This paper presents a thorough analysis of potential-based and non-potential-based cohesive zone models (CZMs) under conditions of mixed-mode separation and mixed-mode over-closure. Problems are identified with the well established potential-based Xu-Needleman (XN) model and a number of new potential-based and non-potential-based models are proposed. It is demonstrated that derivation of traction-separation relationships from a potential function can result in non-physical repulsive normal tractions and instantaneous negative incremental energy dissipation under displacement controlled monotonic mixed-mode separation when the work of tangential separation exceeds the work of normal separation. A modified potential-based (MP) model is proposed so that the zone in which repulsive normal tractions occur can be controlled. The MP model also provides an additional benefit of correct penalisation of mixed-mode over-closure, in contrast to the XN model. In order to fully eliminate the problem of repulsive normal tractions a non-potential-based CZM (NP1) is also proposed. This model is shown to provide physically realistic behaviour under conditions of displacement controlled mixed-mode separation and over-closure. Noting that the form of the traction-separation equations differ for mode I and mode II separation for the XN, MP and NP1 models, an additional non-potential-based model (NP2) is proposed so that near mode-independent behaviour can be achieved in displacement controlled separation, while correctly penalising over-closure. Following from the NP2 model, a non-potential-based model in which coupling is based on the separation magnitude is considered (SMC model). In the final part of the paper the performance of each model under traction controlled mixed-mode separation is investigated by numerically inverting the traction-separation equations. Separation paths for the XN model reveal a strong bias toward mode I separation while the NP1 model exhibits a bias towards mode II separation. Interestingly, the NP2 model exhibits a high degree of mode sensitivity under traction controlled conditions, in contrast to its near mode independence under displacement controlled conditions. It is demonstrated that incorrect weighting of the coupling terms in non-potential models can lead to the existence of a singularity under traction controlled conditions. Finally, it is demonstrated that the potential-based models fail to capture a gradual change from mode II to mode I work of separation, as reported experimentally for traction controlled interface separation. In a follow-on Part II companion paper a number of case studies are simulated, demonstrating that the theoretical findings of the present paper have significant implications for the finite element prediction of interface debonding. © 2013 Elsevier Ltd.

Osteogenesis of mesenchymal stem cells (MSC) can be regulated by the mechanical environment. MSCs grown in 3D spheroids (mesenspheres) have preserved multi-lineage potential, improved differentiation efficiency, and exhibit enhanced osteogenic gene expression and matrix composition in comparison to MSCs grown in 2D culture. Within 3D mesenspheres, mechanical cues are primarily in the form of cell-cell contraction, mediated by adhesion junctions, and as such adhesion junctions are likely to play an important role in the osteogenic differentiation of mesenspheres. However the precise role of N- and OB-cadherin on the biomechanical behaviour of mesenspheres remains unknown. Here we have mechanically tested mesenspheres cultured in suspension using parallel plate compression to assess the influence of N-cadherin and OB-cadherin adhesion junctions on the viscoelastic properties of the mesenspheres during osteogenesis. Our results demonstrate that N-cadherin and OB-cadherin have different effects on mesensphere viscoelastic behaviour and osteogenesis. When OB-cadherin was silenced, the viscosity, initial and long term Young's moduli and actin stress fibre formation of the mesenspheres increased in comparison to N-cadherin silenced mesenspheres and mesenspheres treated with a scrambled siRNA (Scram) at day 2. Additionally, the increased viscoelastic material properties correlate with evidence of calcification at an earlier time point (day 7) of OB-cadherin silenced mesenspheres but not Scram. Interestingly, both N-cadherin and OB-cadherin silenced mesenspheres had higher BSP2 expression than Scram at day 14. Taken together, these results indicate that N-cadherin and OB-cadherin both influence mesensphere biomechanics and osteogenesis, but play different roles.

Osteogenesis of mesenchymal stem cells (MSC) can be regulated by the mechanical environment. MSCs grown in 3D spheroids (mesenspheres) have preserved multi-lineage potential, improved differentiation efficiency, and exhibit enhanced osteogenic gene expression and matrix composition in comparison to MSCs grown in 2D culture. Within 3D mesenspheres, mechanical cues are primarily in the form of cell-cell contraction, mediated by adhesion junctions, and as such adhesion junctions are likely to play an important role in the osteogenic differentiation of mesenspheres. However the precise role of N- and OB-cadherin on the biomechanical behaviour of mesenspheres remains unknown. Here we have mechanically tested mesenspheres cultured in suspension using parallel plate compression to assess the influence of N-cadherin and OB-cadherin adhesion junctions on the viscoelastic properties of the mesenspheres during osteogenesis. Our results demonstrate that N-cadherin and OB-cadherin have different effects on mesensphere viscoelastic behaviour and osteogenesis. When OB-cadherin was silenced, the viscosity, initial and long term Young's moduli and actin stress fibre formation of the mesenspheres increased in comparison to N-cadherin silenced mesenspheres and mesenspheres treated with a scrambled siRNA (Scram) at day 2. Additionally, the increased viscoelastic material properties correlate with evidence of calcification at an earlier time point (day 7) of OB-cadherin silenced mesenspheres but not Scram. Interestingly, both N-cadherin and OB-cadherin silenced mesenspheres had higher BSP2 expression than Scram at day 14. Taken together, these results indicate that N-cadherin and OB-cadherin both influence mesensphere biomechanics and osteogenesis, but play different roles.