Continuum modelling of strong discontinuities in solid mechanics using damage models

Static and cyclic loading, impact, and environmental attack all contribute to the accumulation of damage in composite laminates. The damage can take many forms: delamination and splitting during load cycling, matrix cracking during thermal fatigue, and so on. With this diversity of damage mechanisms, it is no wonder that variability in static strength is significantly enhanced by service in the field. We recognise, therefore, that damage is progressive and is accompanied by a gradual deterioration in strength and stiffness of the laminate. In other words, static strength and life-time are part of the same design phenomenon. One way forward is to identify the broad rules governing fibre composite behaviour. There are two directions: continuum modelling and microscopic modelling. Continuum modelling is useful, but generally demands a formidable experimental programme to determine important design parameters. On a much smaller scale, microscopic modelling provides insight into the damaging mechanisms, but alone is too imprecise to be of much practical use to the design engineer. In parallel, however, they can give guidance towards the development of constitutive laws, the path of model-informed empiricism, which leads to predictive design. In other words, extension of basic damage models of composite failure to generic design features can lead to a formulation of design procedures for composite hardware; this is a powerful route to take.

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Macrohomogeneity condition for strain gradient homogenization of periodic heterogeneous media with interfacial strong discontinuities

Mathematics and Mechanics of Solids ◽

10.1177/1081286520958757 ◽

2020 ◽

pp. 108128652095875

Author(s):

JF Ganghoffer ◽

XN Do ◽

G Maurice

Keyword(s):

Strain Gradient ◽

Heterogeneous Media ◽

Weak Form ◽

Displacement Discontinuity ◽

Order Effects ◽

Interfacial Behavior ◽

Damage Models ◽

Strong Discontinuities ◽

Polynomial Expression ◽

The Hill

The Hill macrohomogeneity condition is revisited in the context of strain gradient homogenization for heterogeneous materials prone to interfacial displacement jumps. The consideration of strain gradient effects is motivated by their use as a regularization method for strain-softening constitutive damage models leading to strain localization and displacement discontinuity. Starting from the weak form of the boundary value problem formulated at the microscopic level, a polynomial expression of the virtual velocity is adopted as the minimum microscopic kinematics consistent with the selected macroscopic kinematics of the strain gradient effective continuum. The effective volumetric and interfacial mesoscopic strains and stress measures for the effective substitution are obtained versus the microscopic strains and stresses. The Hill macrohomogeneity condition is successively formulated for continuous interfaces and discontinuous interfaces witnessing strong discontinuities. It highlights the expressions of the effective stress measures associated to the volumetric and interfacial behavior for both classical and higher-order effects.

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