The answer is that yes, you can gain muscle without gaining significant strength. While there is some correlation due to leverage, size is a physiological phenomenon whereas strength is more neurological and depends on the efficiency with which your nervous system coordinates the firing of motor units. The keys to growing muscle regardless of what your strength might be are:
Mechanical load - you must increase load from workout to workout, on average, to achieve hypertrophy
Chronic progression - you should consistently apply a similar load and not change too frequently or your body will be forced to deal with mechanical and neurological adaptation rather than physiological
Strategic deconditioning - per Bryan Haycock "At this point, it is necessary to either increase the load (Progressive load), or decrease the degree of conditioning to the load (Strategic Deconditioning). The muscle is sensitive not only to the absolute load, but also to the change in load (up or down). Therefore, you can get a hypertrophic effect from increasing the load from a previous load, even if the absolute load is not maximum, assuming conditioning (resistance to exercise induced micro-damage) is not to extensive. There is a limit to the number of increments you can add to increase the load. You simply reach your maximum voluntary strength eventually. This is why Strategic Deconditioning is required for continued growth once growth has stopped (all things remaining equal)."
To summarize, you don't want to change workouts too frequently but eventually you'll have to, and load is king so a training methodology where you can consistently increase load is going to work the best. That means perhaps starting at higher reps, lighter load and progressing to fewer reps, heavy load and then starting over again in what is known as "stair stepping" or "pyramid", i.e. for bench I do 200, 220, 240, 260, then fall back and do 205, 225, 245, 265, etc. to progress.
I know some people want the science so if you really do go out and read the journals, here's a boat load of references Bryan Haycock gave me in an interview many years ago (he developed Hypertrophy Specific Training/HST which is a method based specifically on the science behind hypertrophy or muscle building)
1: Nosaka K, Newton M. Repeated Eccentric Exercise Bouts Do Not Exacerbate Muscle Damage and Repair. J Strength Cond Res. 2002 Feb;16(1):117-122.
2: Nosaka K, Newton M. Concentric or eccentric training effect on eccentric exercise-induced muscle damage. Med Sci Sports Exerc. 2002 Jan;34(1):63-9.
3: Proske U, Morgan DL. Muscle damage from eccentric exercise: mechanism, mechanical signs, adaptation and clinical applications. J Physiol. 2001 Dec 1;537(Pt 2):333-45.
4: Nosaka K, Newton M, Sacco P. Responses of human elbow flexor muscles to electrically stimulated forced lengthening exercise. Acta Physiol Scand. 2002 Feb;174(2):137-45.
5: Allen DG. Eccentric muscle damage: mechanisms of early reduction of force. Acta Physiol Scand. 2001 Mar;171(3):311-9.
6: Clarkson PM. Eccentric exercise and muscle damage. Int J Sports Med. 1997 Oct;18 Suppl 4:S314-7.
7: Paddon-Jones D, Abernethy PJ. Acute adaptation to low volume eccentric exercise. Med Sci Sports Exerc. 2001 Jul;33(7):1213-9.
8: Nosaka K, Sakamoto K, Newton M, Sacco P. How long does the protective effect on eccentric exercise-induced muscle damage last? Med Sci Sports Exerc. 2001 Sep;33(9):1490-5.
9: McHugh MP, Connolly DA, Eston RG, Gleim GW. Exercise-induced muscle damage and potential mechanisms for the repeated bout effect. Sports Med. 1999 Mar;27(3):157-70.
10: Nosaka K, Sakamoto K, Newton M, Sacco P. The repeated bout effect of reduced-load eccentric exercise on elbow flexor muscle damage. Eur J Appl Physiol. 2001 Jul;85(1-2):34-40.
11: Rennie MJ. How muscles know how to adapt. J Physiol. 2001 Aug 15;535(Pt 1):1.
- Nosaka K, Sakamoto K. Effect of elbow joint angle on the magnitude of muscle damage to the elbow flexors. Med Sci Sports Exerc. 2001 Jan;33(1):22-9.
13: Lieber RL, Friden J. Morphologic and mechanical basis of delayed-onset muscle soreness. J Am Acad Orthop Surg. 2002 Jan-Feb;10(1):67-73.
14: Nosaka K, Clarkson PM. Influence of previous concentric exercise on eccentric exercise-induced muscledamage. J Sports Sci. 1997 Oct;15(5):477-83.
15: Carson JA. The regulation of gene expression in hypertrophying skeletal muscle. Exerc Sport Sci Rev. 1997;25:301-20.
16:. Lieber RL, Friden J. Mechanisms of muscle injury after eccentric contraction. J Sci Med Sport. 1999 Oct;2(3):253-65.
17: Nosaka K, Clarkson PM. Muscle damage following repeated bouts of high force eccentric exercise. Med Sci Sports Exerc. 1995 Sep;27(9):1263-9.