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2. Nonstandard micro-inertia terms in the relaxed micromorphic model: well-posedness for dynamics

Author

Ionel-Dumitrel Ghiba, Patrizio Neff, Sebastian Owczarek, Marco Valerio d'Agostino, Faculty of Mathematics and Information Science [Warszawa], Warsaw University of Technology [Warsaw], Alexandru Ioan Cuza University of Iași [Romania], Institute of Mathematics 'Octav Mayer', Romanian Academy, Mécanique des Matériaux et des Structures (M2S), Géomécanique, Matériaux et Structures (GEOMAS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA), Fakultät für Mathematik der Universität Duisburg-Essen, Universität Duisburg-Essen [Essen], and Thework of I.D. Ghiba was supported by Alexandru Ioan Cuza University of Iasi (UAIC) under the grant GI-17458,within the internal grant competition for young researchers.

Subjects
Wave propagation, General Mathematics, media_common.quotation_subject, FOS: Physical sciences, generalized continua, 02 engineering and technology, Inertia, 01 natural sciences, Mathematics - Analysis of PDEs, 0203 mechanical engineering, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], General Materials Science, Fakultät für Mathematik, ddc:510, 0101 mathematics, Mathematical Physics, media_common, Physics, Dynamics (mechanics), Metamaterial, Mathematical Physics (math-ph), 010101 applied mathematics, 020303 mechanical engineering & transports, Classical mechanics, Mechanics of Materials, Mathematik, micro-inertia, Focus (optics), Well posedness, Analysis of PDEs (math.AP)
Abstract

International audience; We study the existence of solutions arising from the modelling of elastic materials using generalized theories of continua. In view of some evidence from physics of metamaterials, we focus our effort on two recent nonstandard relaxed micromorphic models including novel micro-inertia terms. These novel micro-inertia terms are needed to better capture the band-gap response. The existence proof is based on the Banach fixed-point theorem.

Published
2019
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3. On renormalized solutions for thermomechanical problems in perfect plasticity with damping forces

Author

Sebastian Owczarek and Leszek Bartczak

Subjects
Physics, Strain (chemistry), Continuum mechanics, Flow (mathematics), Mechanics of Materials, General Mathematics, Thermal, Evolution equation, General Materials Science, Mechanics, Plasticity, Thermal conduction
Abstract

We consider the quasi-static evolution of the thermo-plasticity model in which the evolution equation law for the inelastic strain is given by the Prandtl–Reuss flow rule. The thermal part of the Cauchy stress tensor is not linearized in the neighbourhood of a reference temperature. This nonlinear thermal part is imposed to add a damping term to the balance of the momentum, which can be interpreted as external forces acting on the material. In general, the dissipation term occurring in the heat equation is an integrable function only and the standard methods can not be applied. Combining truncation techniques and Boccardo-Gallouët approach with monotone methods, we prove an existence of renormalized solutions.

Published
2018
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4. Thermo-visco-elasticity for Norton–Hoff-type models with homogeneous thermal expansion

Author

Sebastian Owczarek, Piotr Gwiazda, and Filip Z. Klawe

Subjects
Physics, Cauchy stress tensor, Applied Mathematics, 010102 general mathematics, General Engineering, General Medicine, Mechanics, System of linear equations, 01 natural sciences, Thermal expansion, 010101 applied mathematics, Computational Mathematics, Linearization, Time derivative, Heat equation, 0101 mathematics, Elasticity (economics), General Economics, Econometrics and Finance, Analysis, Mechanical energy
Abstract

In this work we study a quasi-static evolution of thermo-visco-elastic model with homogeneous thermal expansion. We assume that material is subject to two kinds of mechanical deformations: elastic and inelastic. Inelastic deformation is related to a hardening rule of Norton–Hoff-type. Appearance of inelastic deformation causes transformation of mechanical energy into thermal one, hence we also take into the consideration changes of material’s temperature. The novelty of this paper is to take into account the thermal expansion of material. We are proposing linearization of the model for homogeneous thermal expansion, which preserves symmetry of system and therefore total energy is conserved. Linearization of material’s thermal expansion is performed in definition of Cauchy stress tensor and in heat equation. In previous studies, it was done in different way. Consideration of such linearization leads to system where the coupling between temperature and displacement occurs in two places, i.e. in the constitutive function for the evolution of visco-elastic strain and in the additional term in the heat equation, in comparison to models without thermal expansion. The second coupling was not considered previously. For such system of equations we prove the existence of solutions. Moreover, we obtain existence of displacement’s time derivative, which has not been done previously.

