On the solutions of elastic-plastic problems with contact-type boundary conditions for solids with loss-of-strength zones |
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| Institution: | 1. Centre for Computational Science & Mathematical Modelling, Coventry University, UK;2. School of Engineering, University of Warwick, UK;1. School of Materials Science and Engineering, Sun Yat-sen University, Guangzhou, 510275, China;2. School of Chemical Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, Guangdong, China;3. Guangdong Engineering Center for Petrochemical Energy Conservation, The Key Laboratory of Low-carbon Chemistry & Energy Conservation of Guangdong Province, Guangzhou 510275, China;4. Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong Special Administrative Region, China;5. Department of Chemistry and Bioscience, Aalborg University, Niels Bohrs Vej 8A, Esbjerg, 6700, Denmark;1. Laboratory of Molecular Imaging, Department of Radiology, University of Pennsylvania, Perelman School of Medicine, Philadelphia, PA 19104, USA;2. Center of Excellence in Environmental Toxicology, Department of Systems Pharmacology and Translational Therapeutics, University of Pennsylvania, Perelman School of Medicine, Philadelphia, PA 19104, USA;3. School of Biochemistry, Biomedical Sciences Building, University of Bristol, BS8 1TD, UK;4. Department of Radiation Oncology, Thomas Jefferson University, Philadelphia, PA, USA |
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| Abstract: | A formulation of a quasi-static problem of the mechanics of elastic-plastic bodies with loss-of-strength zones and boundary conditions of contact type: is given which enables the properties of the loading system to be taken into account. With certain constraints on the constitutive relations and using a condition for stability of the softening process in a local zone, theorems are proved on the uniqueness of the solution of the boundary-value problem and on the maximum and minimum of the functionals when the kinematically or statically possible and actual fields are the same. The corresponding generalized variational principles are given. |
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