Computers structures PERGAMON Computers and Structures 80(2002)1159-1176 On a general constitutive description for the inelastic and failure behavior of fibrous laminates- Part I Lamina theory Zheng-Ming Huang Biomaterials Laboratory, Division of Bioengineering, Department of Mechanical Engineering, National Unirersity of singapore, Ria Received 10 April accepted 6 March 2002 abstract plane load, the ultimate failure of the laminate can correspond to its last-ply failure, and hence a stress failure criterion nay be sufficient to detect the maximum load that can be sustained by the laminate. Even in such case, the load shared by each lamina in the laminate cannot be correctly determined if the lamina instantaneous stiffness matrix is inaccu- rately provided, since the lamina is always statically indeterminate in the laminate. If, however, the laminate is subjected to a lateral load, its ultimate failure occurs before the last-ply failure and the only use of the stress failure criterion is no longer sufficient; an additional critical deflection or curvature condition must be employed as well. This necessitates development of an efficient constitutive relationship for laminated composites in order that the laminate strains/de flections until the ultimate failure can be accurately calculated. a general constitutive description for the thermo- mechanical response of a fibrous laminate up to the ultimate failure with applications to various fibrous laminates is presented in these two parts of papers. The constitutive relationship is obtained by combining the classical lamination theory with a recently developed bridging micromechanics model, through a layer -by-layer analysis. The present paper focuses on the lamina analysis. Attention has been given to the applicability of the constitutive theory to the fibrous laminates stacked with a wide variety of composite laminae, including multidirectional tape laminae, woven and braided fabric composites, and knitted fabric reinforced composites, which have different constituent behavior such as elasto-plasticity and elastic-visco-plasticity. The laminate analysis and the application examples will be presented in the subsequent paper. o 2002 Published by Elsevier Science Keywords: Laminated composite; Textile co te; Metal matrix composite; Composite structure; Mechanical property: Constitutive relationship: Lamina theory; Bridging micromechanics model cuon achievement poses on the available materials. In some ndustry, conventional monolithic materials are currently It has been recognised that technological develop- operating at or near their limits and do not offer the ment depends on advances in the field of materials. potential for meeting the demands of further technical Whatever the field may be, the final limitation on advancement [1]. In this regard, composites represent nothing but a giant step in the ever-lasting endeavour of optimisation in materials. Furthermore, most living E-mailaddresses:huangzm@mail.tongji.edu.cn,huangzm@tissuesofourbody,bothhardandsofttissuessuch as bones. skins. dentins. cartilages. and 02/- see front matter a 2002 Published by Elsevier Science Ltd. PI:S0045-7949(02)00074-3On a general constitutive description for the inelastic and failure behavior of fibrous laminates––Part I: Lamina theory Zheng-Ming Huang Biomaterials Laboratory, Division of Bioengineering, Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Cresent, Singapore 119 260 Received 10 April 2001; accepted 6 March 2002 Abstract It is well known that a structural design with isotropic materials can be accomplished only based on a stress failure criterion. This is, however, generally not true with laminated composites. Only when the laminate is subjected to an in￾plane load, the ultimate failure of the laminate can correspond to its last-ply failure, and hence a stress failure criterion may be sufficient to detect the maximum load that can be sustained by the laminate. Even in such case, the load shared by each lamina in the laminate cannot be correctly determined if the lamina instantaneous stiffness matrix is inaccu￾rately provided, since the lamina is always statically indeterminate in the laminate. If, however, the laminate is subjected to a lateral load, its ultimate failure occurs before the last-ply failure and the only use of the stress failure criterion is no longer sufficient; an additional critical deflection or curvature condition must be employed as well. This necessitates development of an efficient constitutive relationship for laminated composites in order that the laminate strains/de- flections until the ultimate failure can be accurately calculated. A general constitutive description for the thermo￾mechanical response of a fibrous laminate up to the ultimate failure with applications to various fibrous laminates is presented in these two parts of papers. The constitutive relationship is obtained by combining the classical lamination theory with a recently developed bridging micromechanics model, through a layer-by-layer analysis. The present paper focuses on the lamina analysis. Attention has been given to the applicability of the constitutive theory to the fibrous laminates stacked with a wide variety of composite laminae, including multidirectional tape laminae, woven and braided fabric composites, and knitted fabric reinforced composites, which have different constituent behavior such as elasto-plasticity and elastic-visco-plasticity. The laminate analysis and the application examples will be presented in the subsequent paper.
2002 Published by Elsevier Science Ltd. Keywords: Laminated composite; Textile composite; Metal matrix composite; Composite structure; Mechanical property; Constitutive relationship; Lamina theory; Bridging micromechanics model 1. Introduction It has been recognised that technological develop￾ment depends on advances in the field of materials. Whatever the field may be, the final limitation on achievement poses on the available materials. In some industry, conventional monolithic materials are currently operating at or near their limits and do not offer the potential for meeting the demands of further technical advancement [1]. In this regard, composites represent nothing but a giant step in the ever-lasting endeavour of optimisation in materials. Furthermore, most living tissues of our body, both hard and soft tissues such as bones, skins, dentins, cartilages, and even cells, are Computers and Structures 80 (2002) 1159–1176 www.elsevier.com/locate/compstruc E-mail addresses: huangzm@mail.tongji.edu.cn, huangzm@ email.com (Z.-M. Huang). 0045-7949/02/$ - see front matter
2002 Published by Elsevier Science Ltd. PII: S 0 0 4 5 - 7 9 4 9 ( 0 2 ) 0 0 0 7 4 - 3