Published
2018
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5. Corrigendum to 'Renormalised solutions in thermo-visco-plasticity for a Norton–Hoff type model. Part I: The truncated case' [Nonlinear Anal. RWA 28 (2016) 140–152]

Author

Sebastian Owczarek and Krzysztof Chełmiński

Subjects
Applied Mathematics, 010102 general mathematics, Mathematical analysis, General Engineering, Fixed-point theorem, General Medicine, Type (model theory), Plasticity, 01 natural sciences, 010101 applied mathematics, Computational Mathematics, Nonlinear system, 0101 mathematics, General Economics, Econometrics and Finance, Analysis, Mathematics
Abstract

We correct an error in the original paper [Renormalised solutions in thermo-visco-plasticity for a Norton–Hoff type model. Part I: The truncated case, Nonlinear Anal. RWA 28 (2016) 140–152]. The proof of Theorem 3.2 is wrong and therefore we present here correct proof based on the same methods.

Published
2017
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6. Students' participation in collaborative research should be recognised

Author

Aditya Borakati, Kenneth McLean, Thomas M. Drake, Ewen M. Harrison, Sivesh K. Kamarajah, Chetan Khatri, Dmitri Nepogodiev, Minaam Abbas, Muhammad Abdalkoddus, Areej Abdel-Fattah, Reem Abdelgalil, Haweya Abdikadir, Ryan Adams, Sarah Adams, Inioluwa Adelaja, Abiola Adeogun, Helena Adjei, Amirul Adlan, Hussamuddin Adwan, Sara Aeyad, Raiyyan Aftab, Amir Afzul, Vani Agarwal, Hosam Aglan, Medha Agrawal, Rishi Agrawal, Fiza Ahmed, Sobia Akhtar, Onyinye Akpenyi, Maithem Al-Attar, Muhammed Al-Ausi, Waleed Al-Khyatt, Alia Al-Mousawi, Zainab Al-Nasser, Anand Alagappan, Justin Alberts, Maryam Alfa-Wali, Abdulmajid Ali, Adnan Ali, Tamara Ali, Bilal Alkhaffaf, Rachael Allen, Kassem Alubaidi, Edemanwan Andah, Richard Anderson, Kirstine Andrew, Andrew Ang, Eshen Ang, Theophilus Anyomih, James Archer, Matt Archer, Steven Arnell, Matthew Arnold, Esha Arora, Nadeem Ashraf, Raees Ashraf, Jordan Ashwood, Usama Asif, Andrew Atayi, Sameera Auckburally, Ralph Austin, Sultana Azam, Aishah Azri Yahaya, Fiyin Babatunde, Simon Bach, Roudi Bachar, Abdul Badran, Caroline Baillie, Edward Balai, Alexander Baldwin, Vartan Balian, Danielle Banfield, Jonathan Bannard-Smith, Connor Barker, Behrad Barmayehvar, Jane Barnfield, David Bartlett, Richard Bartlett, Kwaku Baryeh, Siddharth Basetti, Kellie Bateman, Michael Bath, Andrew Beamish, William Beasley, Simon Beecroft, Ardit Begaj, Gurpreet Beghal, Jessica Belchos, Katarzyna Bera, Tara Bergara, Anna Betts, Aneel Bhangu, Gayathri Bhaskaran, Amina Bhatti, Mihai Bica, Caitlin Billyard, Emily Birkin, Jane Blazeby, Harry Blege, Natalie Blencowe, Christopher Blore, Alex Boddy, Matthew Boissaud-Cooke, Anita Bolina, William Bolton, David Bosanquet, Doug Bowley, Kathryn Boyce, Graham Branagan, Jessica Brayley, Joanna Brecher, Kristina Bresges, Emily Briggs, Ryan Broll, Damien Brown, Elliot Brown, Leo Brown, Robin Brown, Rory Brown, Connor Bruce, Pepa Bruce, Rory Buckle, Emily Budd, Richard