Investigation of the damage variable basic issues in continuum damage and healing mechanics |
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| Institution: | 1. Dept. of Structural Engineering, Norwegian University of Science & Technology, Richard Birkelands vei 1A, 7491 Trondheim, Norway;2. University of Applied Science Augsburg, Institut für Holzbau, An der Hochschule 1, 86161 Augsburg, Germany;1. Faculty of Mathematics, Al. I. Cuza University of Iaşi, 700506 Iaşi, Romania;2. Octav Mayer Mathematics Institute, Romanian Academy, 700505 Iaşi, Romania;3. Università della Calabria, Via Pietro Bucci, 87036 Arcavacata di Rende (CS), Italy;1. Oregon State University Corvallis, College of Public Health and Human Sciences, 255 Hallie Ford Center, Corvallis, OR 97330, USA;2. Disability and Health Policy Division, Center for Development & Disability, University of New Mexico, 2300 Menaul Boulevard NE, Albuquerque, NM 87107, USA;3. Administration for Community Living, US Department for Health and Human Services, One Massachusetts Avenue NW, Washington, DC 20001, USA;1. Department of Mathematics, Modelling and Scientific Computing (MOX) – Politecnico di Milano, Via Bonardi 9, I-20133 Milan, Italy;2. Fondazione CEN, Piazza Leonardo da Vinci, 32, I-20133 Milan, Italy;3. Department of Mathematical Sciences (DISMA) “G.L. Lagrange” – Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy |
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| Abstract: | Consistent mathematics and mechanics are used here to properly interpret the damage variable within the confines of the concept of reduced area due to damage. In this work basic issues are investigated for the damage variable in conjunction with continuum damage and healing mechanics. First, the issue of the additive decomposition of the damage variable into damage due to voids and damage due to cracks in continuum damage mechanics is discussed. The accurate decomposition is shown to be non-additive and involves a term due to the interaction of cracks and voids. It is shown also that the additive decomposition can only be used for the special case of small damage. Furthermore, a new decomposition is derived for the evolution of the damage variable. The second issue to be discussed is the new concept of independent and dependent damage processes. For this purpose, exact expressions for the two types of damage processes are presented. The third issue addressed is the concept of healing processes occurring in series and in parallel. In this regard, systematically and consistently, the equations of healing processes occurring either consecutively or simultaneously are discussed. This is followed by introducing the new concept of small healing in damaged materials. Simplified equations that apply when healing effects are small are shown. Finally, some interesting and special damage processes using a systematic and original formulation are presented. |
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| Keywords: | Continuum damage Healing mechanics Decomposition of damage Damage processes |
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