, strain level, strain rate and hydrostatic pressure. Based on it, it is observed that the analytical description of the material is relatively complex and need a precise experimental study before modeling. As it is discussed later, experiments have to be done in a rigorous way to avoid artificial effects. Using the following case corresponding to a vehicle, Fig. 1-a. It is observed that several materials can be used an
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