Buka, Dermot Burke, Joshua Burke, Alisha Burman, Laura Burney, Amy Burrows, Mohammed Bux, Ronan Cahill, Clementina Calabria, Julian Camilleri-Brennan, Amy Campbell, Bill Campbell, Matthew Cant, Yun Cao, Sophie Carlson, Grace Carr, Luke Carr, Rebecca Carr, Richard Carr, Eleanor Cartwright, Alice Castle, Kirsty Cattle, Daniel Cave, Stephen Chapman, Alexandros Charalabopoulos, Sanjay Chaudhri, Ahmad Chaudhry, Paresh Chauhan, Priyesh Chauhan, Ryad Chebbout, Yunzi Chen, Louisa Chenciner, Jingjie Cheng, Natalie Cheng, Lin Chew, Zenab China, Abhishek Chitnis, Praminthra Chitsabesan, Paul Choi, Sarah Choi, Mariam Choudhry, Chern Choy, Claudia Ciurleo, Henry Claireaux, Peter Coe, Simon Cole, Katy Concannon, Edward Cope, Olivia Corbridge, Jessica Court, Louise Cox, Anna Craig-Mcquaide, Ben Cresswell, Lauren Crozier, Neil Cruickshank, Lucy Cuckow, Helen Cui, Elspeth Cumber, Sarah Cumming, Olivia Cundy, Melissa Cunha, Pedro Cunha, Laura Cunliffe, Jazleen Dada, Prita Daliya, Jeffrey Dalli, Ian Daniels, James Daniels, Ahmed Daoub, Sabeera Dar, Emma Das, Kaustuv Das, Emily Davies, Gareth Davies, Kirsty Davies, Kristen Davies, Rachel Davies, Victoria Dawe, Joshua Lucas de Carvalho, Katie De Jong, Katherine Deasy, Praveena Deekonda, Sahil Deepak, Henal Desai, Karishma Desai, Ryan Devlin, Nishat Dewan, Akashdeep Dhillon, Priya Dhillon, Tanya Dhir, Salomone Di Saverio, Julia Diamond, Peter Dib, Panagiotis A. Dimitriadis, Shiva Dindyal, Matthew Doe, Ciaran Doehrty, Tara Dogra, Arpan Doshi, Alison Downey, Joseph Doyle, Ashleigh Draper, Sarah Duff, Joseph Duncumb, Sophie Dupre, Justine Durno, Michal Dzieweczynski, Nicola Eardley, Sarah Easby, Sam Easdon, Hamdi Ebdewi, Lydon Eccles, Jacob Edwards, Padma Eedarapalli, Mohamed Elbuzidi, Patrick Elder, Lucy Elliott, Malaz Elsaddig, Ysabelle Embury-Young, Sophie Emesih, Alec Engledow, William English, Christos Episkopos, Jonathan Epstein, Rahim Esmail, Taher Fatayer, Nicolò Favero, Nicola Fearnhead, Maxine Feldman, Evelyn Fennelly, Stephen Fenwick, Lucie Ferguson, Stuart Fergusson, Petros Fessas, Isabel FitzGerald, J. Edward Fitzgerald, Harry Fitzpatrick, Daniel Fletcher, Tonia Forjoe, Beniamino Forte, Alex Fowler, Benjamin France, Abraham Francis, Niroshan Francis, Sunil Francis, Sam Freeman, Vicky Fretwell, Teresa Fung, Hugh Furness, Michael Gallagher, Stuart Gallagher, Chuanyu Gao, Lothaire Garard, Shona Gardner, Andrew Gaukroger, Daniel George, Simi George, Jamal Ghaddar, Ali Ghaffar, Shamira Ghouse, Amanda Gilbert, Ashveen Gill, Francesco Giovinazzo, Carey Girling, Lolade Giwa, James Glasbey, Paul Glen, Mary Goble, Jenna Godfrey, Shreya Goel, Wenn Goh, Kajal Gohil, Shyam Gokani, David Gold, David Golding, Andrea Gonzalez-Ciscar, Ross Goodson, Melissa Gough, Shubhangi Govil, Thomas Gower, Christopher Graham, Sam Gray, Patrick Green, Samuel Greenhalgh, Kyriacos Gregoriou, Rhiannon Gribbell, Mary Catherine Gribbon, Charlotte Grieco, Emma Griffiths, Ewen Griffiths, Nathan Griffiths, Sara Griffiths, Cathleen Grossart, Daniel Guerero, Christianne