In this work, we obtain important insights into the multi-scale and multi- physical processes of soft and biological materials, which display complex be- havioral characteristics due to material and geometric complexity during de- formation, damage initiation, and fracture propagation. Hydrogel and certain load-bearing biological tissues are permeated with fluid which leads to rate de- pendent (visco- and poro-elastic) effects as well as a high degree of incompress- ibility, requiring multi-field displacement and pressure theoretical frameworks. The first aim considers how surface stresses due to elastocapillarity effect the swelling and drying kinetics of a spherical hydrogel, leading to a decrease in equilibration time as compared to results where elastocapillarity is not taken into account. This work leads to material insights in complex experimental set- tings such as modeling micro-tissue contractility and studying the behavior of a cell aggregate subjected to ion-gate treatment within a gel. Through use of the phase-field fracture method, soft material damage and fracture can be studied in both a static and dynamic setting. Computational efficiency at the limit of incompressibility is addressed through numerical stabilization schemes which circumvent the inf-sup condition.