Continuum damage model

R. Talreja Further developments in continuum damage modeling of composites aided by micromechanics. ASME App. Mech. Div. 150, 103 (1993)... 

Geologic materials like oil shale are commonly treated as elastic/plastic solids. Fracture under intense loading is then modeled as an extension of plasticity or is treated with a separate fracture model. In applications like rock blasting, the latter approach is preferable, since fracture of rock is qualitatively different from plastic flow. Even so, continuum damage models have been used to model blasting for engineering applications. Some calculations with such a model will be presented below. 

Maimf P, Camanho PP, Ma oigo JA, Davila CG. A continuum damage model for composite laminates part 1 — constitutive model. Mech Mater 2007 39 897-908. 

Hao, H., Wu, C., Zhou, Y. (2002). Numerical analysis of blast-induced stress waves in a rock mass with anisotropic continuum damage models. Part I equivalent material property approach. Rock Mechanics and Rock Engineering, 35(2), 79-94. doi 10.1007/ S006030200012doi 10.1007/s006030200012... 

Govindjee, S. and Simo, J. (1991) A micro-mechanically based continuum damage model for carbon black-filled rubbers incorporating Mullins effect. Journal of the Mechanics and Physics of Solids, 39, 87-112. 

In the FEM simulations, pinned support (Ux = 0, Uy = 0, and Uz = 0) was assumed at the base of the walls. The Plastic Damage model available in ABAQUS was also adopted in the simulations. The materials used in the walls were concrete (concrete brick tmits) and mortar (head/bed joints between bricks). Both materials have been considered as a continuum media and simulated using the continuum damage model. The only material properties available in (Li et al. 2005) were the concrete and mortar ultimate compression strengths. Other needed data was extracted using ACI formulas. Some of the parameters needed in the Plastic... 

Govindjee and Simo [52] combined micromechanical and phenomenological approaches to develop a continuum damage model for carbon black filled elastomers, where the softening effect is considered as the detachment of carbon particles from the elastomer matrix. 

Weitsman, Y.J. A continuum damage model for viscoelastic materials. /. of Applied Mechanics 55. 1988, p773-780. 

B. Nguyen, B. Koeppel, S. Ahzi, M. Khaleel, S. Prabhakar, Crack growth in solid oxide fuel cell materials Ifom discrete to continuum damage modeling. J. Am. Ceram. Soc. 89(4), 1358-1368 (2006)... 

Significant improvements in modeling have been achieved with the use of extended finite element methods (x-FEM) coupled with more accurate constitutive properties and continuum damage mechanics [15,16]. In this and similar approaches, improved failure criteria such as the LaRC 03 are combined with accurate stress—strain curves... 

A future trend in composite bolted joint design is the use of more advanced continuum damage mechanics approaches to model joint failure, so that non-linear shear behaviour and gradual stiffness degradation can be implemented. An important element of joint failure is delamination, and many efforts are being undertaken to implement delamination in finite element models. However, for bolted joints analysis this poses many problems due to the large number of delamination interfaces in thick laminates. 

A structure evolving, damage-allowable thermoviscoplastic model has been developed and reasonably captured the most essential shape memory response of the SMP based syntactic foam during this process. A finite deformation, continuum constimtive model has been developed to study the thermomechanical behavior of the SMP based self-healing syntactic... 

Darabi, M.K., Abu Al-Rub, R.K., and Little, D.N. (2012) A continuum damage mechanics framework for modeling micro-damage healing. International Journal of Solids and Structures, 49, 492-513. 

Kachanov LM (1986) Introduction to continuum damage mechanics. Springer, New York Lee J, Fenves GL (1998) Plastic-damage model for cyclic loading of concrete structures. J Eng Mech ASCE 124(8) 892-900... 

Espinosa, H. D., Zavattieri, P. D., and Dwivedi, S. K. (1998). A finite deformation continuum/discrete model for the description of fragmentation and damage in brittle materials. J. Mech. Phys. Solids, 46(10) 1909 1942. 

Another approach employing concepts of continuum damage mechanics (e.g., Lemaitre and Chaboche 1994) was presented by Perreux and Suri (1997). Studying the effects of cyclic fatigue on [ 55°]3 glass fiber/poly epoxy composite pipes they noticed that in the absence of stress moisture uptake data could be modeled as a process of a two-phase diffusion (see Sect. 3.6). Damage in the axial direction was related to the decrease in the axial stiffness, namely and its effect on... 

Nonlinear continuum models are typically used for research purposes, whose aim is to study in detail the response of critical regions in piers. Material nonlinearity is taken into account using either a standard plasticity model or a combination of plasticity and damage models, the latter being able to affect the elastic component of the deformation as (seismic) damage propagates. Geometric nonlinearity is less critical in R/C piers, except for very tall ones. The type of... 

Gambarotta L, Lagomarsino S (1997) Damage models for the seismic response of brick masonry shear walls. Part II The continuum model and its applications. Earthq Eng Struct Dyn 26 441 62... 

Most adhesives are polymer-based materials and exhibit viscoelastic behavior. Some adhesives are elastomer materials and also exhibit full or partial rubberlike properties. The word elastic refers to the ability of a material to return to its original dimensions when unloaded, and the term mer refers to the polymeric molecular makeup in the word elastomer. In cases where brittle material behavior prevails, and especially, when inherent material flaws such as cracks, voids, and disbonds exist in such materials, the use of the methods of fracture mechanics are called for. For continuum behavior, however, the use of damage models is considered appropriate in order to be able to model the progression of distributed and non-catastrophic failures and/or irreversible changes in material s microstructure, which are sometimes described as elastic Hmit, yield, plastic flow, stress whitening, and strain hardening. Many adhesive materials are composite materials due to the presence of secondary phases such as fillers and carriers. Consequently, accurate analysis and modeling of such composite adhesives require the use of the methods of composite materials. 

Continuum damage mechanics-based models are now available and implemented in commercial finite element software. Damage may be regarded as the growth of microvoids or microcracks in a material (Lemaitre and Desmorat 2005). Continuum damage mechanics was introduced in the late 1950s (Kachanov 1958) and is able to predict the reduced load-bearing capacity of a material before failure. 

The aforementioned constitutive equations predict the continuum deformation in the solder. However, the total functional lifetime of a solder interconnection also includes the initiation and propagation of fatigue cracks. Crack development is addressed by so-called damage models. The... 

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