Guillotte, Rishi Gupta, Claire Guy, Adam Gwozdz, James Haddow, Shazia Hafiz, Constantine Halkias, Elisabeth Hall, Hasseb Hamid, Emma Hamilton, Gurvinder Singh Harbhajan Singh, John Hardman, Rhiannon Harries, Rhydian Harris, Suzanne Harrogate, Megan Harty, Jessica Harvey, Rahima Hashemi, Ahmed Hassane, Helen Hawkins, Thomas Hawthorne, John Hayes, Phoebe Hazenberg, Harry Heath, Madhusoodhana Hebbar, R. Heer, Roisin Hegarty O'Dowd, David Henshall, Philip Herrod, Elizabeth Hester, Emily Heywood, Nick Heywood, Frances Hill, James Hill, Kirsty Hill, May Ho, Marianne Hollyman, David Holroyd, Joseph Home, Steve Hornby, Laura Horne, Charlotte Horseman, Huma Hosamuddin, Amy Hough, George Hourston, Nathan Hudson-Peacock, Belinda Hughes, Katie Hughes, Isabel Huppatz, Penelope Hurst, Mahrukh Hussain, Shoaib Fahad Hussain, Syeda Hussain, Imogen Hutchings, Bilal Ibrahim, Lema Imam, Rory Ingham, Rose Ingleton, Rizwan Iqbal, Jenny Isherwood, Abdurrahman Islim, Omar Ismail, Shashank Iyer, Toby Jackman, Prashant Jain, Nadeem Jamal, Sabine Jamal, Ellen James, Nirmitha Jayaratne, Nathan Jeffreys, Hiral Jhala, Courtney Johnson, Zoe Johnston, Conor Jones, Emma-Jane Jones, Keaton Jones, Victor Jones, Roshan Joseph, Dilan Joshi, Holly Joyce, Claire Joyner, Aditya Kale, Sagar Kanabar, Lina Kanapeckaite, Hadyn Kankam, Sarantos Kaptanis, Edward Karam, Dimitrios Karponis, Anne Karunatilleke, Veeru Kasivisvanathan, Geeta Kaur, Samina Kauser, Nigel Keelty, Denise Kelly, Jessica Kennett, Molly Kerr, Ahmed Kerwan, Apoorva Khajuria, Mostafa Khalil, Mehnoor Khaliq, Ayushah Khan, Hamzah Khan, Haroon Khan, Maaz Khan, Maria Khan, Shahab Khan, Kaywaan Khan, Rachel Khaw, Ashni Kheterpal, Parisa Khonsari, Miraen Kiandee, Samuel Kim, Suji Kim, Sung-Hee Kim, Harry King, Anna Kinsella, Ajit Kishore, Stefan Klimach, Angelos G. Kolias, Anna Kolodziejczyk, Chia Yew Kong, Tseun Han James Kong, Omar Kouli, Sebi Kukran, Sevi Kukran, Geev Kumaran, Vladislav Kutuzov, Chris Laing, Georgina Laing, Kulvinder Lal, Peter Lalor, Joel Lambert, Sai Geethan Lambotharan, Eve Lancaster, Jasmine Latter, Michelle Latter, Kenny Lau, Alexa Lazarou, Madeline Leadon, Gabriel Lee, Jeyoung Lee, Kathryn Lee, Matthew Lee, Samuel Lee, Zong Lee, Edward Leung, Thomas Lewis, Hansen Li, Mimi Li, Wan Jane Liew, Yao Ren Liew, Alexander Light, Lydia Lilis, Diana Lim, Hui Lim, Joseph Lim, Zhi Lim, Siyin Liu, James Lloyd, Andrew Logan, Priya Loganathan, M. Long, Lydia Longstaff, Luisa Lopez Rojas, Richard Lovegrove, Jack Lowe-Zinola, Byron Lu Morrell, Joshua Luck, Andreas Luhmann, Surabhika Lunawat, Jon Lund, Cong Luo, Lorna Luo, Iona Lyell, Panagis Lykoudis, Jonathan Macdonald, Aliya Mackenzie, Conor Magee, Pooja Mahankali-Rao, Kamal Mahawar, Mehreen Mahfooz, Faisal Mahmood, Samir Makwana, Tom Malik, Sohaib Mallick, Jyothis Manalayil, Tinaye Mandishona, Sudhakar Mangam, Maniragav Manimaran, Natarajan Manimaran, Chris Manson, Sufyan Mansoor, Fatima Mansour, Alejandro Marcos Rodrigo, Nicholas Markham, Maria Marks, Paul Marriott, Hannah Marsden, Laura Martin, Tiago Martins, John Mason, Luke Mason, Mariam Masood, Nikhil Math, Ginimol Mathew, Jacob Matthews, Jonathan Mayes, Ursula Mc Gee, Ross Mcallister, Sandra Mcallister, Scott Mccain, Conor Mccann, Emmet Mccann, Cathal McCarthy, Gillian Mccoll, Greg Mcconaghie, Ace Mcdermott, Frank McDermott, Rachel Mcdougall, Mark McDowell, Gordon McFarlane, Richard McGregor, Doug McKechnie, Jillian McKenna, Scott McKinstry, Georgia Mclachlan, E. Mclean, Elizabeth McLennan, Angus McNair, Kenneth Mealy, Lauren Mecia, Alexander Mehta, Aidan Mellan, Arathi Menon, Donald Menzies, Zhubene Mesbah, David Messenger, George Miller, Aseem Mishra, Sona Mistry, Tahira Mohamed, Nisha Mohamed Mushaini, Midhun Mohan, Ameerah Mohd Azmilssss, Ajay Mohite, Krishna Moorthy, Jalal Moradzadeh, Richard Morgan, Gabriella Morley, Alice Mortimer, Hannah Mownah, Paul Moxey, Gagira Mudalige, Umarah Muhammad, Samuel Munday, Ben Murphy, Ciaran Murphy, Caoimhe Murray, Hannah Murray, Michael Murray, Mohammed Ibrar Murtaza, Jameel Mushtaq, Ameer Mustafa, Shams Mustafa, Laura Myers, Sam Myers, Adeeb Naasan, Kiran Nadeem, Hanzla Naeem, Prashant Naik, Arun Nair, Keshav K. Nambiar, Muhammad Naqi, Zehra Naqvi, Yan Ning Neo, Georgia Irene Neophytou, Jonathan Neville, Tom Newman, Benjamin Ng, Guat Ng, Jing Qi Ng, Vincent Ng, Zhan Herr Ng, Maire Ni Bhoirne, James Nicholas, Gary Nicholson, George Ninkovic-Hall, Gemma Nixon, Mike Norwood, Toby Noton, Romman Nourzaie, Richard Novell, Donald Nyanhongo, James O'Brien, Rory O'Kane, Stephen O'Neill, Hugh O'Sullivan, Thomas Oakley, Chinomso Ogbuokiri, Oluwafunto Ogunleye, Su Oh, Emezie Okorocha, James Olivier, Rele Ologunde, Sharif Omara, Alice Ormrod, Caroline Osborne, Joanna Osmanska, Raisah Owasil, Sebastian Owczarek, Ezgi Ozcan, Sri Palaniappan, Francesco Palazzo, Abbas Palkhi, Gargi Pandey, James Park, Jennifer Parker, Anna Parry, James Parsonage, Lauren Passby, Bhavi Patel, Bhavik Patel, Chantal Patel, Dinisha Patel, Kirtan Patel, Panna Patel, Pratiksha Patel, Trupesh Patel, Mariasoosai Pathmarajah, Amogh Patil, Pradeep Patil, Yusuf Patrick, Jessica Pearce, Lyndsay Pearce, Colin Peirce, Bryony Peiris, Amy Pendrill, Sreelata Periketi, Michael Perry, George Petrov, Charlotte Phillips, Grace Pike, Ana Catarina Pinho-Gomes, Parhana Polly, Arachchige Ponweera, Yanish Poolovadoo, Raunak Poonawala, Petya Popova, Dimitri Pournaras, Brooke Powell, Praveena Prabakaran, Esha Prakash, Tapani Pratumsuwan, Anusha Prem Kumar, Helen Puddy, Michael Pullinger, Nikita Punjabi, Oliver Charles Putt, Omar Qadir, Mubasher Qamar, Patrick Quinn, Arham Qureshi, Mohamed Rabie, Angus Radford, Anand Radhakrishnan, Ansh Radotra, Nasir Rafiq, Aria Rahem, Nahim Rahman, Syed Rahman, Ramesh Rajagopal, Nick Rajan, Nikitha Rajaraman, Sumetha Rajendran, Liandra Ramachenderam, Divya Ramakrishnan, Denisha Ramjas, James Rammell, Ritika Rampal, George Ramsay, Ratan Randhawa, Ellis Rea, Stephanie Rees, Saad Rehman, Salwah Rehman, Nabila Rehnnuma, Melina Rejayee, Zakaria Rob, Charlotte Roberts, Grace Roberts, Ben Roberts, Harry Robinson, Stephen Robinson, Ailin Rogers, Alex Rogers, William Rook, Talisa Ross, Chloe Roy, Azelea Rushd, Duncan Rutherford, Michael Saat, Kaushik Sadanand, Rebecca Sagar, Harkiran Sagoo, Arin Saha, Kapil Sahnan, Mohammed Salik Sait, Saif Sait, Damien Salekin, Mostafa Salem, Nadia Salloum, Emma Sanders, Jasmesh Sandhu, N. Sandhu, Lorna Sandison, Laura Sandland-Taylor, Ron Sangal, Chandan Sanghera, Josephine Saramunda, Lauren Satterthwaite, Moritz Schramm, Rupert Scott, Chloe Searle, Harkiran Seehra, Juan Jose Segura-Sampedro, Harpreet Kaur Sekhon Inderjit Singh, Shaikh Sanjid Seraj, Ishani Seth, Rajiv Sethi, Apar Shah, Mario Shaid, Shafaque Shaikh, Awad Shamali, Elizabeth Sharkey, Abhi Sharma, Neil Sharma, Sachin Sharma, Aniruddh Shenoy, Maleasha Shergill, Shahram Shirazi, Imran Siddiqui, Raykal Sim, Lucy Simmonds, Andrew Simon, William Simpson, Bharpoor Singh, J. Singh, Prashant Singh, Anant Sinha, Sidhartha Sinha, Robert Sinnerton, Chaamanti Sivakumar, Brendan Skelly, Richard Slater, Samuel Small, Neil Smart, Yat Wing Smart, Alexander Smith, Charlotte Smith, Jason Smith, Rebecca Smith, Scott Smith, Peter Sodde, Zhi Min Soh, Aniket Sonsale, Ahmed Soualhi, John Spearman, Robert Spencer, Harry Spiers, Philip Stather, Michael Stoddart, Bradley Storey, Howard Stringer, Thomas Stringfellow, Ben Stubbs, Niv Sukir, Nivian Sukirthan, Yasir Suleman, Aparnah Sureshkumar, Ashwin Suri, Timen Swartbol, Hyder Tahir, E. Tian Tan, Huai Ling Tan, Laura Tan, Alethea Tang, Priyal Taribagil, Yao Zong Tay, Beth Taylor, Zara Taylor, Alexandra Thatcher, Rachel Thavayogan, Michael Thomaa, Daniah Thomas, Jenny Thomas, Paul Thomas, Thomas Pinkney, Chris Thompson, Mag Ting, Ethan Toner, Godwin Tong, Jared Torkington, Molly Traish, Miles Triniman, John Trotter, Kwong Tsang, Sanchit Turaga, Hannah Turley, James Turner, Tomas Urbonas, Alexandra Urquhart, Nimai Vadgama, Aashay Vaidya, Gijs van Boxel, Swati Vara, Massimo Varcada, Rebecca Varley, Dee Varma, Martinique Vella-Baldacchino, Sara Venturini, Naina Verma, Saurabh Verma, Gabrielle Vernet, Mark Vipond, Alex von Roon, Qasim Wadood, Kathryn Waite, Lewis Walker, Nathan Walker, Jonathan C.M. Wan, Liyang Wang, Xue Wang, Alex Ward, Thomas Ward, Nienke Warnaar, Lloyd Warren, Oliver Warren, Sam Waters, Angus Watson, Laura Jayne Watson, Dominic Waugh, Daniel Weinberg, Malcolm West, Carla White, Tim White, Katharine Whitehurst, Robert Whitham, Tharindri Wijekoon, Manuk Wijeyaratne, Richard Wilkin, Alex Wilkins, Adam Williams, Gethin Williams, Luke Williams, Robert Williams, Andrew Williamson, Jacinthe Willson, Andrew Wilson, Holly Wilson, James Wilson, Lizzie Wilson, Megan Wilson, Michael Wilson, Rebekah Wilson, Tim Wilson, Evelina Woin, Esther Wright, Jenny Wright, Nicholas Wroe, Joanne Wylie, Yiwang Xu, Satheesh Yalamarthi, Angela Yan, Narisu Yang, Eda Yardimci, Ibrahim Yasin, Ismael Yasin, Noor Yasin, Joseph Yates, Jih Dar Yau, Tricia Yeoh, Joshua Yip, Cissy Yong, Vasudev Zaver, Tatiana Zhelezniakova, and Adreana Zulkifli

Subjects
Medical education, Manchester Cancer Research Centre, business.industry, ResearchInstitutes_Networks_Beacons/mcrc, MEDLINE, General Medicine, 030230 surgery, Collaborative research, 03 medical and health sciences, 0302 clinical medicine, Foundation Programme, Medicine, Surgery, 030212 general & internal medicine, business
Published
2017
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8. Thermo-visco-elasticity for Norton-Hoff-type models with Cosserat effects

Author

Filip Z. Klawe and Sebastian Owczarek

Subjects
General Mathematics, 010102 general mathematics, General Engineering, 02 engineering and technology, Function (mathematics), Type (model theory), 01 natural sciences, 020303 mechanical engineering & transports, 0203 mechanical engineering, Applied mathematics, 0101 mathematics, Elasticity (economics), Mathematical economics, Mathematics
Abstract

We consider the quasi-static evolution of thermo-visco-elastic material. The main goal of this paper is to present how taking into account the additional effects may improve the result of solutions' existence. We added a micropolarity effect to thermo-visco-elastic model regarding Norton-Hoff-type constitutive function. This additional phenomenon improves the regularity of solution. Copyright (C) 2016 John Wiley & Sons, Ltd.

Published
2016
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9. Renormalized solutions in thermo-visco-plasticity for a Norton–Hoff type model. Part I: The truncated case

Author

Sebastian Owczarek and Krzysztof Chełmiński

Subjects
Continuum mechanics, Applied Mathematics, 010102 general mathematics, General Engineering, General Medicine, Function (mathematics), Type (model theory), Plasticity, Term (logic), Thermal conduction, 01 natural sciences, 010101 applied mathematics, Computational Mathematics, Monotone polygon, Limit (mathematics), 0101 mathematics, General Economics, Econometrics and Finance, Analysis, Mathematical physics, Mathematics
Abstract

We prove existence of global in time strong solutions to the truncated thermo-visco-plasticity with an inelastic constitutive function of Norton–Hoff type. This result is a starting point to obtain renormalized solutions for the considered model without truncations. The method of our proof is based on Yosida approximation of the maximal monotone term and a passage to the limit.

Published
2016
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10. The Armstrong–Frederick cyclic hardening plasticity model with Cosserat effects

Author

Sebastian Owczarek, Patrizio Neff, and Krzysztof Chełmiński

Subjects
Pointwise, Limit of a function, Applied Mathematics, Mathematik, Approximation process, Calculus, Hardening (metallurgy), Applied mathematics, Plasticity, Solution concept, Analysis, Quasistatic process, Mathematics
Abstract

We propose an extension of the cyclic hardening plasticity model formulated by Armstrong and Frederick which includes micropolar effects. Our micropolar extension establishes coercivity of the model which is otherwise not present. We study then existence of solutions to the quasistatic, rate-independent Armstrong–Frederick model with Cosserat effects which is, however, still of non-monotone, non-associated type. In order to do this, we need to relax the pointwise definition of the flow rule into a suitable weak energy-type inequality. It is shown that the limit in the Yosida approximation process satisfies this new solution concept. The limit functions have a better regularity than previously known in the literature, where the original Armstrong–Frederick model has been studied.

Published
2014
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11. Convergence of a monotonisation procedure for a non-monotone quasi-static model in poroplasticity

Author

Sebastian Owczarek

Subjects
Applied Mathematics, Constitutive equation, Mathematical analysis, Porous media, Young measure, Nonlinear system, Monotone polygon, Inelastic deformation, Ordinary differential equation, Convergence (routing), Initial value problem, Boundary value problem, Coercive approximation, Biot model, Analysis, Mathematics
Abstract

Existence theory to quasi-static initial-boundary value problem of poroplasticity is studied. The classical quasi-static Biot model for soil consolidation coupled with a nonlinear system of ordinary differential equations is considered. This article presents a convergence result for the coercive and monotone approximations to solution of the original non-coercive and non-monotone problem of poroplasticity such that the inelastic constitutive equation is satisfied in the sense of Young measures.

Published
2010
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12. Convergence of coercive approximations for a model of gradient type in poroplasticity

Author

Sebastian Owczarek

Subjects
Nonlinear system, Partial differential equation, Biot number, Differential equation, General Mathematics, Numerical analysis, Convergence (routing), Mathematical analysis, General Engineering, Initial value problem, Boundary value problem, Mathematics
Abstract

We study the existence theory to the quasi-static initial-boundary-value problem of poroplasticity. In this article the classical quasi-static Biot model is considered for soil consolidation coupled with a nonlinear system of differential equations. This work, for the poroplasticity model of monotone-gradient type, presents a convergence result of the coercive approximation to the solution of the original noncoercive problem. Copyright © 2008 John Wiley & Sons, Ltd.

Published
2008
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13. A Galerkin Method for Biot Consolidation Model

Author

Sebastian Owczarek

Subjects
Consolidation (soil), Biot number, General Mathematics, Existence theorem, Mechanics of Materials, Approximation process, Calculus, Initial value problem, Applied mathematics, General Materials Science, Uniqueness, Boundary value problem, Galerkin method, Mathematics
Abstract

The main aim of this paper is to prove the existence and uniqueness of solutions to an initial-boundary value problem corresponding to the Biot model. The existence theorem is proved by Galerkin method and the passage to the limit in the approximation process is shown in a standard way. Assuming that the given data satisfy some natural regularity requirements a better regularity of solutions is obtained than it could be found in the literature.

Published
2008
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14. A first regularity result for the Armstrong-Frederick cyclic hardening plasticity model with Cosserat effects

Author

Krzysztof Chełmiński, Patrizio Neff, and Sebastian Owczarek

Subjects
Applied Mathematics, Mathematical analysis, Hölder condition, Plasticity, Dirichlet distribution, symbols.namesake, Mathematics - Analysis of PDEs, Mathematik, FOS: Mathematics, Hardening (metallurgy), symbols, Analysis, Quasistatic process, Analysis of PDEs (math.AP), Mathematics
Abstract

The purpose of this article is to prove the H\"older continuity up to the boundary of the displacement vector and the microrotation matrix for the quasistatic, rate-independent Armstrong-Frederick cyclic hardening plasticity model with Cosserat effects. This model is of non-monotone and non-associated type. In the case of two space dimensions we use the hole-filling technique of Widman and the Morrey's Dirichlet growth theorem., Comment: arXiv admin note: text overlap with arXiv:1304.5801

Published
2015

15. Existence of a solution to a non-monotone dynamic model in poroplasticity with mixed boundary conditions

Author

Sebastian Owczarek

Subjects
Applied Mathematics, 010102 general mathematics, Mathematical analysis, Constitutive equation, Mathematics::Analysis of PDEs, Inelastic deformation, 01 natural sciences, Mathematics::Numerical Analysis, 010101 applied mathematics, Condensed Matter::Materials Science, Monotone polygon, Boundary value problem, 0101 mathematics, Porous medium, Non monotone, Analysis, Mathematics, Young measure
Abstract

In this note, we investigate a non-monotone and non-coercive dynamic model of poroplasticity with mixed boundary conditions. The existence of the solution to this non-monotone model, where the inelastic constitutive equation is satisfied in the sense of Young measures, is proved using the coercive and monotone approximations.

Published
2016
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16. Poroplasticity with Cosserat effects

Author

Patrizio Neff, Krzysztof Chełmiński, and Sebastian Owczarek

Subjects
Monotone polygon, Fundamental theorem, Applied Mathematics, Constitutive equation, Mathematical analysis, Mathematik, Computational Mechanics, Inelastic deformation, Limit (mathematics), Type (model theory), Mathematics, Young measure
Abstract

We prove existence of solutions to a non-monotone and non-gradient type quasi-static model of poroplasticity with Cosserat effects. It is shown that this model possesses global in time solutions, where the inelastic constitutive equation is satisfied in the sense of Young measures. The methods of proof are a monotone approximation, energy estimates, the fundamental theorem on Young measures, and a passage to the limit with the monotone approximation. c

Published
2012

17. The Armstrong-Frederick Plasticity model with Cosserat effects

Author

Sebastian Owczarek, Patrizio Neff, and Krzysztof Chełmiński

Subjects
Limit of a function, Energy inequality, Approximation process, Limit (mathematics), Type (model theory), Plasticity, Quasistatic process, Mathematics, Mathematical physics
Abstract

We propose an extension of equations formulated by Armstrong and Frederick which includes micropolar effects. We study existence of solutions to the quasistatic Armstrong-Frederick model with Cosserat effects which is still of non-monotone type. It was shown that the limit in the Yosida approximation process satisfies the energy inequality. The limit functions have a better regularity than it could be found in the literature, where the original Armstrong-Frederick model was studied. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Published
2013
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